Puzzles
A wide catalog of mechanics for digital puzzles, paper logic problems and physical puzzles. Each position contains an action or rule and a conditional example of application.
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Mechanics catalog
1Search and recognitionOverview and example ↗Find the desired object, sign or pattern in the presented information.10
Variants and applications
- Search by silhouette. Definition: Match a contour with an object, taking into account rotation and overlap. Conditional example: Find a detail by its shadow.
- Finding differences. Definition: Compare states or images and note the changed elements. Conditional example: Find rearranged objects in a room. Terms: spot the difference.
- Search for the superfluous. Definition: Derive a general property of a set and select an element that violates it. Conditional example: Eliminate a figure without an axis of symmetry.
- Continuation of the pattern. Definition: Define a change rule and restore the next or missing element. Conditional example: Continue a series of rotating figures. Terms: visual matrices.
- Recognition by fragment. Definition: Restore the whole from a limited part of the characteristics. Conditional example: Identify the mechanism from the cross-section.
- Combining layers. Definition: Combine transparent or partial images to reveal information. Conventional example: Overlay two halves of a card.
- Reading negative space. Definition: Find a figure or message in the spaces between objects. Conditional example: Read the number between the columns.
- Counting hidden structures. Definition: List all shapes, intersections or combinations, including composite ones. Conditional example: Count triangles of different sizes.
- Detecting change. Definition: Remember the state and determine what has changed after the break. Conditional example: Name the missing exhibit.
2Matches and field clearingOverview and example ↗Create valid groups and choose the order in which they are deleted.10
Variants and applications
- Matching pairs. Definition: Find two elements that coincide or complement each other. Conditional example: Connect a key with a suitable well.
- Paired disclosure from memory. Definition: Reveal hidden elements and remember positions for later matching. Conditional example: Find pairs of symbols under cards. Terms: memory; concentration.
- Collecting a line of matches. Definition: Rearrange elements for a row of a given length. Conditional example: Change adjacent stones and collect a three. Terms: match-3; three in a row.
- Deleting a linked group. Definition: Select identical elements that touch; deletion rearranges the field. Conditional example: Remove a group to connect two others. Terms: SameGame; collapse.
- Targeted addition to the group. Definition: Launch an element into a cluster and achieve a coincidence or collapse. Conditional example: Hit a colored cluster with a ball. Terms: bubble shooter.
- Carrying out a chain of matches. Definition: Carry out a continuous route along compatible elements. Conditional example: Connect adjacent runes of the same type.
- Merging identical objects. Definition: Combine compatible elements into an object of the next level. Conditional example: Merge two identical tiles into one. Terms: merge; 2048; Threes.
- Clearing a filled line. Definition: Place shapes so that completely filled rows or columns disappear. Conditional example: Close a gap in the bottom row. Terms: line clear; Tetris.
- Removing available pairs. Definition: Remove matching elements only when access conditions are met. Conditional example: Disassemble a multi-layer tile layout. Terms: mahjong solitaire; Mahjong solitaire.
- Rearrangement of cards by rank. Definition: Build sequences according to the rules of suit, rank and access to hole cards. Conditional example: Release a card under a long column. Terms: solitaire; solitaire
3Sorting and orderingOverview and example ↗Achieve a given distribution through constrained operations and buffers.9
Variants and applications
- Sorting by containers. Definition: Distribute elements according to characteristics with limited capacity of containers. Conditional example: Arrange balls by color. Terms: ball sort.
- Layer-by-layer transfusion. Definition: Transfer the available top layer, taking into account compatibility and free volume. Conditional example: Collect each color in a separate flask. Terms: water sort.
- Stack sorting. Definition: Rearrange the order, having access only to the tops of the stacks. Conditional example: Rearrange books through one spare shelf.
- Sorting through queues. Definition: Rearrange the order through operations with the beginning and end of queues. Conditional example: Divert cars through dead-end branches.
- Order by neighboring exchanges. Definition: Restore the sequence by changing only adjacent elements. Conditional example: Arrange numbers in ascending order.
- Order by dependency. Definition: Arrange elements with the conditions “earlier”, “later”, “between”. Conditional example: Determine the order of five operations.
- Nesting by size. Definition: Move nested or composed elements, respecting the order of sizes. Conventional example: Move a tower of disks to another rod. Terms: Tower of Hanoi.
- Hidden classification. Definition: Find the principle of dividing a set into groups. Conditional example: Combine words according to non-obvious meanings.
- Sorting by several criteria. Definition: Satisfy different distribution criteria at the same time. Conditional example: Arrange parts according to shape and material.
4Assembly, packing and fittingOverview and example ↗Compose a whole from parts, taking into account shape, proximity and free space.10
Variants and applications
- Image assembly. Definition: Connect fragments according to the pattern and geometry of the boundaries. Conditional example: Restore a broken drawing. Terms: jigsaw; puzzle
- Coordination of boundaries. Definition: Place tiles so that adjacent sides satisfy the rule. Conditional example: Match halves of symbols. Terms: edge matching; domino
- Tiling with figures. Definition: Cover an area with a set of shapes without overlaps or illegal spaces. Conventional example: Fit all pentominoes into a rectangle. Terms: polyomino; pentomino.
- Silhouette assembly. Definition: To create a given contour from a fixed set of parts. Conditional example: To obtain a silhouette of a bird from seven parts. Terms: tangram; tangram.
- Packing volume. Definition: Fit volumetric parts into a given shell. Conditional example: Assemble a cube from spatial elements. Terms: Soma cube; catfish cube.
- Arrangement of uneven items. Definition: Place objects with different shapes and orientations in a limited space. Conditional example: Fit all the equipment in a suitcase. Terms: inventory tetris.
- Assembly in layers. Definition: To compose an object from layers, taking into account overlaps, holes and heights. Conditional example: To assemble a relief along horizontal sections.
- Coordination of orientations. Definition: Arrange parts so that the outer edges or directions coincide with the goal. Conditional example: Place the desired symbol on each side of the structure.
- Mosaic restoration. Definition: Select and orient fragments to continue the overall pattern. Conditional example: Fill in the gaps in the ornament.
- Accurate object coverage. Definition: Select a subset of elements that covers each goal exactly once. Conditional example: Cover all marks with patterns without repetitions.
5Sliding and rearrangingOverview and example ↗Change the system configuration with limited transformations.10
Variants and applications
- Moving through the void. Definition: Move tiles only to the adjacent free space. Conditional example: Restore the order of tags. Terms: 15-puzzle; tag.
- Clearing the passage with blocks. Definition: Move parts in limited directions to produce a target block. Conventional example: Bring a long block out of a tight field. Terms: Klotski; Rush Hour.
- Shift of a whole series. Definition: Rearrange elements by general row or column shift only. Conventional example: Align characters by cyclic shifts.
- Rotate a local fragment. Definition: In one move, rotate several adjacent elements as a group. Conditional example: Arrange numbers by rotating 2x2 squares.
- Rotate layers of a volumetric object. Definition: Restore a state by rotating connected layers or sections. Conditional example: Collect the colored faces of a cube. Terms: twisty puzzle; Rubik's cube.
- Chained cyclic permutations. Definition: Change the order on rings that have common elements. Conditional example: Separate colors along two intersecting circles.
- Exchanges according to the permitted schedule. Definition: Swap only pairs connected by given connections. Conditional example: Arrange exchange tokens along the edges of the star.
- Reversal of a segment. Definition: Change the sequence only by reversing the selected section. Conditional example: Order a stack by turning its upper part. Terms: pancake sorting.
- Removal by jumping. Definition: Jump over tiles and remove them for the target end position. Conventional example: Leave one tile in the center. Terms: peg solitaire; tapeworm.
- Exchange of counter groups. Definition: Swap two groups through steps and jumps with limited direction. Conditional example: Swap two groups of frogs.
6Pushing, Carrying and ClutchingOverview and example ↗Plan access to objects and the consequences of their movement.10
Variants and applications
- Pushing without pulling. Definition: Place objects on targets, avoiding irreversible jamming. Conventional example: Place boxes on warehouse marks. Terms: Sokoban; sokoban.
- Pushing and pulling. Definition: Take into account different conditions for approaching, capturing and releasing an object. Conditional example: Pull a trolley out of a dead end.
- Pushing the chain. Definition: Transfer movement to several objects in one line. Conditional example: Move a column of stones to several targets.
- Sliding towards an obstacle. Definition: Choose a move taking into account the impossibility of stopping at an arbitrary point. Conditional example: Deliver an ice block to the desired stop.
- Rolling with orientation. Definition: Move the body so that the desired edge or position coincides with the target. Conditional example: Roll the cube with the red edge down.
- Control of an elongated body. Definition: Plan transitions between standing and lying states of a long object. Conditional example: Pass a block across narrow bridges.
- Carry with limited hands. Definition: Choosing what to take, leave and temporarily place when carrying restrictions. Conditional example: Deliver three tools while carrying one.
- Rope connection. Definition: Move objects with limited distance, tension and hooks. Conditional example: Draw a load around an obstacle without tangling the rope.
- Attaching and unhooking. Definition: Change the composition of a moving group by connecting and separating parts. Conditional example: Attach a load to a platform, then release it.
- Change in body length. Definition: Consider how growth or shortening changes traversability and support. Conditional example: Extend a creature to an adjacent ledge.
7Routes and detoursOverview and example ↗Find a path with restrictions on visits, turns and resource consumption.11
Variants and applications
- Exit from the labyrinth. Definition: Find a connected route between the entrance and exit. Conditional example: Go through corridors with dead ends.
- Visiting each position. Definition: Go through all the desired cells or vertices without visiting again. Conventional example: Paint the entire floor with one route. Terms: Hamiltonian path.
- Passing each edge. Definition: Draw a path using each required connection exactly once. Conditional example: Trace the picture with one stroke. Terms: Eulerian trail; one line.
- Checkpoints in order. Definition: Build a route through the required points in a given sequence. Conditional example: Visit runes from the first to the sixth.
- Route according to turn rules. Definition: Observe prohibitions and mandatory changes of direction. Conditional example: After each red node, turn left.
- One way route. Definition: Consider the direction of transitions and the impossibility of reverse movement. Conditional example: Find an exit in a network of one-way doors.
- A route with a budget of turns. Definition: Connect points using a limited number of bends. Conventional example: Connect two tiles with no more than two turns.
- Route through keys and locks. Definition: Choose the order of gaining access, taking into account the location of keys and closed passages. Conditional example: Take the blue key before entering the red zone.
- Vanishing path. Definition: Take into account the destruction or change of cells after passing. Conditional example: Cross all fragile slabs and exit.
- A route of a given length. Definition: Achieve a goal in an exact number of steps or with an exact consumption of reserves. Conditional example: Arrive at the exit exactly at the twelfth step.
- Rebuilding the labyrinth. Definition: Changing the passages themselves to create an accessible route. Conventional example: Rotating sections of the corridor before moving.
8Connections, networks and loopsOverview and example ↗Build connections with conditions of connectivity, degrees of nodes and intersections.10
Variants and applications
- Connecting network segments. Definition: Rotate or place sections connecting sources and receivers. Conventional example: Assemble a continuous pipeline. Terms: pipes; Net.
- Connection of specified pairs. Definition: Connect paired terminals by paths, observing intersection restrictions. Conditional example: Connect identical numbers with non-intersecting lines. Terms: Numberlink.
- Bridges between islands. Definition: Build a connected network with a given number of bridges at nodes. Conditional example: Connect islands using numerical clues. Terms: Hashiwokakero; Khasi.
- Single closed loop. Definition: Construct one loop without branches and self-intersections. Conditional example: Draw a border around the required cells. Terms: loop puzzle.
- Contour by number of edges. Definition: Construct a loop by matching the number of its sides around each clue. Conventional example: Surround a square with a three with three edges. Terms: Slitherlink.
- Contour based on turn marks. Definition: Draw a loop through marks that define the local behavior of the line. Conditional example: Coordinate straight lines and turns for different beads. Terms: Masyu.
- Network without loops. Definition: Connect all nodes without creating closed routes. Conditional example: Provide power to all stations with one tree.
- Unraveling the graph. Definition: Move the nodes so that the edges no longer intersect. Conditional example: Separate the points, maintaining all connections. Terms: planarity; untangle.
- Breaking selected connections. Definition: Remove or block connections, preserving the desired one and destroying the unwanted reachability. Conditional example: Isolate an infected node without shutting down the hospital.
- Flow distribution. Definition: Direct a flow with restrictions on the capacity and balance of nodes. Conditional example: Deliver water to three reservoirs without overloading.
9Number and symbol gridsOverview and example ↗Fill positions with values, matching intersecting constraints.15
Variants and applications
- Uniqueness in rows and columns. Definition: Arrange characters without repetition in each row and each column. Conditional example: Fill in a Latin square. Terms: Latin square.
- Uniqueness in additional areas. Definition: Match the constraints of rows, columns and given blocks. Conditional example: Distribute numbers across a Sudoku field. Terms: Sudoku; Sudoku.
- Arithmetic areas. Definition: Select numbers that satisfy the result of the operation within each cell group. Conditional example: Obtain the product of 24 in three cells. Terms: KenKen; killer sudoku.
- Inequalities between neighbors. Definition: Fill out a table with greater than and less than conditions between positions. Conditional example: Arrange numbers by inequality signs. Terms: Futoshiki.
- Heights and visibility. Definition: Restore values based on how many objects are visible from the edge. Conditional example: Arrange towers based on the number of visible roofs. Terms: Skyscrapers.
- Balanced binary grid. Definition: Fill the field with two characters with restrictions on series, number and repetition of lines. Conditional example: Distribute two types of chips equally. Terms: Takuzu; Binairo.
- Number of neighbors. Definition: Determine the filled cells by the number of marked adjacent positions. Conditional example: Restore a safe minefield. Terms: Minesweeper; sapper.
- Lengths of consecutive groups. Definition: Restore the shaded cells based on the lengths of the series in rows and columns. Conditional example: Draw an image using numerical clues. Terms: nonogram; Japanese crossword; Picross.
- Overlapping amounts. Definition: Fill in intersecting number series with a given sum and prohibit repetitions. Conditional example: Reconcile horizontal and vertical sums. Terms: Kakuro; kakuro.
- Distance between repetitions. Definition: Place values with a distance limit to the same value. Conditional example: Place identical numbers at acceptable distances. Terms: Ripple Effect.
- Arrangement without mutual attack. Definition: Place the pieces so that none falls into the forbidden zone of the other. Conditional example: Place eight queens without mutual attacks. Terms: eight queens; eight queens.
- Restoration of the fleet. Definition: Place objects given by length according to the sums of rows, columns and touch restrictions. Conditional example: Find the position of ships by edge numbers. Terms: Battleships; sea battle.
- Pair formation with no touch allowed. Definition: Compare objects of two types in the neighborhood and agree on their number along the lines. Conditional example: Place a tent near each tree. Terms: Tents; tents.
- Pairs of poles on a field. Definition: Fill paired positions with poles according to marginal quantities and neighborhood prohibitions. Conditional example: Arrange magnets, avoiding contact of identical poles. Terms: Magnets.
- Diagonals by degrees of nodes. Definition: Draw diagonals in cells, observing the numbers of adjacencies and prohibition of cycles. Conditional example: Connect the corners of cells using numerical marks. Terms: Slant; Gokigen Naname.
10Areas, Shading and CoveringOverview and example ↗Determine the boundaries and composition of areas according to local and global rules.10
Variants and applications
- Partition into rectangles. Definition: Divide the field into rectangular areas of a given area. Conventional example: Surround the number 6 with a rectangle of six cells. Terms: Shikaku.
- Areas of a given size. Definition: Divide the grid into connected groups, the size of which is determined by the value. Conditional example: Collect an area of five fives. Terms: Fillomino.
- Islands and the common sea. Definition: Select islands of the required size and a coherent surrounding area. Conventional example: Separate numerical islands by a continuous sea. Terms: Nurikabe.
- Symmetrical areas. Definition: Divide the field into regions with given centers or axes of symmetry. Conditional example: Construct rotationally symmetric “galaxies”. Terms: Galaxies; Tentai Show.
- Quotas within regions. Definition: Distribute marks among rooms with given quantities and neighborhood restrictions. Conditional example: Paint exactly two cells in each room.
- Removing repetitions by painting. Definition: Eliminate repetitions while maintaining the connectivity of the remaining cells and the admissible proximity. Conditional example: Color over extra numbers in the lines. Terms: Hitori.
- Continuous painting. Definition: Select cells so that the selected color forms one connected structure. Conditional example: Connect all black fragments without forbidden squares.
- Coloring of neighboring areas. Definition: Assign colors so that neighboring areas satisfy constraints. Conventional example: Color a map with a limited palette. Terms: graph coloring.
- Shading according to viewing range. Definition: Block lines of sight so that the required number of cells are visible from the marks. Conditional example: Limit the view of numerical observers. Terms: Kurodoko; Kuromasu.
- Filling with the capture of neighbors. Definition: Change the color of a connected area, absorbing neighboring groups. Conditional example: Combine the entire field in several recolors. Terms: Flood-It.
11Deduction and the hidden stateOverview and example ↗Recover the unknown from system constraints, observations, and responses.10
Variants and applications
- Correspondence table. Definition: Establish one-to-one relationships between several sets of features. Conditional example: Determine who lives in which house. Terms: zebra puzzle; logical table.
- True and false statements. Definition: Determine the state of the world and the truthfulness of speakers based on compatible statements. Conditional example: Find out which of the guards is lying. Terms: knights and knaves.
- Chains of conditions. Definition: Derive the only valid combination from implications and exceptions. Conditional example: Determine the culprit using the conditions “if” and “only if”.
- Feedback code. Definition: Select a hidden sequence based on information about matching features and positions. Conditional example: Restore the code based on the number of exact and inaccurate matches. Terms: Mastermind; bulls and cows; bulls and cows.
- Black box research. Definition: Deduce an internal device based on its response to input influences. Conditional example: Restore the location of obstacles based on the beam outputs. Terms: Black Box.
- Troubleshooting. Definition: Identify a broken component based on symptoms and test results. Conditional example: Find one damaged circuit node.
- Selecting an informative check. Definition: Select a question or experiment that distinguishes the remaining hypotheses. Conditional example: Find a hidden number in a limited number of questions.
- Inference from the awareness of others. Definition: Use participants' knowledge and public statements about what they know or don't know. Example: Determine the color of your hat after everyone else answers. Terms: hat puzzles; general knowledge.
- Proof of impossibility. Definition: Detect an invariant or contradiction that excludes the required configuration. Conditional example: Explain why the layout cannot be assembled with valid moves.
12Numbers, operations and combinatoricsOverview and example ↗Construct expressions and distributions that satisfy numerical conditions.11
Variants and applications
- An expression with a target result. Definition: Make a calculation from given numbers and operations. Conditional example: Get 24 from four numbers.
- Restoring operations. Definition: Insert missing characters, parentheses or values for a true equality. Conditional example: Arrange operations between four digits.
- Letter arithmetic. Definition: Replace letters with numbers while maintaining equality and matching rules. Conditional example: Decipher the addition column. Terms: cryptarithm; alphametic.
- Matching amounts. Definition: Arrange numbers so that given lines or groups have the required amount. Conditional example: Construct a magic square.
- Dividing the number set. Definition: Divide numbers into groups with given amounts or properties. Conditional example: Divide weights into two equal groups.
- Cyclic arithmetic. Definition: Manage values that cross the modulo boundary. Conditional example: Set the clock by connected turns of the hands.
- Numerical pattern. Definition: Derive a rule for a number sequence under sufficient restrictions. Conditional example: Recover a gap in a series with a given type of rule.
- Rearranging and changing numbers. Definition: To achieve equality by moving, flipping or adding elements of a record. Conventional example: To move one matchstick in a digital equality. Terms: matchstick arithmetic.
- Counting valid options. Definition: Count configurations with restrictions, avoiding repeated counting. Conditional example: Find the number of different routes along a small grid.
- Choice with a probabilistic condition. Definition: Derive a probability or strategy in an explicitly specified random model. Conditional example: Select the sequence of tests with the highest chance of success.
- Derivation of a winning state. Definition: Find a move that guarantees a goal for all admissible responses of the opponent. Conditional example: Leave the opponent a losing configuration of heaps. Terms: Nim; him.
13Measuring, exchanging and allocating resourcesOverview and example ↗Obtain accurate values through a limited set of actions.8
Variants and applications
- Search for different weights. Definition: Identify an unusual item based on the results of comparative weighings. Conditional example: Find a heavier coin using two weighings.
- Getting weight with a set of weights. Definition: Dial the required value with restrictions on the use of both cups. Conditional example: Measure the mass with three weights.
- Measuring by transfusion. Definition: Obtain an exact volume using vessels of known capacity. Conditional example: Measure four liters with two jugs.
- Measuring time. Definition: Obtain the desired interval using a clock or processes with known properties. Conditional example: Measure the interval with two hourglasses.
- Divide into equal shares. Definition: Divide a heterogeneous resource according to an explicitly specified equality criterion. Conditional example: Divide a set of ingots into parts of equal mass.
- Chains of exchanges. Definition: Achieve the desired set through allowed resource conversions. Conditional example: Exchange tokens at three different rates.
- Route with supplies. Definition: Distribute a limited resource between movement, storage and replenishment. Conditional example: Cross the desert, leaving fuel depots in advance.
- Transportation with incompatibilities. Definition: Transfer all participants, respecting the capacity of the transport and restrictions on the remaining groups. Conditional example: Transport cargo that cannot be left with a certain passenger. Terms: river crossing.
14Letters and wordsOverview and example ↗Construct and transform words with restrictions on composition and arrangement.10
Variants and applications
- Anagram. Definition: Rearrange the letters to form a valid word or phrase. Conventional example: Collect a name from the jumbled letters.
- Intersection of words by definitions. Definition: Fill in the words so that the answers agree in common cells. Conditional example: Solve a crossword puzzle. Terms: crossword; scanword.
- Search for words in the field. Definition: Find given or displayed words in a grid of characters. Conditional example: Find the names of tools along the diagonals. Terms: word search; filword.
- A chain of adjacent letters. Definition: Collect words along a valid path through letter positions. Conditional example: Compose a word without using a cell twice. Terms: Boggle.
- Step-by-step transformation of a word. Definition: Change a word through valid intermediate words using a fixed operation. Conditional example: Transform one word into another by replacing one letter. Terms: word ladder.
- Pass recovery. Definition: Select letters or fragments according to context and restrictions. Conditional example: Fill in the missing vowels in a message.
- Laying words from tiles. Definition: Distribute a limited set of letters among related words. Conditional example: Collect a compact grid from all given letters.
- Splitting merged text. Definition: Restore the boundaries of words and parts of a message. Conditional example: Break a continuous line into a meaningful phrase.
- A word on positional feedback. Definition: Guess a word using information about the presence of letters and their positions. Conditional example: Identify a word by the colored marks of attempts. Terms: Wordle.
- Converting parts of a word. Definition: Add, remove or replace meaningful parts according to condition. Conditional example: Get a chain of words by changing the prefix.
15Ciphers, languages and meaningOverview and example ↗Find correspondences between signs, words and interpretations.11
Variants and applications
- Replacement code. Definition: Restore the table of correspondences between symbols and original characters. Conditional example: Read a note with a replaced alphabet. Terms: cryptogram; cryptogram.
- Rearrangement cipher. Definition: Display the reading order of characters or blocks. Conditional example: Read text by rearranged columns.
- Decryption by key. Definition: Apply the found key to a table, book or encoding algorithm. Conditional example: Retrieve letters by page and line numbers. Terms: book cipher.
- Study of unknown writing. Definition: Deduce the meaning of signs from repetition, context and parallel messages. Conditional example: Read the signs of a fictitious language.
- Grammar output. Definition: Identify the rules of utterance structure and apply them to new examples. Conditional example: Compose a valid phrase in an artificial language.
- Rebus. Definition: Convert pictures, arrangement and conditional operations into a word or phrase. Conditional Example: Read an expression from a picture and letters removed.
- A game of meanings. Definition: Find an answer that simultaneously satisfies different meanings or definitions. Conditional example: Choose a word with two desired meanings.
- Composite word clue. Definition: Divide the hint into a definition and an instruction to convert a word. Conditional example: Get an answer through an anagram of the specified fragment. Terms: cryptic crossword.
- Semantic analogy. Definition: Restore the relationship between concepts and transfer it to another pair. Conditional example: Select the fourth word according to the type of connection.
- Rethinking the condition. Definition: Find a compatible interpretation by revising an implicit assumption. Conditional example: Explain a situation by understanding one of the words differently. Terms: lateral thinking; Danetka.
- General semantic mediator. Definition: Find a concept that connects several different clues. Conditional example: Choose a word that forms expressions with three others.
16Geometry, cutting and foldingOverview and example ↗Convert a form and display its properties.10
Variants and applications
- Cutting and rearranging. Definition: Divide a figure into parts from which the required shape is assembled. Conditional example: Turn a rectangle into a square with several cuts.
- Division of area. Definition: Make cuts to obtain parts of equal or specified area. Conditional example: Divide a polygon into three equal parts.
- Construction with a limited number of lines. Definition: Cover or connect points with a limit of straight lines and breaks. Conditional example: Connect nine points with four segments.
- Folding the sheet. Definition: Select a sequence of folds to obtain a shape or align marks. Conditional example: Align holes with several folds. Terms: origami; origami.
- Drawing after bending. Definition: Restore the appearance of a folded or unfolded sheet using holes and cuts. Conditional example: Predict the pattern after unfolding.
- Rearranging hinged surfaces. Definition: To obtain the desired edge or pattern through the allowable bends of a composite structure. Conditional example: To reveal the hidden side of a flexagon. Terms: flexagon; flexagon.
- Development and volume. Definition: Compare a flat development with a spatial body. Conditional example: Select a development of a cube with the desired adjacent faces.
- Constructing a figure with tools. Definition: Obtain an exact object using allowed geometric operations. Conditional example: Construct the center of a circle using allowed actions.
- Completing symmetry. Definition: Add or move elements to obtain a given symmetry. Conditional example: Complete a pattern relative to two axes.
- Separation of area and perimeter. Definition: Change shape by maintaining one geometric property and changing another. Conditional example: Increase the perimeter while maintaining the area.
17Mechanical puzzlesOverview and example ↗Output the sequence of physical transformations of a prefabricated object.11
Variants and applications
- Analysis of the coupled structure. Definition: Find the order of removing mutually interlocking parts. Conditional example: Disassemble a wooden knot. Terms: burr puzzle.
- Assembly with closing part. Definition: Assemble mutually interlocking parts in an order that allows completion. Conditional example: Insert the last bar into a volumetric lock.
- Separation of rigid rings and wires. Definition: Pass elements through permissible positions without deformation. Conventional example: Remove a metal ring from a frame.
- Unraveling the flexible connection. Definition: Change the position of the cord and rings, maintaining fastenings and integrity. Conditional example: Release a loop from a fixed rod.
- Sequential removal of rings. Definition: Remove and return elements with dependencies between valid states. Conditional example: Remove a set of related rings according to a rule. Terms: Chinese rings; Chinese rings.
- The secret of discovery. Definition: Find hidden degrees of freedom and the order of body shifts. Conditional example: Open a box without a visible latch. Terms: puzzle box.
- Unusual lock mechanism. Definition: Deduce the method of operation of the key and internal locks based on the observed reaction. Conditional example: Open a lock that allows several key modes.
- Sequential opening of tools. Definition: Use parts found inside an object to unlock the next steps. Conventional example: Remove a pin and apply it to a hidden hole.
- Explanation of an impossible object. Definition: Restore the assembly method or device of a seemingly impossible design. Conditional example: Deduce how a large part ended up inside a narrow shell.
- Vessel with hidden channels. Definition: Draw the arrangement of cavities and air holes for the desired transfusion. Conditional example: Empty the vessel by closing the correct hole.
- Procedure for removing fasteners. Definition: Remove fasteners, taking into account access blocking, support and temporary storage space. Conditional example: Release the bottom plate by removing the screws in the required order. Terms: screw puzzle; nuts and bolts.
18Forces, supports and movementOverview and example ↗Receive the target state from the physical interaction of objects.14
Variants and applications
- Fall control. Definition: Create an order of falls that will deliver the object to the target. Conditional example: Remove the support under the desired load.
- Changing the direction of gravity. Definition: Change the direction of the general fall for characters and objects. Conditional example: Throw a load from the wall to the ceiling.
- Static balance. Definition: Place masses and supports so that the structure remains stable. Conventional example: Hold the platform horizontally with two weights.
- Transfer of the center of mass. Definition: To change the distribution of mass to tip, roll or hold. Conventional example: Pour a load inside a figure so that it goes over the edge.
- Levers and power transmission. Definition: Select the location of the shoulders and mechanisms for the desired movement. Conditional example: Lift a heavy door with a light counterweight.
- Inertia and impulse. Definition: Obtain the desired movement through acceleration, deceleration and impulse transfer. Conditional example: Accelerate the cart to the far platform.
- Trajectory calculation. Definition: Select the angle, force or initial launch position. Conditional example: Hit the target with a projectile after rebound.
- Cutting ties. Definition: Choose the order of removing the hangers, taking into account swinging and falling. Conditional example: Cut two ropes in the required sequence.
- Physical chain reaction. Definition: Build a sequence of collisions and triggers. Conditional example: Launch a ball that will activate several levers. Terms: Rube Goldberg.
- Attraction and repulsion. Definition: Move bodies through changes in poles and locations of force sources. Conditional example: Pass a metal ball between magnets.
- Buoyancy. Definition: Change the density, volume or level of a liquid to move a body. Conditional example: Raise a platform by filling a reservoir.
- Friction and adhesion. Definition: Changing surfaces and contact to allow or stop movement. Conventional example: Covering an inclined path with non-slip areas.
- Drawing a physical object. Definition: Create a shape that will become a body, support or constraint in the simulation. Conventional example: Draw a hook holding a rolling ball.
- Construction of the supporting system. Definition: Assemble a structure that can withstand given loads in the accepted physics model. Conditional example: Build a bridge from a limited number of beams.
19Materials, environments and transformationsOverview and example ↗Change object properties and use process propagation.10
Variants and applications
- Fluid redirection. Definition: Create channels, barriers and reservoirs for the desired distribution of liquid. Conditional example: Bring water to the wheel through several locks.
- Pressure and communicating volumes. Definition: Control the pressure difference and the connection of containers. Conditional example: Open the valve, equalizing the pressure in the chambers.
- Transition between states of matter. Definition: Change the state of aggregation for the sake of support, passage or transfer. Conditional example: Freeze a flow, then melt a temporary bridge.
- Heating and cooling. Definition: Distribute heat through conductors, insulation and sources. Conditional example: Heat the sensor without overheating the neighboring node.
- Spread of fire. Definition: Manage flammable chains, obstacles and ignition time. Conditional example: Light the wick on both sides for the desired order.
- Conductive materials. Definition: Assemble a physical circuit from objects with different conductivities. Conditional example: Close the power supply with metal objects.
- Change of material. Definition: Change the properties of a body according to explicit transformation rules. Conditional example: Make a block light, and then heavy again.
- Reactions of substances. Definition: Select substances and the order of mixing in a given reaction model. Conditional example: Obtain a solution that dissolves one of two partitions.
- Managed growth. Definition: To guide the spread of a plant, crystal or other growing structure. Conventional example: To grow a branch through three anchor points.
- Selective destruction. Definition: To remove material according to the rules of strength, dissolution or propagation of damage. Conventional example: To destroy soft rock while preserving the supporting frame.
20Light, color and opticsOverview and example ↗Control rays, lighting and the composition of visible information.10
Variants and applications
- Beam reflection. Definition: Direct the beam with mirrors to the receivers. Conditional example: Bring the laser through several turns.
- Refraction. Definition: Change the path of the beam at the boundaries of media or through lenses. Conditional example: Pass the beam through an optical wedge to the sensor.
- Splitting and combining rays. Definition: Spread rays in several directions and coordinate their properties. Conditional example: Activate two receivers with one source.
- Mixing colors. Definition: Obtain the desired color using an explicitly specified mixing model. Conditional example: Add red and green light on the sensor.
- Color filters. Definition: Choose which components of light pass to the target. Conditional example: Cut off the extra channel in front of the three-color lock.
- Constructing a shadow. Definition: Arrange objects and the source so that the shadow takes the desired shape. Conditional example: Collect the silhouette of a key with shadows of different parts.
- Light coverage. Definition: Arrange sources to illuminate all targets while limiting mutual visibility. Conventional example: Illuminate a reticle without pointing the lamps at each other. Terms: Akari.
- Obtaining information by reflection. Definition: Construct a line of sight through reflective surfaces. Conditional example: Read a hidden sign in a mirror.
- Orientation filters. Definition: Match the orientation of the filters and the properties of the transmitted signal. Conventional example: Pass light through several rotating plates.
- Revealing a hidden image. Definition: Change lighting or viewing mode to see inaccessible features. Conventional example: Read tags in a different spectral channel.
21Sound, rhythm and memoryOverview and example ↗Extract structure from timing signals and reproduce it.10
Variants and applications
- Repeating the melody. Definition: Remember and reproduce a sequence of pitches or sounds. Conditional example: Press the bells in the order heard.
- Rhythm restoration. Definition: Convey a pattern of durations and pauses. Conditional example: Repeat the knock that opens the mechanism.
- Height adjustment. Definition: Match the heights of the sources with a given ratio. Conditional example: Adjust the pipes according to the control chord.
- Localization by sound. Definition: Infer the direction or position of the source based on audio characteristics. Conditional example: Find the desired corridor based on spatial sound.
- Separation of sound layers. Definition: Identify a useful signal among simultaneous sources. Conditional example: Hear the code against the background of working mechanisms.
- Record conversion. Definition: Changing the speed, direction or order of parts of a recording for the sake of decoding. Conditional example: Assembling a phrase from mixed up audio fragments.
- Sound matches. Definition: Establish a connection between sounds and objects, actions or signs. Conditional example: Compare signals to the four gates.
- Displaying a form based on a response. Definition: Use echo or resonance to identify a hidden structure. Example: Find a hollow wall by a different response.
- Action sequence memory. Definition: Reproduce the order of spatial or subject events after hiding the sample. Conditional example: Repeat the route of flashing platforms. Terms: Simon.
- Multi-state memory. Definition: Hold and compare states that cannot be seen at the same time. Conditional example: Configure the remote control according to the diagram in the next room.
22Perspective and imageOverview and example ↗Change the result through point of view, framing and transition between image and object.10
Variants and applications
- Collecting images from a point of view. Definition: Find the angle from which the disparate parts form a sign. Conditional example: Combine fragments of a number on different walls.
- Scale through perspective. Definition: Change the size of an object according to the rule of its apparent size when carried. Conditional example: Make a small object a large support. Terms: forced perspective; Superliminal.
- Connection through projection. Definition: Combine elements in an image to create a game transition. Conventional example: Align two separate sections of a bridge from the desired angle.
- The image is part of the world. Definition: Place an image so that its content becomes traversable geometry. Conventional example: Insert a photo of a staircase into a wall.
- State capture by camera. Definition: To store an object or configuration in an image for later use. Conventional example: To photograph a bridge and restore it in another location.
- State from observation. Definition: Control objects whose behavior depends on whether the observer sees them. Conditional example: Allow the mechanism to readjust by turning the camera away.
- Changing the visible overlap. Definition: Hiding or revealing parts of the scene to change the available information or rule. Conventional example: Covering the extra part of the character in front of the reader.
- Rebuilding the scene through a picture. Definition: Change the image and get a corresponding change in space. Conditional example: Rearrange the drawn rooms on the plan.
- Transition between frames. Definition: To carry a character or object across the boundaries of panels and images. Conventional example: To connect doors on adjacent pages.
- External and internal view. Definition: Compare different representations of one object and change them consistently. Conditional example: Rotate the layout from the outside, then go through it from the inside.
23Space, dimensions and topologyOverview and example ↗Solve problems through the arrangement of space and connections between its parts.10
Variants and applications
- Transition through portals. Definition: Create or select connections between remote areas. Conditional example: Connect two rooms with a pair of passages.
- Closed field. Definition: Count going over the edge as a return on the other side. Conventional example: Go around an obstacle over the edge of the net.
- Recursive rooms. Definition: Use nested spaces that can represent each other or themselves. Conventional example: Enter a box containing another version of a room. Terms: Patrick's Parabox.
- Transition between scales. Definition: Change available paths and interactions when moving to another scale. Conditional example: Go through a gap after zooming out.
- Transition between 2D and 3D. Definition: Use the differences between flat and volumetric representations. Conditional example: Avoid an obstacle after changing dimensions.
- Switching world layers. Definition: Choose between consistent versions of a space with different geometries. Conditional example: Go through a missing wall in another layer.
- Rearrangement of premises. Definition: Change the proximity of rooms and their entrances. Conditional example: Assemble a passage from module rooms.
- Bending space. Definition: Combine remote areas by transforming the map itself. Conditional example: Fold the map so that two doors touch.
- Connectivity inconsistent with conventional geometry. Definition: Derive rules for transitions where the neighborhood does not correspond to the usual spatial model. Conditional example: Use a corridor leading to different places from different sides.
- Changing the node configuration. Definition: Convert loops and weaves while maintaining specified connections. Conditional example: Untie a virtual knot without cutting the thread.
24Time and causalityOverview and example ↗Change the availability of actions through temporary states and dependencies.11
Variants and applications
- Rewinding the state. Definition: Return the system to the previous state and change the further sequence. Conditional example: Rewind the fall and select another moment of the jump.
- Different times for objects. Definition: Start, stop or reverse the time of individual objects independently. Conditional example: Return a bridge to the past, maintaining the current position of the load.
- Stop the process. Definition: Freeze movement or processes, while maintaining the possibility of other actions. Conditional example: Fix a flying platform in a convenient position.
- Record and playback of actions. Definition: Leave the executable sequence of your own behavior. Conditional example: Record the path of the double to the pressure plate.
- Repeating cycle. Definition: Plan actions on a repeating schedule using knowledge of past attempts. Conventional example: Get into a passage before it floods.
- Changing the past for the sake of the future. Definition: To change an early state and use the consequences in a later one. Conditional example: To plant a plant in the past and climb it in the future.
- Action in the availability window. Definition: Coordinate actions with periodic or irreversible changes in the environment. Conditional example: Pass the gateway at the moment of phase coincidence.
- Synchronization of cycles. Definition: To change the beginning, period or delay of repeating processes. Conditional example: To combine the opening of three rotating valves.
- Order of cause and effect. Definition: Arrange events so that each creates the conditions for the next. Conditional example: First fix the support, then trigger the collapse.
- Time loop coordination. Definition: Construct actions that are compatible with already observed consequences. Conditional example: Transfer an object to a past version of oneself without contradiction.
- Time dependent on actions. Definition: Take into account the rule that connects the flow of processes with the move or movement of the player. Conditional example: Move forward so that a moving danger does not block the path.
25Switches, states and signalsOverview and example ↗Manage discrete states and command propagation.10
Variants and applications
- Switching a group of states. Definition: With one action, change the selected element and certain neighbors. Conditional example: Extinguish all lamps with related switches. Terms: Lights Out.
- Multi-step switch. Definition: Place elements that cycle through several states. Conditional example: Combine symbols on three connected reels.
- Pressing and holding organs. Definition: To support a condition by weight or constant presence. Conditional example: To leave a weight on the plate for an open door.
- State machine transitions. Definition: Select a sequence of inputs that leads the system to the desired state. Conditional example: Open an automatic lock with a sequence of signals.
- Boolean operations. Definition: Assemble or configure a circuit from operations on logical values. Conditional example: Open a door with exactly two active sensors.
- Delay and order of pulses. Definition: Set up the propagation of signals with different travel times. Conventional example: Deliver two pulses to the receiver simultaneously.
- State memory. Definition: Use elements that preserve the previous input or result. Conditional example: Capture a short pulse with a latch.
- Signal frequency and duration. Definition: Create a sequence of pulses with the required parameters. Conditional example: Transmit three short signals after one long one.
- Associated controls. Definition: Set up a system where one knob simultaneously changes several parameters. Conditional example: Align three scales with two knobs.
- Feedback. Definition: Set up a circuit whose output affects the subsequent state of the inputs. Conditional example: Achieve a stable cycle without self-blocking.
26Algorithms and programmingOverview and example ↗Create a procedure that solves a problem in a given execution model.11
Variants and applications
- Sequence of commands. Definition: Compose a program from elementary actions before launching it. Conditional example: Guide the robot along the route with commands.
- Repeatable block. Definition: Use a loop instead of an expanded sequence. Conditional example: Describe the traversal of repeating columns in one block.
- Conditional execution. Definition: Select actions based on sensor readings or input properties. Conditional example: Turn only in front of the red square.
- Subroutines. Definition: Decompose the solution into callable parts with a limit on the size of the program. Conditional example: Move the repeated lifting into a separate procedure.
- Recursive procedure. Definition: Construct a solution by calling the same operation again for a smaller or nested problem. Conditional example: Traversal of a tree of unknown depth.
- Registers and limited memory. Definition: Convert data when the number of stored values is small. Conditional example: Sort a stream with two registers.
- Stack computing. Definition: Construct a calculation using operations on the top of the stack. Conditional example: Get a formula without named variables.
- Coordination of performers. Definition: Organize independent programs with data exchange and shared resources. Conditional example: Coordinate two processors without waiting for each other.
- Program correction. Definition: Find and change erroneous actions in a finished procedure. Conditional example: Correct one command that violates the route.
- Solution for all valid inputs. Definition: Create an algorithm that works on a set of cases, rather than on a single sample. Conditional example: Build a sorter for any valid stream.
- Optimization of the procedure. Definition: Improve a correct program according to a given metric. Conditional example: Reduce execution time with the same result.
27Machines, production and logisticsOverview and example ↗Build a system for converting and delivering objects.8
Variants and applications
- Conveyor routing. Definition: Build supply paths taking into account directions, intersections and forks. Conditional example: Deliver parts to different assembly stations.
- Dividing the input stream. Definition: Recognize and guide objects by properties. Conditional example: Distribute different workpieces according to outputs.
- Processing chain. Definition: Select operations, their order and relative position. Conditional example: Rotate, drill and connect two parts.
- Manipulator control. Definition: Set up grips and movements to transform objects. Conventional example: Pass a workpiece between two mechanical arms.
- Assembly of structures based on connections. Definition: Change the graph of connections of parts or conditional atoms. Conditional example: Assemble a given molecule from input fragments.
- Performance matching. Definition: Eliminate the discrepancy between speeds and buffer capacity. Conditional example: Supply parts to two stations without overflowing.
- Layout based on multiple metrics. Definition: Find an acceptable or more profitable scheme in terms of area, price and speed. Conditional example: Fit a working machine into a smaller rectangle.
28Multiple objects and agent behaviorOverview and example ↗Consider common commands, different abilities, and reactive behavior.11
Variants and applications
- Mirror or reverse commands. Definition: Match figures that react differently to the same input. Conventional example: Guide a pair moving in opposite directions.
- Switch managed role. Definition: Select a character with a suitable ability and leave the rest in useful states. Conditional example: One holds the slab, the other moves on.
- Changing the controlled body. Definition: Transfer control to an object, receiving its properties and restrictions. Conditional example: Move into a stationary mechanism to open a path.
- Follow-up management. Definition: Use the rules of pursuit and maintaining distance. Conditional example: Lead a companion through forks with decoys.
- Redirecting the enemy. Definition: Use a predictable reaction from a hostile agent. Example: Lure a guard onto a pressure plate.
- Luring and repelling. Definition: Change the route of agents with signals, smells or objects. Conditional example: Separate creatures into different pens.
- Agent flow routing. Definition: Direct multiple characters by changing the environment or assigning actions. Conventional example: Lead a group through a dangerous area without casualties.
- Positional task with captures. Definition: Obtain a given result through allowed moves and removal of pieces. Conditional example: Perform checkmate in a given number of moves. Terms: chess problem; chess puzzle
- Dividing routes in time. Definition: To carry out several participants, excluding collisions and blocking of passages. Conditional example: To separate trains on single-track sections.
- Creating and merging copies. Definition: Change the number of agents for simultaneous actions, then coordinate their state. Conditional example: Divide a character to press two plates and put them back together.
29Items, tools and environmentOverview and example ↗Deduce ways to use objects and create access conditions.10
Variants and applications
- Application of a tool by property. Definition: Select an object based on the observed function and properties of the target. Conditional example: Retrieve a metal key with a magnet.
- Combining items. Definition: Create a new tool from available components. Conditional example: Connect a rope and a hook.
- Parsing an object into useful parts. Definition: To obtain components for another task from a complex object. Conditional example: To disassemble a flashlight for the sake of a battery.
- Restoring the device. Definition: Identify missing parts and restore working configuration. Example: Repair a lift using available parts.
- Selecting the use of one item. Definition: Distribute an object between several possible functions and return it when necessary. Conditional example: Use a board as a bridge, then as a lever.
- Adjusting the key shape. Definition: Change the geometry of an object so that it fits the mate. Conditional example: Align the protrusions of a prefabricated key.
- Using the environment as a tool. Definition: Get the effect of a stationary object instead of a portable object. Conditional example: Break a shell with a door mechanism.
- Access dependency chain. Definition: Line up actions, each of which opens the next tool or place. Conditional example: Get a handle, open a cabinet and get a lens.
- Temporary replacement of a missing part. Definition: Use a compatible item until a permanent solution is obtained. Conventional example: Support the mechanism with a wedge while the fastener is removed.
- Study of the properties of an object. Definition: Conduct meaningful testing to understand the acceptable use of an object. Example: Determine which surfaces hold an unknown fastener.
30Investigation and reconstructionOverview and example ↗Collect explanations of events from partial and contradictory information.8
Variants and applications
- Linking evidence. Definition: Establish relationships between the facts found. Conditional example: Connect the trace, tool and damage.
- Detecting a contradiction. Definition: Compare the claim with independent evidence. Conditional example: Refute the stated time of arrival with camera footage.
- Restoring chronology. Definition: Arrange events according to temporal relationships and causal restrictions. Conditional example: Determine the order of events in a room.
- Establishing identity and role. Definition: Match unknown participants with names and actions. Conditional example: Determine who owned the found things.
- Restoring the event mechanism. Definition: Construct an explanation consistent with all significant traces. Conditional example: Find out how the locked installation worked.
- Search the information archive. Definition: Select queries and transitions that reveal new relevant fragments. Conditional example: Find the desired record using words from another document.
- Filling out the explanation being verified. Definition: Substitute findings into a structure that requires an agreed upon full version. Conditional example: Fill in the names and actions in the description of the incident.
- Reconciliation of partial evidence. Definition: Combine several limited points of view into a common model. Notional example: Compare observations from different rooms.
31Cooperative information tasksOverview and example ↗Distribute knowledge and actions among participants.8
Variants and applications
- Separated information. Definition: Exchange descriptions when everyone sees only part of the conditions. Conditional example: One reads the instructions, the other sees the device.
- Divided control. Definition: Combine actions when different participants control different parts of the system. Conditional example: One changes the power supply, the other connects the contacts.
- Restoration as described. Definition: Convey the structure in words so that the other participant reproduces it. Conditional example: Describe a layout invisible to the partner.
- General conclusion from personal facts. Definition: Get an answer that no participant can deduce from their information. Conditional example: Collect a code from intersecting evidence.
- Concerted joint action. Definition: To fulfill different conditions in one time interval. Conditional example: To keep two regulators in the target ranges.
- Creation of a communication protocol. Definition: Come up with a way to transmit data through a limited channel. Conditional example: Transmit a route with three types of signals.
- Transferring tasks between roles. Definition: Prepare a state that allows the next participant to complete his part. Conditional example: Pass an object through a sequence of different work areas.
- Checking the solution in parts. Definition: Compare local checks of participants to confirm the overall configuration. Conditional example: Each checks its own set of constraints of the overall design.
32Discovery of rules and metapuzzlesOverview and example ↗Make the decision about the method of reading, managing or checking itself.11
Variants and applications
- Output of an unknown rule. Definition: Find a pattern using examples and check it on new cases. Conditional example: Find out what patterns an unknown checking mechanism accepts.
- Transfer the found rule. Definition: Apply a familiar principle in a new representation. Conventional example: Recognize the previous number law in a sound pattern.
- Editing existing rules. Definition: Change the wording that defines the properties and interactions of objects. Conditional example: Make a wall passable by changing a rule.
- Change of victory condition. Definition: Control which state the system considers a decision. Conventional example: Reassign an object considered an output.
- Control reassignment. Definition: To change the mapping between input and action as part of a decision. Conventional example: Rearrange commands so that an impossible route becomes feasible.
- Retrieval of secondary response. Definition: Obtain a new result from already solved problems using an additional rule. Conditional example: Take the indicated letters from ten answers. Terms: meta extraction.
- Assembling a metatask from the results. Definition: Use solutions or elements of several problems as details of the next one. Conditional example: Add cards from completed levels into a general scheme. Terms: metapuzzle.
- Transferring state between tasks. Definition: Change one level for the sake of an opportunity in another. Conditional example: Transfer the setting of a mechanism from the previous room.
- Interface as a game object. Definition: Use menus, windows and presentation elements according to the rules provided. Conventional example: Drag the border of the game window to move an obstacle.
- Self-reference and recursive condition. Definition: Solve a problem whose condition or answer refers to its own structure. Conditional example: Write a description that correctly counts its elements.
33Physics-accurate puzzlesOverview and example ↗Combine the found solution with continuous motion control.6
Variants and applications
- Tilting maze. Definition: Direct the ball by changing the slope, taking into account inertia and holes. Conditional example: Roll the ball towards the exit past the gaps.
- Dynamic balance maintenance. Definition: Constantly compensate for deviations while maintaining a given position. Conditional example: Keep a ball on a moving platform.
- Extraction through a narrow gap. Definition: Pass an object along an acceptable path without unacceptable contact. Conditional example: Reach a shaped part through a narrow passage.
- The exact moment of release. Definition: Select the phase of movement for the object to transition to the required trajectory. Conditional example: Release the load from the rotating arm above the receiver.
- Independent axis control. Definition: To coordinate several continuous inputs for one route. Conventional example: To move the pointer with two separate controls.
- Precise placement and styling. Definition: Place unstable objects taking into account acceptable support. Conditional example: Build a stable tower from uneven parts.
Notes
This is the author's working classification, and not a generally accepted standard and not a proven complete list. New combinations of rules and new ways of interacting remain possible.
The catalog contains action families and more specific rule templates. For example, connecting pairs and contouring by numbers are related to general line work, but create different problems. Therefore, the number of positions does not mean as many independent base mechanics.
The sections serve as navigation and partially overlap. Each position is placed in one main section. Push, signal and time loop can all be involved in the same puzzle at the same time.
Puzzle, escape room, adventure, match-3 and mechanical puzzle describe different levels of classification. Here the main subject of the description is: what the player is doing and what rule makes achieving the goal non-trivial.
A paper or physical problem can be reproduced digitally. The runtime itself does not make new mechanics.
Search, memorization, rhythm and dexterity are included in the broad scope of the request. In their pure form, some of them are closer to perceptual or performance tasks; What makes them a puzzle is the task of choosing a way to achieve a goal.
The examples in the lines are conditional and serve as templates for the design. Terms and names of games help to look for analogues, but do not indicate complete equivalence of the rules. The brief definitions do not replace the full rules for named puzzles.
Primary sources support only signed rules and examples. They do not endorse the author's entire classification, coverage, balance, or test results.
If the answer requires an external fact without being able to infer it from the data provided, it's closer to a quiz. If multiple equal answers remain, additional restrictions or explicit permission for multiple solutions are needed.
Inference by contradiction, invariants, parity, elimination of candidates and enumeration are methods of solution. They only become a separate game rule when the system explicitly requires or verifies the appropriate action.
Modifiers
group: Time; Options: General timer; Time limit per move; Repeating time windows; Actions only in a given rhythm
group: Action budget; Options: Move limit; Limit of turns or switching; Consumable Tools; Exact rather than maximum action quota
group: Information; Options: Partial visibility; Hidden properties; Deferred check result; Limited number of measurements
group: Reversibility; Options: Free cancellation; Cancel with resource consumption; One-time changes; The need to return after achieving the goal
group: Purpose and verification; Options: Exactly one solution or several valid ones; Any correct solution or optimum; Multiple simultaneous goals; Solution for one case or for all inputs
group: Field and objects; Options: Other mesh geometry; Changeable boundaries; Objects with multiple properties; Converting properties as a task progresses
group: Randomness; Options: Random starting configuration; Known probabilities of outcomes; Full or partial information about future elements; Repeatable seed for comparing solutions
group: Execution; Options: Discrete strokes or continuous control; Physical accuracy; Simultaneous actions; Individual solution or division of roles
group: Feedback; Options: Final check only; Local error indication; Partial confirmation; Numerical assessment of solution quality
Conditionals
Warehouse with reflections
Related options: push-only; mirror-ray; pressure-controls; Rule: The boxes simultaneously block the beams and hold the doors.
Unknown language archive
Related options: document-search; symbol-system; timeline; Rule: The meanings of the signs help restore the order of events, and he clarifies the translation.
Factory in the loop
Related options: command-sequence; record-replay; shared-resource-schedule; Rule: The recorded performer works next to the player; equipment has to be divided.
Rooms inside boxes
Related options: recursive-space; push-only; pair-routing; Rule: Moving boxes changes routes inside nested rooms.
Joint optical design
Related options: asymmetric-information; color-filter; signal-delay; Rule: One participant sees the circuit, the other adjusts the lights and delays.
Crossing with memory
Related options: river-transfer; state-memory; consumable-terrain; Rule: The composition of the cargo and already disappeared crossings must be taken into account together.
How to use the catalog
Separate player action, signal recognition, game rule, and feedback. The related variants here preserve the context of application and are not necessarily independent physical primitives.
When prototyping, test one rule and failure conditions first. The presence of an API, sensor, or source does not prove that all scenarios work. For devices, test feature availability, calibration, and alternate input on the actual target hardware.
Sources and examples
Sources support particular techniques or methodology, not every family variant. Design examples and mechanic combinations are illustrative.
- Nikoli: puzzle catalog
Official list of types and links to their full rules.
- Nikoli: Sudoku
Uniqueness of numbers in rows, columns and blocks.
- Nikoli: Numberlink
Connecting pairs of numbers with lines without intersections.
- Nikoli: Hashiwokakero
A connected network of bridges by numbers near the islands.
- Nikoli: Slitherlink
One path with a specified number of edges around the tooltips.
- Nikoli: Masyu
A loop with different rules for straight sections and turns of beads.
- Nikoli: Shikaku
Rectangular areas with a given area.
- Nikoli: Fillomino
Connected number areas of appropriate size.
- Nikoli: Nurikabe
Number islands and connected black area.
- Nikoli: Hitori
Removing repetitions by shading under connectivity and tangency constraints.
- Nikoli: Akari
Illumination of white cells with lamps that do not illuminate each other.
- Hempuli: Baba Is You
Effective rules are represented by objects that can be manipulated.
- Patrick Traynor: Patrick's Parabox
Recursive system of nested boxes, including self-nesting.
- Zachtronics: Opus Magnum
Building machines and optimizing solutions for speed, simplicity and compactness.
- Zachtronics: Zachademics
Description of programmable mechanisms that manipulate conventional molecules.
- Steel Crate Games: Keep Talking and Nobody Explodes
The participant sees the device, and the partners have instructions and communicate with him.
- Mobius Digital: Outer Wilds
Time loop and places changing over time. An example from a related adventure genre.
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