Learn the move.
See the reason.
Practical lessons with specific positions to work through. Choose a game below, then compare its lessons. Tile Shift, Memory Match, Light Switch, Sum Select, Clue Grid, Bridge Links, and Loop Trace include fixed practice boards you can retry. Number Merge and Line Three also have separate diagram exercises. Numbered series run from beginner rules to strategy and then independent practice.
Tile Shift
Play Tile Shift ↗Tile Shift: a reversed row pair adds two unavoidable slides.
Turn a distance total of seven into a proven nine-slide minimum, then load the exact board and test a matching route.
02Tile ShiftTile Shift: why the distance total can rise on a good move.
Load a fixed board, watch its tile distance rise from four to six, and replay an eight-slide solution that restores the displaced tiles.
03Tile ShiftCan this sliding puzzle be solved? Count before you slide.
Diagnose a hand-arranged 4 × 4 puzzle with an inversion count, two contrasting boards, and a self-check.
04Tile ShiftStop chasing tiles. Start thinking in loops.
Replay a four-move loop on a fixed board, reverse it, and see exactly which tiles stay in place.
Memory Match
Play Memory Match ↗Memory Match: calculate the turns left in a six-card finish.
Follow twelve possible layouts to the last pair, comparing two first-card choices with an explicit rule for every later turn.
02Memory MatchMemory Match: replay one layout and account for every turn.
Retry a fixed board, compare checked ten-turn and nine-turn routes, and separate completed turns, reveals, and button presses.
03Memory MatchMemory Match: which card should you reveal first?
Compare two reveal orders on a six-card endgame, count the possible matches, and separate knowledge from luck.
04Memory MatchGive every memory card an address.
Replace vague impressions with a simple row-and-column map, and get useful information from a mismatch.
Light Switch
Play Light Switch ↗Light Switch: twelve different presses can leave the board unchanged.
Verify a nonempty switch pattern with no net effect, then replay three clearing routes on the same board without confusing state with move count.
02Patterns & constructionLight Switch: combine two patterns by cancelling their overlap.
Build a new solvable board from two known patterns, cancel shared switches, and replay six-press and four-press routes on the same fixed example.
03Patterns & proofLight Switch: test a hand-made board before you chase it.
Use two marked-square counts to reject impossible 5 × 5 diagrams, then check your reasoning in an editable board exercise.
04Light SwitchLight Switch: a solution is not always the shortest.
Retry one fixed board in eleven and five presses, inspect all 32 top-row trials, and prove which solution is shortest.
05Light SwitchLight Switch: move the problem down the board.
Learn row-by-row light chasing, then replay a worked board to see why a different top-row choice matters.
Number Merge
Play Number Merge ↗Number Merge: will the next tile leave any legal move?
Check all four directions on a full board, then use one fixed position to separate a blocked swipe from a finished game.
02Number MergeNumber Merge: can the next tile break your plan?
Check all ten spawns on one board, distinguish an 80% surviving merge from a 2% bonus, and test your predicted Up points.
03Number MergeNumber Merge: why the score differs from the tile total.
Follow four checked moves to separate merge points, the sum of the board, and the largest tile.
04Number MergeIn Number Merge, read the board after the move.
Compare two moves on one full board, count space after the spawn, and separate immediate score from room to continue.
Line Three
Play Line Three ↗Line Three: a possible win is not a forced win.
Read a complete five-route game tree, distinguish a draw you can secure from a win that needs a mistake, and work backward to the first choice.
02Patterns & coordinatesLine Three: rotate the whole position, not just the winning square.
Transfer a winning move through rotations and reflections, and learn when similar-looking squares are no longer interchangeable.
03Line ThreeLine Three: could this board occur in a legal game?
Check turns, stop-at-win rules, and a valid two-line finish. Edit seven examples in a position checker verified against every labeled board.
04Line ThreeLine Three: defend opposite corners with a forcing move.
See why an edge can stop a corner trap, follow the forced replies to a draw, and test a rotated position.
05Line ThreeLine Three: look for threats before opportunities.
Read urgent threats first, then verify a real two-way fork by following each possible reply.
Sum Select
Play Sum Select ↗Sum Select: equal numbers can make different answers.
Separate value patterns from physical selections, fill a six-row count ledger, and explain all 18 answers on one repeated-value board.
02Search & proofSum Select: find every answer without counting one twice.
Use a largest-tile ledger to find all nine solutions on one fixed board, then retry pairs, triples, and a four-tile answer.
03Sum SelectSum Select: rule out groups with odd and even checks.
Load a target-19 board, narrow the search to exactly one odd tile, and compare nine shortest answers with a tempting wrong total.
04Sum SelectSum Select: choose what to leave out.
Turn a large target into a smaller omission sum, check six worked answers, and distinguish fewer omissions from fewer selected tiles.
05Sum SelectFind the missing piece of a sum.
Use remainders, check every two-tile answer on a worked board, and distinguish equal values from reusable tiles.
Clue Grid
Play Clue Grid ↗Clue Grid for beginners: read the clues and finish your first board.
Learn what each clue means, practise the two cell actions, and complete a new fixed seventeen-square puzzle without guessing.
Lesson 2Solving strategyClue Grid strategy: keep every possible run until the crossings decide.
Use overlap and complete line candidates on a new fixed board, then follow eight justified steps to a checked solution without choosing an unproved endpoint.
Lesson 3Practice challengeClue Grid practice: solve the short-run challenge before opening the answers.
Try a new board with no run longer than three, record reasons for your marks, then compare three checkpoints and a complete ten-check solution.
Bridge Links
Play Bridge Links ↗Bridge Links for beginners: count each bridge and connect every island.
Learn single and double bridges on a new eight-island board, follow seven deductions, and check why matching every number is only part of the goal.
Lesson 2Solving strategyBridge Links strategy: count the capacity, then keep an exit.
Solve a new six-island board by bounding each neighbour’s capacity and rejecting sealed pairs. Compare all three number-perfect arrangements, then replay the one connected answer.
Lesson 3Practice challengeBridge Links practice: rule out the crossing, then test the extra line.
Try an original eight-island challenge before revealing the reasoning. Use a forced crossing exclusion, test a tempting double, and compare your ten-edit answer with a complete lane ledger.
Loop Trace
Play Loop Trace ↗Loop Trace for beginners: count the sides and close one loop.
Learn the difference between dots, cell clues, lines and crosses. Load one checked three-by-three board, practise the edge controls, then follow an eight-line loop and verify every number.
Lesson 2Solving strategyLoop Trace strategy: check the dot before completing the cell.
Use a zero cell and a three to start a new board, compare a tempting cell-completing branch, then alternate dot checks with cell counts to justify a twelve-line solution.
Lesson 3Practice challengeLoop Trace advanced practice: force an edge, then count the loops.
Try a new board without zero clues, test a missing-edge assumption, and distinguish one valid loop from a number-perfect drawing with two loops.
Rectangle Rooms
Play Rectangle Rooms ↗Rectangle Rooms for beginners: one number, one matching area.
Learn how opposite corners define a room, practise a refused placement, and divide one checked four-by-four board into four rectangles with a complete area ledger.
Lesson 2Solving strategyRectangle Rooms strategy: check the candidates, then the uncovered cells.
Compare nine candidate rectangles, reproduce two locally legal dead ends, and use a blank corner cell to force the right room on a different checked board.
Getting started & behind the board
Choose a puzzle that fits the break you have.
Match a game to your available attention, control preferences, and appetite for a longer problem.
02Behind the boardHow we make a puzzle solvable before you start.
Three construction methods explain why a shuffled board can be a fair challenge instead of an impossible one.