Learn the move.
See the reason.
Practical lessons with specific positions to work through. Choose a game below, then compare its lessons. Sum Select and Light Switch include fixed practice boards you can retry.
Tile Shift
Play Tile Shift ↗Tile 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.
02Tile 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.
03Tile 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: 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.
02Memory 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.
03Memory 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: 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.
02Light 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: 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.
02Number 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.
03Number 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: 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.
02Line 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.
03Line 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: 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.
02Sum 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.
03Sum 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.
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.