How to Solve Spot the Difference Puzzles: The Grid Method
Scan both pictures cell by cell, sort changes by kind and check your tally. A six-step method, a worked tile puzzle and a practice puzzle with answer.
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Rep-Tile Puzzles: How to Cut a Shape Into Copies of Itself
Learn to cut a shape into smaller copies of itself: count cells, fill tight corners first, avoid bad pockets, then try a worked and a practice puzzle.
How to Solve a Polycube Puzzle: Volume, Colour and Layers
Pack cube pieces into a box with four checks: volume, a 3D checkerboard colour count, awkward pieces first and layer by layer, plus a practice puzzle.
How to Solve a Pentomino Puzzle: Area, Corners and Colours
Fill a board with the 12 five-square pieces. Check area and colour, mark tight corners, place awkward pieces first, then try a worked and a practice box.
Sliding Block Puzzles: Clear the Blocker Chain, Free the Target
Work back from the target: trace the blocker chain, count free cells, move small pieces first. A worked tray, a parking-style grid and a practice puzzle.
Gear Train Puzzles: Which Way Does the Last Gear Turn?
Meshing gears turn opposite ways, so count the contacts. Learn why odd rings jam, how belts change direction, and solve a worked gear train puzzle.
Tangled Cord Puzzles: How to Remove Every Crossing
Move one dot at a time, count crossings in pairs and fix a triangle first. A worked tangled cord puzzle, a practice puzzle and the networks that never lie flat.
Dot-to-Dot Path Puzzles: How to Join Every Dot Exactly Once
Join every dot once in a single path: count partners, fix forced links, use hop-length and arrow rules. With a worked row example and a practice grid.
Rook and Queen Tour Puzzles: How to Visit Every Square Once
Solve rook and queen tour puzzles: step and slide moves, open and closed tours, the snake plan, forced corner lines and a worked 5 by 5 example.
Map Colouring Puzzles: How to Use the Fewest Colours
Colour every region so neighbours differ, with as few colours as possible. Dots and lines, greedy colouring, backtracking, a worked map and a practice puzzle.
How to Solve a Maze: Five Methods for Maze Puzzles
Keep a hand on the wall, fill dead ends, mark junctions, work backwards or search every branch. One worked maze puzzle and a practice maze with answer.
Shortest Route Puzzles: How to Find the Fewest Steps by Hand
Spread outward from the start, settle the nearest place first and trace back. Worked road map, rook board example, reachability check and a practice puzzle.
One-Stroke Drawing Puzzles: How to Solve Them by Counting Lines
Count the lines at each dot to see if a figure can be drawn in one stroke and where to start. Method, worked example, arrow version and practice puzzles.
Why Some Puzzles Are Computationally Hard, Even for Computers
Why some puzzles are hard for computers: positions grow too fast to check, best answers are NP-hard, and clever estimates cannot remove the worst cases.
Puzzle With a Unique Solution: How Designers Make Sure
A good puzzle has exactly one answer. How designers and researchers check every possibility so a puzzle ends with a single solution.
How Many Latin Squares Are There? Counting Puzzle Grids
Latin squares go from 12 of order 3 to a 37-digit count at order 10. How the counts were found, how larger ones are estimated, and how grid loops are counted.
How Puzzle Difficulty Is Measured: Solve Rates to Dead Ends
Puzzle difficulty is measured by solve rates, ratings, dead ends and solution length. What research says each method shows and misses.
How Computers Solve Puzzles: Search, Estimates and Logic
Computers solve puzzles by searching a network of positions. See breadth-first search, A*, greedy search and logic programs on one worked example.
Equal Sum Square Puzzles: How to Fill Every Row and Column
Fill a square so every row and column adds to the same total. The one-gap rule, the centre rule, a worked four by four puzzle and a practice grid.
Coin Total Puzzles: Largest Unpayable Total and Fewest Tokens
Which totals can two token values pay, what is the largest one they cannot, and how few tokens will do? A ladder method, worked example and practice.