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Computer Science · Algorithms
Puzzle Algorithms Lab
Twist a Rubik's Cube, move a tower of disks, steer a drone through a 3D city and watch brute force explode, one clever algorithm at a time.
Computer Science · Algorithms
Puzzle Algorithms Lab
Twist a Rubik's Cube, move a tower of disks, steer a drone through a 3D city and watch brute force explode, one clever algorithm at a time.
The course
7 worlds · 29 lessons
World 1 · Turn the Cube
FREERead the notation and learn how the pieces move- 01Faces and moves: how to read cube notationSix letters describe every turn · 8 min
- 02Pieces and patterns: corners, edges and centres26 pieces, 54 stickers, and two things to track · 9 min
- 03Moves that do not commute: why order mattersR then U is not the same as U then R · 10 min
- 04A warm-up on 2×2: a smaller cube, the same ideasOnly corners, so only the first idea is needed · 8 min
World 2 · Solve It Layer by Layer
PROA plan you can follow from a scramble to a solved cube- 01The white cross: start with a planFour edges, matched to the centres · 9 minPRO
- 02First-layer corners: one at a timeThe four-move trick R' D' R D · 10 minPRO
- 03Second-layer edges: insert from aboveTwo mirror-image sequences · 9 minPRO
- 04The last layer: cross, orient, permuteFour small jobs, each one keeping the layers below · 14 minPRO
- 05Count and check: how many moves is that?Measuring a solution · 9 minPRO
World 3 · God’s Number
PROHow many positions, and how few moves are ever needed?- 01How many positions? A number bigger than you can countThe multiplication principle and factorials · 11 minPRO
- 02Why you cannot twist one corner: hidden rulesInvariants: what no move can change · 11 minPRO
- 03Twenty moves: the God’s number storyThe hardest cube in the world needs only 20 moves · 11 minPRO
- 04How computers solve it: a two-phase ideaShrink the search by solving in stages · 11 minPRO
World 4 · Towers of Hanoi and Recursion
PROA puzzle that teaches the most famous idea in programming- 01Three pegs, one rule: the puzzleMove the whole tower, one disc at a time · 8 minPRO
- 02Recursion: solving a problem by solving a smaller oneThe idea behind the pattern · 11 minPRO
- 03Two to the n, minus one: counting the movesFrom the recursion to a formula · 9 minPRO
- 04The legend of 64 discs: when exponential means impossibleSome answers exist but cannot be reached · 10 minPRO
World 5 · Find the Way: A* vs Dijkstra
PROHow maps, games and robots find the best route- 01Shortest path on a grid: from BFS to weightsGraphs, steps and costs · 10 minPRO
- 02Dijkstra: always expand the cheapestA priority queue and a growing wave · 11 minPRO
- 03A*: Dijkstra with a compassEstimating the rest of the way · 12 minPRO
- 04A drone in a 3D city: more dimensions, same ideaAdding a height layer and designing costs · 11 minPRO
World 6 · The Delivery Problem (TSP)
PROThe route puzzle that brings computers to their knees- 01Visit every stop once: the travelling salesmanThe shortest round trip · 9 minPRO
- 02Brute force blows up: factorial growthWhy checking every tour stops working · 10 minPRO
- 03Good-enough routes: heuristicsFast answers that are close to the best · 11 minPRO
- 04When computers cannot be quick: hard problemsEasy to check, hard to find · 10 minPRO
