State-Space & Positions
📋 What it is
Every arrangement of a puzzle is a “state”; the set of all reachable states is its state space.
🗣️ Coach says
Think of every possible board arrangement as a dot, with lines to the arrangements one move away. Solving a puzzle is finding a PATH through this web from start to goal. Seeing puzzles as maps of states is how computers solve them.
🧠 Memory hook
Each arrangement = a dot. Each move = a line. Solving = finding a path.
😂 Giggle
Why did the riddle wear a disguise?
Because the answer was never quite what it seemed!
😲 Whoa!
A Rubik’s Cube has 43 quintillion states — yet any scramble can be solved in 20 moves or fewer (“God’s number”), a fact proven only in 2010 using huge computers.
✅ Quick check: If a puzzle has few pieces but they can be in many arrangements, is the state space small or large?
Say your answer out loud first — then reveal.
Large — the number of arrangements (states) can explode even with few pieces, like a Rubik’s Cube.
State-space size grows with the number of arrangements, not just the piece count.
🧪 Try it! (2 minutes)
Draw 3 simple states of a tiny puzzle as dots and connect the ones one move apart. That’s a state space.