Some numbers can't be caught — but they can be trapped. Build fences on the number line, squeeze them ten times tighter with every zoom, and discover which numbers never stop running.
Your target hides on the number line. Place a fence: if its square is at most the target's radicand, and the next fence's square is past it, the target is trapped between them. Trap it, zoom in ×10, and trap it again — one decimal digit per zoom.
A number is about to reveal its decimal expansion. Lock in your prediction first: will the digits terminate, repeat forever, or never settle at all? Then the reveal shows the expansion — and the reason.
Three machines that turn Part 1's discoveries into airtight moves: convert any repeating decimal to a fraction, undo squares and cubes, and shrink a trap forever.
Every repeating decimal hides a fraction. The machine proves it with algebra: name it x, shift it, subtract, solve.
Squaring and cubing are actions — roots undo them. Solve x² = p and x³ = p, then classify the answer.
The Fence Hunt, industrialized. Every press tightens the trap by a factor of ten — and the target still never gets caught exactly.
| Trap | Lower fence² | Upper fence² | Trap width |
|---|
Ten questions. Wrong answers get a hint that names the exact machine or hunt move that proves the right idea.