Tower Transfer: Move a Four-Disk Stack in the Fewest Legal Moves
Drag one top disk at a time across three pegs, where a big disk can never rest on a small one. Every move asks you to plan ahead, and slowly reveals how one giant task hides a smaller copy of itself.
Why You Can't Just Grab the Biggest Disk First
Most players reach straight for the largest disk and stall the instant they notice three others pinning it down. This game makes that wall visible: the peg physically refuses a big-on-small drop, so a greedy grab bounces right back. Once the move counter climbs past your guesses, the trick surfaces — clearing the top three disks is the exact puzzle you just solved, only shorter. Undo lets you test a branch, watch it dead-end, and back out without restarting, so the recursive rule (move n−1, move the biggest, then move n−1 again) becomes something you feel instead of memorize.
Spotting the Doubling, Then Proving the Rule Behind It, Grades 3–8
Grade 3–4 players practice reading and continuing a growing number sequence as they notice each added disk roughly doubles the move count, the very skill named in generating shape-and-number sequences (4.OA.C.5). By grades 5–8 that doubling hardens into an explicit rule, 2ⁿ − 1, carrying sequence generation (5.OA.B.3) toward looking for structure and expressing regularity in repeated reasoning (MP.7, MP.8). The recursion habit it builds — shrink a hard problem to a smaller copy of itself — is the same move that later powers algebra and proof.
Learning Points
- spatial transformation
- multi-step planning
- working memory
- strategy review
Steps and completion rules
- Select a source peg with a disk, then choose a legal destination peg.
- Use the middle peg to hold smaller disks while making room for a larger one.
- Move all four disks to the right peg, using Undo when comparing alternative sequences.
Teacher / Parent Note
Plan how to move the top three disks before moving the largest, treating the smaller transfer as the same kind of problem.