Tower of Hanoi: familiar rules, different starting stacks

Tower of Hanoi is now playable on TAPA GAME. Move one top disk at a time, placing it on an empty peg or a larger disk. The aim is to collect the whole tower on the right peg. This version has twenty stages with different legal starting arrangements.

Plan around the largest disk

A large disk cannot move while smaller disks sit above it. Before moving it, decide where those smaller disks can wait. The spare peg is temporary storage, but it has to remain legal at every step.

If the right peg already contains smaller disks, you may need to clear it before sending a larger disk there. A move away from the destination can therefore be part of the route to the destination.

Read the starting arrangement

The stages do not all begin with every disk on the left peg. Look at all three stacks before following a familiar Hanoi sequence. A smaller disk may already be in a useful place, or it may block the next large transfer.

Thinking in small subproblems helps. First free the disk you need to move. Then clear its destination. Finally rebuild the smaller stack above it. You do not need to remember a long sequence if you can explain the next transfer.

Moving between pegs

Select the source peg and then the destination with taps, or use the arrow keys and Enter. U undoes a move and R retries the stage.

A good first check is whether the largest unfinished disk can reach the right peg yet. If it cannot, identify the exact smaller stack that needs to move out of the way. That gives the next few moves a purpose.