How to Play Towers of Hanoi: The Classic Ring Stacking Puzzle

Towers of Hanoi is the oldest puzzle on this site by a wide margin: three poles, a stack of graded rings on the first one, and one goal. Move the entire stack onto the third pole. You may move only one ring at a time, only the top ring of a pole, and you may never set a ring down on top of a smaller ring.

That single restriction is the whole puzzle. It sounds like a formality until you try it, at which point you discover that getting the bottom ring across requires every other ring to be parked somewhere first, and that parking them requires the same trick one size down. The puzzle is a recursion you can hold in your hands.

The board here is tap to move rather than drag. Tap a pole to lift its top ring, tap another pole to set it down. A move the rules forbid is refused on the spot with a red flash and never counts against you, so you can probe the board without being punished for a misjudged tap.

A five ring tower can be solved in thirty one moves and no fewer. Your score is how close you get to that number, so this is a puzzle about efficiency rather than speed. There is no clock anywhere in the game.

How to play Towers of Hanoi

1. Choose Daily for the five ring tower everybody plays today, or Quick Game for a freshly scrambled starting position at any ring count from three to eight.
2. Tap a pole to pick up its top ring. The ring lifts clear of the stack and turns yellow, so the board always shows what a second tap will move.
3. Tap a different pole to set that ring down. Tap the pole it came from instead to put it back and change your mind, which does not count as a move.
4. A ring can only land on an empty pole or on a ring bigger than itself. Try anything else and the target pole flashes red, the ring stays in your hand, and your move count is untouched.
5. The board is solved the moment every ring is stacked on pole C, the dashed one marked as the goal. Your run is then checked against the server and scored.
6. Scoring is efficiency out of a hundred. A perfect run scores a hundred, and each move above the minimum costs a little, down to a floor so that finishing always beats giving up.

Strategy and tips

• Look at the smallest ring first. In a perfect solution it moves on every other move, always in the same direction around the three poles, and once you notice which direction that is the rest of the puzzle almost plays itself.
• Think about the biggest ring, not the smallest. The bottom ring can only move once in a perfect run, and only when every other ring is stacked on the spare pole. Work out how to build that stack and you have solved the puzzle.
• A tower of five is a tower of four plus one ring. Move the top four to the middle pole, move the biggest to the goal, then move the four across. Every size is the same problem one step smaller, which is why the move count doubles and adds one each time you add a ring.
• Start at three rings in Quick Game if the pattern has not clicked yet. Seven moves is short enough to see the whole shape of the solution at once, and the shape does not change as the tower grows.
• Undoing a move is not free. There is no undo button because putting a ring back is itself a move, and the score counts moves, so it is cheaper to pause and look than to shuffle rings while you think.
• A quick game does not always start as a neat tower. The scrambled positions can be closer to solved than a full tower, so check where the big rings already are before planning as if you were starting from scratch.

What makes Towers of Hanoi different

There is no clock and no hidden information. Everything about the position is on screen from the first second, and nothing is timed, so the only thing your score measures is whether you found the efficient route. Nearly every other daily on this site is scored partly on speed.

An illegal move is refused rather than punished. The board simply will not let a big ring land on a small one, so you can test an idea by tapping it instead of by reasoning it through first. Your move count only ever goes up when something actually moved.

The daily is always the classic full tower rather than a scrambled position. That is deliberate: the score is measured against the mathematical minimum for the ring count, which is only the true minimum when you start from a full tower. A scrambled daily would hand some days a position two moves from solved and others the whole climb.

It is a solved puzzle and that is the point. Unlike a word or picture puzzle, the answer is not secret, and knowing the method does not spoil it - executing thirty one moves without a slip is still a task. The result card says how many moves you took and nothing about how you took them.

Quick Game lets you choose the size, from three rings up to eight. Eight rings is two hundred and fifty five moves at best, which turns a two minute puzzle into a genuine sitting, and no other game here scales its own difficulty by that much.

Frequently asked questions

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