Tower of Hanoi Speed Guide: Five Rounds in Two Minutes

Updated October 2026

The Tower of Hanoi on ujem is not a single relaxed puzzle. It is a two-minute race through five towers of growing height, from three disks up to seven, and your score is the tallest tower you managed to finish before the clock ran out. Knowing how to solve the puzzle is only the entry ticket. Finishing all five rounds needs an algorithm you can run without thinking and a tapping rhythm that does not break. This guide covers the exact rules of the timed mode, the numbers behind it, and a method for getting faster.

How the timed mode actually works

Press Start and a 120-second countdown begins. The first round puts three disks on the left peg, and your job is to rebuild the whole stack on the right peg. The moment the last disk lands there, the round counts as cleared and, after a short pause of 0.6 seconds, a fresh round appears with one more disk: four, then five, six and finally seven. If you clear the seven-disk tower the game ends at once, keeping whatever time is left on the clock.

Your score is the size of the last tower you completed, plus a tiebreak: the time that was left on the clock at the moment you finished that tower, to a tenth of a second. The result card and the Hall of Fame show it as, for example, 6 · 18.4s, and a 6 finished with 18.4 seconds to spare ranks above a 6 finished with 9.0. Run out of time halfway through the five-disk round and you score 4, with the time that was left when your four-disk tower landed. Fail to finish the opening three-disk round and you score 0. The number of moves never counts directly; it only matters through the time it costs. The clock is real elapsed time, so it keeps running during the pause between rounds and while the page is in the background. There is no penalty for an illegal move other than the time it wastes: the target peg flashes red and nothing moves.

Each move takes two taps. The first tap on a peg lifts its top disk, highlighting that peg. The second tap on a different peg drops the disk there. Tapping the highlighted peg again puts the disk back down. After an illegal attempt the disk stays lifted, so you can simply tap the correct peg next. The whole column of a peg is the touch target, which means you can tap anywhere from the base to the top of the screen.

The budget: how fast you really need to be

A tower of n disks needs at least 2ⁿ − 1 moves. That gives 7 moves for three disks, 15 for four, 31 for five, 63 for six and 127 for seven. Adding them up shows what each score costs if you never waste a move:

• Score 3: 7 moves.
• Score 4: 22 moves in total.
• Score 5: 53 moves in total.
• Score 6: 116 moves in total.
• Score 7: 243 moves in total.

The four pauses between rounds eat 2.4 seconds, leaving roughly 117.6 seconds of actual play for a perfect run. That works out to just over two moves per second, or about four taps per second sustained for two minutes with no wrong turns. A score of 6 is far gentler: around one move per second. A score of 5 only needs about one move every two seconds, so it is the natural first goal for anyone who knows the method. The jump from 6 to 7 is brutal because the last round alone is more than half of all the moves in the game.

The method that never needs a decision

Every optimal solution alternates between two kinds of move. On odd-numbered moves (the first, third, fifth and so on) you move the smallest disk. On even-numbered moves you make the only legal move that does not touch the smallest disk. There is always exactly one such move, because of the two other pegs' top disks, only the smaller one can go on the larger one. So the entire puzzle reduces to one question: which way does the smallest disk travel?

The answer depends on whether the tower is odd or even, and this is the detail that catches people out in this mode. Think of the pegs as a loop: left, middle, right, then back to left.

• Odd rounds (3, 5 and 7 disks): the smallest disk steps left → right → middle → left, and repeats. Its very first move goes straight to the target peg.
• Even rounds (4 and 6 disks): the smallest disk steps left → middle → right → left, and repeats. Its first move goes to the middle peg.

Because the rounds alternate between odd and even, the direction flips every time a new round appears. If your first move of a round is wrong, you are already on a longer path. A simple cue is to look at the disk count shown above the board when the round starts: odd means the first move goes all the way right, even means it goes to the middle.

Thinking in blocks instead of single moves

The step-by-step rule is reliable but it can feel like reading a tower one letter at a time. The recursive picture is faster for the brain. To move a tower of n disks to the right peg, you first move the top n − 1 disks out of the way onto the middle peg, then move the largest disk to the right, then bring the n − 1 tower across on top of it. Each of those smaller towers is solved the same way.

In practice this means you can recognise chunks. A three-disk shuffle is a seven-move phrase you will play dozens of times inside the bigger rounds. Once your fingers know that phrase in both directions, a seven-disk tower stops being 127 separate choices and becomes a sequence of familiar phrases joined by single moves of the larger disks. Watching for the moment the largest remaining disk becomes free is the best progress check: in the seven-disk round it moves exactly once, at the halfway point, move 64.

Tapping technique on a phone

Speed in this game is mostly about the hand, not the head. Hold the phone in one hand and tap with the thumb of the other, or use both thumbs with the left thumb covering the left peg and the right thumb covering the middle and right. Because a peg's whole column responds, aim low near the disks where your thumbs rest naturally rather than stretching up the screen.

• Say the smallest disk's direction, not each move. Track only "small disk goes next" and let the in-between move happen by sight.
• Never double-check a legal move. If the other move is obvious, tap it. Hesitation costs more than the occasional red flash.
• Use the 0.6-second pause. When a round clears, glance at the new disk count and set your direction before the board even redraws.
• Avoid accidental deselects. Tapping the lifted peg a second time drops the disk back where it was, which costs two taps and breaks the rhythm.

Common ways a run falls apart

The most frequent loss is a wrong first move in an even round, usually after a fast odd round when the hand keeps the old direction. The second is losing the alternation: moving the smallest disk twice in a row, which simply undoes progress. If you notice the small disk heading back to where it just was, stop and restart the rhythm from the current position; any legal position can still be finished, just not optimally. The third is panic on the seven-disk round when the clock shows under 15 seconds and turns red, which tends to cause illegal taps. At that point a score of 6 is already secure, so there is nothing to lose by staying calm.

A training ladder

1. Solve the opening three- and four-disk towers slowly while saying the smallest disk's direction out loud. Aim for zero red flashes.
2. Target a score of 5. That needs about one move every two seconds, so focus on accuracy and the odd/even switch.
3. Target 6 by building the three-disk phrase into muscle memory in both directions.
4. Only then chase 7. Measure where the clock stands when the seven-disk round appears; if you reach it with more than about 63 seconds left you have a real chance, since that round needs 127 moves.

Your best score is kept on your device, and any score above zero can be submitted to the Hall of Fame from the time-up card.