Move all disks to the right peg. A larger disk can never sit on a smaller one.
Tap a peg to lift its top disk, then tap another peg to drop it there. A disk can only land on an empty peg or on a larger disk. Move the whole tower to the rightmost peg.
You have 120 seconds for a ladder of rounds: 3 disks, then 4, 5, 6 and 7. Each finished tower starts the next round automatically, and the clock keeps running. An illegal drop just flashes red — there is no penalty except the time you lose.
Your score is the largest tower you finished. Between equal towers, the one finished with more time left on the clock ranks higher (shown as, for example, 6 · 18.4s). Finishing the 7-disk round ends the game at once and keeps whatever time you had left.
The Tower of Hanoi has a perfectly mechanical solution, so once you see the pattern you never have to think again. The smallest disk moves on every other turn and always travels in the same circular direction. With an odd number of disks (3, 5, 7) send it leftward, wrapping from the left peg round to the right one; with an even number (4, 6) send it rightward, wrapping from the right peg back to the left. The rounds alternate, so flip the direction every round.
Between each move of the smallest disk there is exactly one other legal move available, and you should always take it. If you ever feel stuck, you have almost certainly moved the small disk in the wrong direction at some point. The five rounds need at least 7 + 15 + 31 + 63 + 127 = 243 moves — about two moves a second for the whole ladder — and the time left when you finish your biggest tower breaks ties, so settling into that "small disk, only-other-move, small disk" rhythm beats hesitating over every choice.