Daily Tower of Hanoi
The rule
Move the whole stack to the right hand peg. One disc at a time, and a disc may never sit on a smaller one.
Tap a peg to lift the top disc, then tap another peg to put it down. Dragging a disc works too, and the keys 1, 2 and 3 pick the pegs.
The disc count changes daily. However you play it, the fewest moves possible is always two to the power of the number of discs, minus one, so seven discs cannot be done in fewer than 127 moves.
In your hands
There is a 3D printed Tower of Hanoi in the shop, sized for a pocket.
If you get stuck
Think about the biggest disc. Nothing may ever rest on it, so before it can move, every other disc has to be out of its way on the spare peg. Solving for the biggest disc turns the puzzle into the same puzzle with one disc fewer, which is why the move count doubles each time you add one.
Why the Minimum Is 2n minus 1
To move a stack of n discs you must first move the top n minus 1 of them off onto the spare peg, then move the bottom disc across, then move that pile of n minus 1 back on top. That is twice the work of an n minus 1 stack plus one move, and a stack of one takes one move, so the count is 1, 3, 7, 15, 31 and so on. Nothing cleverer exists: the sequence is forced by the rules, which is rare in a puzzle and is why this one has been taught for a hundred and forty years.
The One You Can Hold
This is the oldest puzzle on the site by a long way. Edouard Lucas put it on sale in Paris in 1883, wrapped in a story about priests moving sixty four golden discs, a job that would take roughly five hundred and eighty five billion years at one move a second. The version here is the same puzzle in wood and plastic rather than legend.
The Tower of Hanoi travel puzzle is a 3D printed set small enough to go in a pocket, which is the way this one is best met: it is the puzzle people tend to teach each other rather than solve alone. It sits with the rest of the mechanical puzzles.
More to Play
There are twenty one daily sudoku variants, a minesweeper with the guessing removed, tents and a nonogram with hand drawn pictures. For puzzles you can hold, see mechanical puzzles.