Tower of Hanoi

There are three pegs ($1$, $2$, $3$). Peg $a$ holds $n$ disks: the largest at the bottom, smaller and smaller upwards. All disks must be moved to peg $b$. Rules: one move takes a single disk — the top one of some peg — and puts it on another peg; a larger disk may never be placed on a smaller one.

Move the disks with the fewest possible moves and print the moves in order.

A single line with $n$, $a$, $b$ ($1 \le n \le 10$; $a, b \in \{1, 2, 3\}$, $a \ne b$).

The first line contains the number of moves. Then each move on its own line: the peg to take the disk from and the peg to put it on.

To move $n$ disks from $a$ to $b$: move the top $n - 1$ disks to the third peg ($6 - a - b$), put the largest disk on $b$, then move the $n - 1$ disks from the third peg to $b$. Base case: $n = 0$ — do nothing. There are $2^n - 1$ moves, and the shortest sequence is unique.

First example: small disk $1 \to 2$, large disk $1 \to 3$, small disk $2 \to 3$.