P1213 [IOI 1994 / USACO1.4] The Clocks

Consider nine clocks arranged in a $3 \times 3$ grid: ```plain |-------| |-------| |-------| | | | | | | | |---o | |---o | | o | | | | | | | |-------| |-------| |-------| A B C |-------| |-------| |-------| | | | | | | | o | | o | | o | | | | | | | | | | |-------| |-------| |-------| D E F |-------| |-------| |-------| | | | | | | | o | | o---| | o | | | | | | | | | |-------| |-------| |-------| G H I ``` The goal is to find a shortest sequence of moves that sets all hands to $12$ o'clock. The table below lists $9$ different methods of rotating hands; each method is called a move. Applying moves $1 \sim 9$ rotates the hands of the indicated clocks by $90$ degrees clockwise. | Move | Affected clocks | | :--: | :-------------: | | 1 | ABDE | | 2 | ABC | | 3 | BCEF | | 4 | ADG | | 5 | BDEFH | | 6 | CFI | | 7 | DEGH | | 8 | GHI | | 9 | EFHI | For example: ```plain 9 9 12 9 12 12 9 12 12 12 12 12 12 12 12 6 6 6 5 -> 9 9 9 8 -> 9 9 9 4 -> 12 9 9 9 -> 12 12 12 6 3 6 6 6 6 9 9 9 12 9 9 12 12 12 ``` **But this might not be the correct method; see below.**

Three lines, each containing three positive integers, giving the initial time of each clock (the meaning of the numbers is the same as in the example above).

A single line containing the shortest sequence of moves that sets all hands to $12$ o'clock, listed in order and separated by single spaces. If there are multiple solutions, output the lexicographically smallest one. (For example, `5 2 4 6` is lexicographically smaller than `9 3 1 1`.)

Problem translation from NOCOW. USACO Training Section 1.4. Translated by ChatGPT 5