Paint and puzzles

A bot starts with the paint its mode gives and holds at most 65,535. Each trail tile costs 1 paint, and each solved puzzle pays 4, up to that limit.

Puzzles are Lights Out boards with 2 or 3 colors. Each light holds a color from 0 to num_colors - 1, and 0 is off. Toggling a light by an action number adds that number, modulo num_colors, to the light and to its up, down, left and right neighbors. A solution grid holds one action number per light and solves the board when it turns every light off.

For example, on a 3-color board, toggling the middle light by 2 changes these lights:

Before    Added     After
0 0 0     0 2 0     0 2 0
0 1 0     2 2 2     2 0 2
0 0 0     0 2 0     0 2 0

The middle light becomes (1 + 2) mod 3 = 0.

Board sizes, as num_rows by num_cols:

• 2 colors: 12 by 4, 15 by 4, 16 by 4, 6 by 5, 13 by 5 and 5 by 6.
• 3 colors: 7 by 3, 12 by 3, 13 by 3 and 11 by 5.

Every board has a solution.

Write the address of a 268-byte, word-aligned buffer to REQUEST_PUZZLE. An accepted request sets MMIO_STATUS to OK and adds 1 to AVAIL_PUZZLES. A bot can request 2,000 puzzles in a match. Later requests get TOO_MANY_PUZZLES, and a bad buffer gets BAD_ADDRESS.

The puzzle arrives 1,000 to 5,000 cycles after the request, or after the bot's previous puzzle arrives if that is later. The game then writes it to the start of the buffer, whether or not the bot has interrupts enabled, and raises the REQUEST_PUZZLE interrupt. If the buffer breaks the buffer pointer rules by then, it gets neither the puzzle nor the interrupt. The game writes these fields:

1. Write the puzzle's index to CURRENT_PUZZLE. Puzzles are numbered from 0 in request order, so AVAIL_PUZZLES - 1 is the latest.
2. Write the address of the solution grid to SUBMIT_SOLUTION: num_rows * num_cols bytes, row by row, each an action number from 0 to num_colors - 1.
3. Read MMIO_STATUS. OK means the bot got its 4 paint. Each puzzle pays once.