Chessboard puzzle game

This script implements a puzzle game described here. I heard about it thanks to 3blue1brown and Stand-up Maths who played it and explained it here.

Two players are faced with a challenge by a judge.
The judge will show player 1 (P1) a square chessboard covered in coins. Each coin will be put heads or tails by the judge at their will.
The judge will show player 1 a tile of the chessboard where a key will be hidden. Player 1 must then flip one and only one coin and then leave the room without communicating with Player 2.
Player 2 is then shown the chessboard (as modified by the single flip made by Player 1) and must guess the correct tile where the key is hidden.
Player 1 and 2 can agree upon a strategy before starting, but the judge will know what they said and can act accordingly when choosing the coin disposition on the chessboard.
No tricks: the players can not communicate after Player 1 is told where the key is; each coin may be only H or T, its orientation is meaningless, and it cannot be put in other states (e.g. on its side).

The script generates three pdf files: Problem, Key and Solution.

Key.pdf shows the initial 8x8 grid, filled with random heads (H) or tails (T), with an orange coin where the invisible key is hidden. This is how the grid looks like when the judge shows it to Player 1 asking them to flip one and only one coin.
Problem.pdf shows the same grid with just one coin flipped by Player 1. This is how the grid looks like when the judge shows it to Player 2 after Player 1 has flipped one coin.
Solution.pdf shows the same grid, with an orange coin and a purple coin. The orange one is where the key is hidden, the purple-background coin is the one to flip to communicate where the key is.

Show player 1 the Key.pdf: a grid with one key hidden.
Ask player 1 to flip one and only one coin. They should choose the purple-background coin in Solution.pdf, thus producing the same grid shown in Problem.pdf.
Show Player 2 Problem.pdf and ask them to identify where the key is. They should point to the orange coin in Key.pdf and Solution.pdf.