The impossible chess board problem must have something to do with the idea of solving tree eval with little memory (https://youtu.be/wTJI_WuZSwE?si=lgTc65RhXQesKchR)! When the chess board is random, it feels impossible to add additional information. However, by choosing which cell to flip and knowing that you followed a certain operation, you can encode the position information in the random data, without needing more cells.