board problem

on another thread

This is hard to explain via text, I will simply redirect you to the following page: Nim Sum from Interactive Mathematics Miscellany and Puzzles

I hope this answers or will help answering your question.

hi, thanks, its the same case i see but just the rows are going from the top to bottom, whilst mine are going from the bottom upwards.

how am i meant to prove the conjecture that they are using? they have not included that, and written at the bottom to "Prove the above Proposition."