Critical Line volume 31

This month’s Critical Line puzzle is brought to you by Oliver Chambers. Can you figure out the winning strategy for this probability game? 

$$n > 10$$ coins lie in a line on a table. Initially all coins show heads. Two players, $$A$$ and $$B$$, take it in turns to find a block of $$10$$ consecutive coins with the leftmost coin showing heads and flipping those $$10$$ coins over (such that the heads show tails and vice versa). If a player is not able to make a move then they lose the game.

  • Show that the game always terminates
  • If Player $$A$$ may decide whether to play first or second. Is there a winning strategy? If so, what is it?



For your chance to win a $50 book voucher, send your solutions to


Volume 30 solution – Jevon Fullbrook

I received two possible correct solutions, from four puzzlers: Roger Bohlsen, Matthew Floyd, Brayden Slade & Hemant Rupani. There were many incorrect solutions which unfortunately failed to meet the criteria of either; creating non-connected white squares or having a sequence of blanks intersecting more than two regions.

Hemant was the first correct solution submitted, congratulations Hemant!

Two examples of correct solutions submitted are shown below:

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