 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? ### 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: CPD: Actuaries Institute Members can claim two CPD points for every hour of reading articles on Actuaries Digital.