Puzzles (The Critical Line)
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 Amay 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 ActuariesMag@actuaries.asn.au
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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