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 2 kids 3 boxes (Posted on 2017-07-01)
Two kids are given three boxes of chocolates with a total of 32 pieces.
Rather than sharing evenly, they play the following game:
Each in turn, they pick one of the three boxes, empty its contents in a jar ; then pick some chocolates from one of the remaining boxes and transfer them to the temporarily empty box so that no box stays empty.

The game ends with the current player’s loss when this is no longer possible.

Example start:
Initial state : (7,8,17)
Kid A empties the 1st box: (0,8,17),
then transfers 3 pieces from the 2nd box to the 1st creating new situation (3,5,17)
and now Kid B goes on.

What is the optimal strategy?

Source: The French "Le Monde"
My remark: Although we don’t know the initial quantities of chocolates in each box, the kids do. Please assume: (a,b, 32-a-b) for conformity sake.

 Subject Author Date Solution Brian Smith 2017-07-01 22:15:03

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