Did you solve it? Are you as smart as Spock?

2009, STAR TREKZACHARY QUINTO Character(s): Spock Film 'STAR TREK' (2009) Directed By J.J. ABRAMS 06 April 2009 SSU81988 Allstar/PARAMOUNT (USA/DE 2009) **WARNING** This Photograph is for editorial use only and is the copyright of PARAMOUNT and/or the Photographer assigned by the Film or Production Company & can only be reproduced by publications in conjunction with the promotion of the above Film. A Mandatory Credit To PARAMOUNT is required. The Photographer should also be credited when known. No commercial use can be granted without written authority from the Film Company.

Earlier today I set the following puzzle, a pre-commemoration of World Logic Day on January 14. Here it is again with the solution.

Middle management

Andy, Bea, and Celine have a jar of ten cookies. They will take turns putting their hands in the jar to take out cookies for themselves. Andy is first, then Bea, then Celine. On each turn, they can take as many as they like.

They agree to the following conditions:

1) No one wants to end up with the most, or the least number of cookies. (To have the most looks greedy, to have the least looks lame.) Finishing with joint most, or joint least, is as undesirable as finishing with most or least.

2) They want as many cookies as possible. (Always better to have as many cookies as you can.)

If condition 1 has priority over condition 2, but both are desirable, how many cookies does each friend end up with?

The friends are not allowed to communicate or form alliances. They do not need to take all the pieces, and one or more could take nothing. Assume that they are acting rationally and in their best interests.

Solution

Andy will take 4 cookies, Bea takes 6, Celine is left with none.

Workings

Say Andy takes 6, 7, 8, 9 or 10 cookies. He will end up having the most cookies, which fails condition 1. So he doesn’t do that.

Say Andy takes 5 cookies. Bea will take 4, which means she will end in the middle and Andy still fails condition 1. So he doesnt do that either.

Say Andy takes 4 pieces. Bea cannot fulfil condition 1. (If Bea takes, 1 or 2 , then Celine takes 3 and Celine wins. If Bea takes 3, Celine will take 3, and both have joint-least. If Bea takes 4 or more she will have the most, or joint most, cookies.) So, Bea realises her best outcome is to fulfil condition 2. She takes all the remaining cookies, and Celine is left with 0.

If Andy wins by taking 4 pieces, he is not going to take any less pieces – since that falls foul of condition 2. He wants both to be middle, and to have as many cookies as possible. So he takes 4 pieces.

I hope you enjoyed today’s puzzle. Live long and prosper. I’ll be back in two weeks.

Thanks to Deniz Sarikaya of World Logic Day for today’s puzzle. A list of WLD events are listed here.

If you would like a harder set of puzzles, try this Christmas Puzzle competition.

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

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