Can you solve it? Are you as smart as Spock? | Mathematics

An annual festival is held on all days of the year.

January 14th is the day of the year.

Therefore, an annual holiday is held on January 14th.

What it does: World Logic Day is a date endorsed by UNESCO in the academic calendar to promote the study of deductive reasoning. It falls next week, but there is an issue that will help lift your spirits.

Middle managers

Andy, Bea and Celine have a jar of ten cookies. They take turns putting their hands in the jar and pulling out cookies for themselves. Andy goes first, then Bea, then Celine. Each turn they can take as much as they want.

They agree to the following terms:

1) Nobody wants to have the most or the least amount of cookies. (Having the most looks greedy, and having the least looks stupid.) Ending up with the most or the fewest joints is just as undesirable as ending up with the most or the fewest.

2) They want as many cookies as possible. (It's always best to have as many cookies as possible.)

If condition 1 takes precedence over condition 2 but both are desired, how many cookies will each friend receive?

Friends are not allowed to communicate or form alliances. They don't have to take all the pieces, and one or more don't have to take anything. Let us assume that they act rationally and in their own interests.

I'll be back at 5pm UK time with a solution.

UPDATE: The solution can be read here..

NO SPOILERS PLEASE. Instead, discuss your favorite counter-intuitive arguments.

Thanks to Deniz Sarikaya from World Logic Day for today's puzzle. List of WLD events: listed here.

If you want a more challenging set of puzzles, try this Competition “Christmas Riddles”.

I've been doing puzzles here on Mondays since 2015. I'm always on the lookout for great puzzles. If you would like to offer one, write to me.

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