# Solution to "Looking Glass Zoo"

There were three nephews and two nieces. A boy won. He got two pairs right but interchanged two sexes.

Satisfactory proofs of this result are hard to find. The author gave a proof using matrix theory, but even he omitted the crucial point, just saying 'It has been proved that'!

I used a "brute force" computer program as follows:-

There are 24 permutations of 4 animals and the sexes allow 2*2*2*2 variations to each permutation giving an initial set of 444 possible lists. The paragraph beginning "Curiouser and Curiouser" gives rules that must be obeyed by all boys' lists and all girls' lists. My program applied these rules to all possible lists and found that 76 of the initial set obeyed the boy's rule and 12 obeyed the girl's rule. (Incidentally, all the girls scored zero! Not at all politically correct).

My program then applied the rule beginning "Here's a queer thing" to all groups of 5 and 6 children, remembering that there must be at least two girls (an 'all boys' team could be bigger). It reduced the running time by starting with groups of 2 girls, failing to add a third girl and then adding boys to them. It found several groups of five, all with the composition and scores stated and no groups of 6.

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