[A] For 18 points. Some high tables, but not Balliol's, of course, are rather given to Pronouncements as a mode of conversation. The idea is to have a pearl of wisdom available for any conceivable topic. Alice was dining at one such place recently, and happened to mention her beloved kitten Fang, and her remarkable green eyes. The dons were prepared. In short order she was informed that no fish-loving kitten is unteachable; that no tailless kitten will play with a gorilla; that kittens with whiskers always love fish; that no teachable kitten has green eyes; and that kittens with tails always have whiskers.
“That doesn't sound very nice,” said Alice . “I hope my kitten never plays with a gorilla.”
Assuming that the dons were right for once, can you reassure her?
[B] For 20 points. Tom, Dick and Harry comprise the Oriel underwater wrestling team. One is fattest, another is tallest, and the third is heaviest. Tom is older than the heaviest, and Dick is older than the fattest. For each of the following claims, either prove that it is true, or prove that it is false, or show why neither proof is possible:
[1] Harry is the youngest
[2] Harry is the tallest
[3] Dick is the heaviest
[4] The tallest is the oldest
[5] If the tallest is Dick's brother, then Harry is the fattest
[C] For 26 points. Tweedledum always tells the truth, and Tweedledee never does – or is it the other way round? Anyway, I heard one of them say “My brother, when asked, says he is Tweedledee.”
Can you work out who said it? And can you work out which one always tells the truth?
[D] For 22 points. Ian Plummer, the College Computing Officer, has a typically Wonderland brief. He is to mend the computers of precisely those Balliol Fellows who do not mend their own. And he is not to mend any others . Does Ian mend his own computer? And is he a Balliol Fellow?
As always, solutions should aim for accuracy, rigour, brevity, elegance and wit. The Editor's decision is final.
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