Sunday 17 April 2016

Unique solution

When the family left after the Easter holiday, I found a book near the surface of one of the heaps in the living-room. Someone must have found it on a shelf and started reading it. My Best Mathematical and Logic Puzzles by Martin Gardner.  Gardner had an endless fund of cleverness, turning out a column called Mathematical Games every month without fail for 25 years!  Two of my favourite books growing up, each read ragged, were his Mathematical Puzzles and Diversions and More MP&D.  All three books cited here were full of stuff first launched in the SciAm column. After the death of his wife, he returned home to Norman OK and died there, alert to the last, in May 2010 at the age of 95. He's probably done more to inspire smart young people and encourage them to think a little bit more than any other writer in the 20thC.  The nice thing about his books and his puzzles is that they engage at a variety of levels: some fiendishly difficult; some requiring a lot of grunt work; but many yielding to insight and/or a clear marshalling of data. When you can't work it out yourself, the answer rarely makes you think either that was dumbass or I'm a dumbass but rather that was clever, I could be that clever, I'll try harder next time . . . and another critical thinker is launched.

On a something for the weekend basis, here's one of the puzzles. I read, gave up on, wrote a Blob, slept, did a day's work, slept and looked at again. If you don't give up, you too can crack it.

Three schools -- Democritus, Pythagoras & Anaxagoras  -- competed in an athletics meet. Each school entered one man, and one only, in each event. Susan, a student at Pythagoras High, went to cheer her boy friend, the school's shot-put champion. When Susan returned home later in the day, her father asked how her school had done.
"We won the shot-put all right," she said, "but Anaxagoras High won the track meet. They had a final score of 22. We finished with 9. So did Democritus High."

"How were the events scored?" her father asked. "I don't remember exactly ," Susan replied, "but there was a certain number of points for the winner of each event, a smaller number for second place and a still smaller number for third place. The numbers were the same for all events." (By "number" Susan of course meant a positive integer.)

"How many events were there altogether?" "Gosh, I don't know, Dad. All I watched was the shot-put."
"Was there a high jump?" asked Susan's brother. Susan nodded.
"Who won it?"  Susan didn't know.

Incredible as it may seem, this last question can be answered with only the information given. Which school won the high jump?

Better still put this to your favourite numerate 13 year old. Answer. No peeking until you've given it some time!  Anaxagoras Who? Pythagoras on The Blob. Democritus.

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