Solving Mathematical Problems

Posted by tpc at June 19th, 2007

a personal perspective by Terence Tao. This is a new edition of a book which was written by Tao more than 15 years ago, which means when he was only 15! It’s a thin little book that takes a leisurely look at solving some competition type problems. The coverage is not huge, but the author take pains to go through in great detail various strategies one can adopt in solving problems. Quite a nice book but very pricey for 102 pages.

I found exercise 2.1 quite fun.

In a parlour game, the ‘magician’ asks one of the participants to think of a three-digit number abc_{10}. Then the magician asks the participant to add the five numbers acb_{10}, bac_{10}, bca_{10}, cab_{10} and cba_{10}, and reveal their sum. Suppose the sum was 3194. What was abc_{10}?

My solution is this. If we add all the six permutations, we know that the sum equals
(2a+2b+2c) \times 100 + (2a+2b+2c) \times 10 + (2a+2b+2c)
= (a+b+c) \times 222.
So we just need to know the multiples, 1 \times 222, \ldots, 27 \times 222. Take the smallest multiple larger than the given number, and check by subtracting the difference and summing the digits. You do not have to do it with more than 5 different multiples.

15 \times 222 = 3330; 3330 - 3194 = 136.
But 1+3+6 = 10, so incorrect.
now 16 \times 222 -3194 = 136 + 222 = 358.
And 3+5+8 = 16 and we found our number.

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Why teach arithmetic

Posted by tpc at June 10th, 2007

Found a very nice post by Alane Tentoni on the topic, together with a link to a great story by Asimov about a future where people cannot do maths without a computer.

via Carnival of Math IX

Posted in Teaching, Technology| 1 Comment |