Numbers; the anaesthetist

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The Independent Online
It is the 31st of August 1995.

Thirty-one is an interesting number. As one less than 25, it is the answer to the question about five weights and some kitchen scales: if you have weights of 1, 2, 4, 8 and 16 units that may be put into one pan of the scales, you can weigh any amount up to 31 units - and no five weights can do any better without failing on some smaller amount.

Of course, if you are allowed to put weights in either pan, then you can manage anything up to 40 units with only four weights of 1, 3, 9 and 27.

31 = 1 +5 + 52 and also:

31 = 1 + 2 + 22 + 23 + 24 which makes it one of only two known numbers expressible in two different ways as the sum of successive powers starting with 1. (The other one is 8191 - work it out for yourself.)

Meanwhile, 31 is:

The days in the gestation period of a rabbit;

The bones in the human leg;

The percentage of the world's olives that come from Italy.

And 62, which is 2x31, is the number of self-portraits by Rembrandt and the opus number of Eric Satie's first work.

Mixed doubles:

Rap urge nips choir - take octet.

That sentence hides three words linked by a common theme. To find the missing words, all you have to do is group the six words into three pairs, then rearrange the letters within each pair.

A Chambers Encyclopaedic Dictionary awaits the first correct answer opened on 14 September. Entries to: Saturday Pastimes, the Independent, 1 Canada Square, Canary Wharf, London E14 5DL.

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