Tables seating four
Russian peasants were said to perform multiplication knowing only how to add, and to multiply and divide by 2. I showed my niece how to multiply 25 by 31 by this method, as shown in the first box.
In the left column, the numbers are divided by 2 successively, any resulting halves being ignored, until 1 is reached. The right column consists of an equal number of values, each after the initial 31 being double the previous one. A simple rule, which I left my niece to discover, tells us which of the values in the right column we must add to get the required total of 775.
My brother-in-law then sent me the following problem, which uses the above method to multiply p by P, and which, with the relevant addition, gives the correct result, ENIGMA, where each of these six letters represents a different non-zero digit. He has inserted a 4 wherever it occurs in the calculation, leaving all other place-holders unspecified, as shown in the second box.
What is ENIGMA?
WIN £15 will be awarded to the sender of the first correct answer opened on Wednesday 21 November. The Editor’s decision is final. Please send entries to Enigma 1720, Â鶹´«Ã½, Lacon House, 84 Theobald’s Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).
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Answer to 1714 Penny-farthing: He was travelling at 28.8 km/hr
The winner David Barley of Gillingham, Kent, UK
