Secret passages
KATHRYN and her school friends have been using a Lorenz-type code to pass covert messages to each other. Each letter is expressed as a five-digit binary number such that A = 1 = 00001, M = 13 = 01101 and so on, but other symbols are represented by 00000 and by 11011 upwards. A fixed letter, say M, is chosen as a “coder”, known only to the sender and receiver. To transmit a letter, say D, it is added to the coder by the “exclusive-NOR” rule 1 + 1 = 1, 1 + 0 = 0, 0 + 1 = 0, 0 + 0 = 1. So, for example, D + M = 00100 + 01101 = 10110 = V. When the sent letter V is added by the recipient to the coder M, the original letter reappears: 10110 + 01101 = 00100.
She has sent her name to her friends as seven letters. KATHRYN and its coded version together consist of 14 different letters, so what was the coded version?
WIN £15 will be awarded to the sender of the first correct answer opened on Wednesday 25 September. The Editor’s decision is final. Please send entries to Enigma 1764, Â鶹´«Ã½, Lacon House, 84 Theobald’s Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).
Answer to 1758 Path-o-logical: the paths are 156 metres long
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The winner Helen Wickins of Studley, Warwickshire, UK
