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 鈥渃oder鈥�, known only to the sender and receiver. To transmit a letter, say D, it is added to the coder by the 鈥渆xclusive-NOR鈥� 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 拢15 will be awarded to the sender of the first correct answer opened on Wednesday 25 September. The Editor鈥檚 decision is final. Please send entries to Enigma 1764, 快猫短视频, Lacon House, 84 Theobald鈥檚 Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).
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Answer to 1758 Path-o-logical: the paths are 156 metres long
The winner Helen Wickins of Studley, Warwickshire, UK