Sunday Times Teaser 2753 – No Question About It!
by H Bradley & C Higgins
Published: 28 June 2015 (link)
“Sign Works” make rectangular signs of all sizes. Pat ordered a sign for the pub with the following instructions. “The length must be twice the width. Furthermore, the dimensions should be such that if you take its length (in centimetres), square the sum of its digits and take away the length itself, then you get the width. On the other hand, if you take its width (in centimetres), square the sum of its digits and take away the width itself, then you get the length.” This was enough information for the sign-maker to calculate the dimensions of the sign.
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Brian Gladman permalink123456for w in range(1, 100):if (3 * w == sum(int(x) for x in str(w)) ** 2== sum(int(x) for x in str(2 * w)) ** 2):print('width = {}, length = {}.'.format(w, 2 * w))
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geoffrounce permalink12345678for width in range(1, 100):length, semiperim = 2 * width, 3 * widthd1, d2 = width // 10, width % 10d3, d4 = length // 10, length % 10if (d1 + d2) ** 2 == semiperim == (d3 + d4) ** 2:print('Length = {} cm, Width = {} cm'.format (length, width))
