Sunday Times Teaser 2883 – Happy Xmas
by Graham Smithers
Published December 24 2017 (link)
I wrote down three perfect squares. In each square precisely three of its digits were even, the rest being odd. Then I consistently replaced digits by letters, with different letters for different digits. In this way the the three squares became appropriately
HAPPY XMAS TIMES
What number does TIMES represent?
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Brian Gladman permalink123456789101112131415161718192021222324252627282930313233from itertools import product# find squares that can match the shapes of HAPPY, XMAS and TIMESha, xm, ti = {}, {}, {}for i in range(32, 317):# the square, its digits, and the number of digitssq = i * idgts = [int(x) for x in str(sq)]nd, ndd = len(dgts), len(set(dgts))# consider only those with three even digitsif [x & 1 for x in dgts].count(0) == 3:# squares matching HAPPYif nd == 5 and ndd == 4 and dgts[2] == dgts[3]:ha[sq] = dgts# squares matching XMASif nd == ndd == 4:xm[sq] = dgts# squares matching TIMESif nd == ndd == 5:ti[sq] = dgts# consider all combinations of possible squares for HAPPY, XMAS and TIMESfor h, x, t in product(ha.keys(), xm.keys(), ti.keys()):# check that there are ten different and consistent letter valuesH, A, P, p, Y = hd = ha[h]X, M, a, S = xd = xm[x]T, I, m, E, s = td = ti[t]if (a, m, s) == (A, M, S) and len(set((hd + xd + td))) == 10:print('HAPPY XMAS TIMES')print(' '.join(''.join(str(x) for x in w) for w in (hd, xd, td)))
