Sunday Times Teaser 2863 – Little Time
by Graham Smithers
Published August 6 2017 (link)
Do you have a little time to try this Teaser? I have taken a four-figure number and a six-figure number and I have consistently replaced digits by letters to give the words LITTLE and TIME.
If you take the digits of TIME and write down all the four-figure numbers which use exactly those digits in some order and then add up all those numbers, then your total will be LITTLE.
What number is TIME?
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Brian Gladman permalink12345678910111213141516171819202122from itertools import permutationsfrom functools import reduce# permute digits for the letters in LITTLEfor E, I, L, T in permutations(range(10), 4):# compute the numeric value of LITTLElittle = reduce(lambda x, y : 10 * x + y, (L, I, T, T, L, E))# since in all the permutations of four digits each digit occurs# in each position six times, LITTLE must be a multiple of 6666q, r = divmod(little, 6666)if not r:# compute M from T, I, M and the now known sum of T, I, M and EM = q - (T + I + E)# check that M is a valid digit different from E, I, L and Tif 0 <= M < 10 and M not in (E, I, L, T):time = reduce(lambda x, y : 10 * x + y, (T, I, M, E))print(f'TIME = {time} (LITTLE = {little}).')
