Sunday Times Teaser 3276 – First and Last Multiple
by Howard Williams
Published Sunday July 06 2025 (link)
Johann enjoys playing with numbers and making up numerical challenges for his elder brother Jacob. He has worked out a new challenge, which involves Jacob trying to find the whole-number square root of a six-digit number. He explained that the sum of its individual digits is exactly five times the sum of its first and last digits. To make it easier, he tells him that no number is repeated in the six digits, there are no zeros, and the last three digits are in descending numerical order.
What is the square root of the six digit number?
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BRG permalink12345678# check possible square root valuesfor r in range(317, 1000):ds = tuple(int(x) for x in str(r * r))if (not 0 in ds and sum(ds) == 5 * (ds[0] + ds[-1])and len(set(ds)) == 6 and ds[3] > ds[4] > ds[5]):print(f"The root is {r} [{''.join('\u221a(' + str(r * r) +')')}].")
