Sunday Times Teaser 3333 – Hey, Diddle, Diddle…
by Stephen Hogg
Published Sunday August 09 2026 (link)
Kat and Fidel each held an investment bond. They were over the moon when these matured with different four-figure values (whole numbers of dollars). Unfortunately, a fraction (equivalent to under ten per cent, and the same for both bonds) was deducted as fees, leaving four-figure whole-number nett values. “Fees, what a diddle!” complained Kat. Fidel agreed, adding that in another sense each maturity value was a DIDDLE. Kat was puzzled. Fidel explained that a DIDDLE was a whole number with Different Increasing Digits (left to right) that is DivisibLe Exactly by each digit.
Later, walking his little dog, Fidel stopped at Withespoon’s “Prancing Cow” pub, where he told his friend, Dishran, these things, but no values. Dishran, an accountant, knew the “fees” fraction and calculated the values with certainty.
Give the nett values
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BRG permalink123456789101112131415161718192021222324from itertools import combinationsfrom collections import defaultdictfrom math import gcdf2n = defaultdict(list)# consider four inceasing digits for the gross valuesfor a, b, c, d in combinations(range(1, 10), 4):gross = 1000 * a + 100 * b + 10 * c + d# check that the gross values divide by all their digitsif all(gross % dgt == 0 for dgt in (a, b, c, d)):# consider a fee up to 10% of the gross valuesfor fee in range(1, (gross - 1) // 10 + 1):# collect nett and gross values indexed on the fee as a fractiong = gcd(fee, gross)f2n[fee // g, gross // g] += [(gross - fee, gross)]# look for a fee fraction giving two possible answersfor ff, l_ng in f2n.items():if len(l_ng) == 2:print(f"Nett Values: ${l_ng[0][0]} and ${l_ng[1][0]} [fee: ({ff[0]} / {ff[1]}) "f"Gross Values: ${l_ng[0][1]} and ${l_ng[1][1]}].")
