Sunday Times Teaser 3337 – Hidden PINs
by Andrew Skidmore
Published Sunday September 06 2026
Richard has opened a bank account. The bank has issued him with a telephone PIN and a debit card PIN; both are four-figure numbers. The telephone PIN is a perfect square; its square root can be obtained from the card PIN if the first two digits are deleted from the card PIN. The card PIN is composed of four different digits in decreasing order; none of these digits occur in the telephone PIN.
If I told you whether the telephone PIN has a repeat digit you would be able to find both PINs.
What is the debit card PIN?
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BRG permalink1234567891011121314from itertools import combinations# consider the four digits for the card PIN (in decreasing order)for cp4 in combinations(range(9, -1, -1), 4):# compute the card and telephone PINscp = int(''.join(str(d) for d in cp4))tp = (cp % 100) ** 2# the two PINs do not share any digitsif tp >= 1000 and not set(cp4).intersection(int(d) for d in str(tp)):# the telephone PIN has a repeated digitif len(set(str(tp))) < 4:print(f"Card PIN = {cp} (Telephone PIN = {tp}).")
