Sunday Times Teaser 3326 – Interesting Figures
By Andrew Gibbons
Published Sunday June 21 2026
At a cricket match, Tom Leggie bowled fewer than 100 overs (O), of which fewer than 10 were maidens (M), took more than one but fewer than 11 wickets (W), and had an average of runs conceded per over (R/O) that was less than 6. I noticed something interesting about his bowling analysis (O-M-R-W): writing the numbers together with no gaps or overlap, then reading from right to left, they comprised a perfect square followed immediately by a prime containing the same number of digits, and they could also be read (again in their entirety, right to left) as a prime number followed by a perfect square number containing more digits. None of the perfect squares or primes was a single digit, and no zeros were involved.
What was Tom’s bowling analysis (O-M-R-W)?
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BRG permalink12345678910111213141516171819202122232425# produce two and three digit primesprms = {3, 5, 7}prms |= {2} | {n for n in range(11, 100, 2) if all(n % p for p in prms)}prms2d = {n for n in range(11, 100, 2) if all(n % p for p in prms)}prms3d = {n for n in range(101, 1000, 2) if all(n % p for p in prms)}# produce three and four digit squaressqrs3d = {s * s for s in range(10, 32)}sqrs4d = {s * s for s in range(32, 100)}# consider reversed values as three digit squares followed by 3 digit primesfor p in prms3d:for s in sqrs3d:res = (str(s) + str(p))# now consdider them as two digit primes followed by four digit squareif (pp := int(res[:2])) in prms and (ss := int(res[2:])) in sqrs4d:ans = res[::-1]for i, j in ((2, 3), (1, 2)):O, M, R, W = int(ans[:i]), int(ans[i:j]), int(ans[j:5]), int(ans[5])if R < 6 * O and W > 1:print(f"OMRW = {ans} ["f"(O, M, R, W) = ({O}, {M}, {R}, {W})"f" ({s}, {p}), ({pp}, {ss})]")
