Enigma 1598: Twin squares
11 January 2012
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From New Scientist #2763, 5th June 2010 [link]
For my birthday, my wife Astrid made identical sets of cards. On each card a letter of ASTRIDOWEN is displayed, together with its own characteristic digit chosen from 0-9. On the day, Astrid’s sister Enid sat on our three-seater settee with our twins Eden and Toni and, when they held up the cards with their respective names, the numbers on the cards satisfied:
ENID2 = EDENTONI (read off as an eight-digit number).
When my brother Ewan arrived, we found that:
EWAN2 = TONIEDEN.
The twins then made up a set of cards for their “taid” (Welsh grandfather).
What eight-digit number corresponds to TAIDOWEN?