The Spanish translation of “ELEVEN PLUS TWO = TWELVE PLUS ONE” is “ONCE MAS CUATRO = CATORCE MAS UNO”.
- both of these are anagrams, with the same multiset of letters on the left and right sides;
- both are mathematically true (11 + 2 = 12 + 1, and 11 + 4 = 14 + 1).
(Or perhaps TRECE MAS DOS = DOCE MAS TRES, but that’s not as good in Mark Dominus’ sense since it involves less rearrangement of the letters – you can just swap “CE” and “S”)
Etymologically this all makes sense. “Eleven” descends from Old English enleofan, literally “one left”, and “twelve” from Old English twelf, literally “two left”. Spanish “once” is more straightforward – it descends from Latin “undecim”, from “unus” (one) and “decim” (ten); and “catorce” is from Latin “quattuordecim”, from “quattuor” (four) and “decim” (ten). And Latin “unus”, “quattuor” give Spanish “uno”, “cuatro”.
I’d known about the English anagram before. I had thought the Spanish ones were new, but it seems to be an independent rediscovery. I came to this problem through this reddit thread, where the poster Lucpel18 wondered if it was possible to solve a system with for example
and so on. This can be done up to 10. It can’t be done for 12 and the obstruction is precisely the anagram above. In looking through the comments to that Reddit post I found a link to some previous investigations by Lee Sallows, in which he finds the Spanish anagram.
But it’s not possible to assign the letters in English (or any language with a similar numbering system) a value so that the value of all number-word is just the sum of its letters. Why not?
Constructive argument. SEVENTY-SIX and SIXTY-SEVEN have the same letters but do not have the same numerical value. (In German: FUNFUNDVIERZIG and VIERUNDFUNFZIG, that is, “five-and-forty” and “four-and-fifty”.)
Fancy argument. The lengths of the words for numbers only grow logarithmically in the size of the numbers. (This suggests the original multiplicative formulation… but we still have that pesky little obstruction at 67 and 76.)