Enigma 1624: French magic numbers
14 December 2011
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From New Scientist #2789, 4th December 2010 [link]
In a magic square the sums of each row, column and major diagonal are equal. There is a remarkable relationship between the two magic squares shown here. Each integer in the one on the left when written as a word in English contains the number of letters indicated by the corresponding integer in the one on the right: “twenty-five” has 10 letters, “eight” has five letters, and so on.
I wondered whether I could create a new magic square on the left such that every integer in it when written as a word in French contains the number of letters indicated by the corresponding integer in the square that we already have on the right. It isn’t possible to do this, but I have created a new square in which seven of the integers fulfil this requirement and the other two are each just one letter short of the number of letters required.
As in the English example, all the integers in my new square are considerably less than 100.
What is my new square?