# French Alphamagic Squares

From reader Ian Duff: An alphamagic square is a magic square that remains magic when the number in each of its cells is replaced by the letter count of that number’s written name. For example, each row, column, and long diagonal in this square yields the same sum:

``` 5  22  18
28  15   2
12   8  25
```

… and that remains true if we replace 5 with 4 (because FIVE has 4 letters), 22 (TWENTY-TWO) with 9, and so on:

```4   9   8
11  7   3
6   5  10
```

That example is the only 3×3 English alphamagic square in which each cell contains a distinct positive integer less than 100. There are no such truly sub-100 alphamagic squares in French, but there are two if we permit the derived squares to contain repeated numbers:

```39  57  18          10  13   7
17  38  59    ->     7  10  13
58  19  37          13   7  10

75  87  57          14  15  13
55  73  91    ->    13  14  15
89  59  71          15  13  14
```

39 is TRENTE-NEUF, which has 10 letters, and so on.

(Thanks, Ian.)