S U R F
C A L M
E X P O
T I N Y

Each of the above letters represents a positive integer smaller than 200. In some order they represent an arithmetic sequence. Overall, the grid as presented is a magic square, with each row, each column and each of the two large diagonals adding to the same value.

Also, each of the letters in P-R-I-M-E-S represents a prime number, and in themselves they also form an ascending arithmetic sequence, in the order P-R-I-M-E-S.

What is this magic square?

After building my latin square of numerals 1 through 16 I was not looking for a sequence of primes but rather a sequence of numerals which formed an AP building through the letters of P-R-I-M-E-S.

From there I was looking toward the two sequences formed by ±1 either side of multiples of 6:
 5  11  17  23  29....
1    2   3    4    5   6
 7  13  19  25  31....

Yes there are issues there with the 25, thus my AP constant was not going to be 6.

Anyway, the essence of what I was looking for was to apply a multiplier to the digits of the original latin square; the sequence of odd numbers works fine in the above table for as far as I have shown (but it does fail).

Well, I think that explains what I had in mind.  To arrive at the solution I just did not persevere, but that was my fault because I didn't have the correct base latin configuration in the first place.

Posted by brianjn on 2011-08-06 23:39:31