perplexus.info :: Numbers : Prime Magic Square

Prime Magic Square (Posted on 2011-08-04)


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?

Submitted by Charlie

Rating: 5.0000 (1 votes)

Solution: (Hide)

157 87 37 47 27 57 147 97 127 117 7 77 17 67 137 107

The only six-in-a-row arithmetic sequence of primes under 200 was 7, 37, 67, 97, 127, 157, and the only pattern for a magic square, with a sequence in the order where P, R, I, M, E and S were found, was

16 9 4 5 3 6 15 10 13 12 1 8 2 7 14 11

These combined, via a linear relation, to produce the answer square.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
hint	Charlie	2011-08-10 19:29:40
re(4): Far too less - assumptions right? Well yes...	brianjn	2011-08-06 23:39:31
re(3): Far too less - assumptions right? Well yes...	Ady TZIDON	2011-08-06 16:46:50
re(2): Far too less - assumptions right? Well yes...	brianjn	2011-08-06 07:28:21
re: Far too less - assumptions right?	brianjn	2011-08-06 03:21:12
Far too less -observations and thoughts	brianjn	2011-08-05 06:29:44

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