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Brillig

03-12-2003 12:01 PM

OT - Prime square puzzle

Most of us are familiar with the concept of magic squares: the arrangement of the numbers from 1 to n^2 into a square such that the sum of the numbers on each row and each main diagonal is equal to the same number. E.g., a 3x3 magic square is

Code:



2        9        4

7        5        3

6        1        8

A concept I've been twiddling with lately is that of prime squares: the arrangement of the numbers from 1 to n^2 into a square such that the sum of the numbers on each row and each main diagonal is a prime number.

For n=1 and n=2, it is trivial to prove that a prime square does not exist. (1 is not a prime number). I think that I have a proof that n=3 is not possible as well.

I have, however, constructed a prime square of size 4. Can you?

Bee	03-12-2003 12:42 PM

Code:

7     8    3    16

15    9    6    4

2     5   14    13

10   12   11    1

Anrhydeddu

03-12-2003 12:47 PM

34 is a prime number?

Bee	03-12-2003 12:51 PM

Did I misunderstand? I thought the diagonals had to be a prime number, but the rest was supposed to be a normal magic square.

SplitPersonality1

03-12-2003 01:04 PM

edit: false alarm

cool puzzle Brillig. Have you solved 5x5 yet?

re-edit: got it

Code:

3        7        9        10

5        4        13        15

1        6        8        2

14        12        11        16

Aylmar

03-12-2003 01:06 PM

Response to false alarm. :)

Brillig

03-12-2003 01:07 PM

Sorry if I was unclear, Bee - all the columns and rows are supposed to add up to prime numbers.

Sp1, nope, haven't even started yet :)

Bee	03-12-2003 01:22 PM

ok. If I understand it correctly this time...:D

is this correct?

Code:

1  2  5  11

6  4  7  12

9  8  10  14

13 3  15  16

Vince

03-12-2003 01:25 PM

39 isn't prime...11+7+8+13 on the upper right to lower left diagonal.

Bee	03-12-2003 01:38 PM

Quote:

Originally posted by Vince
39 isn't prime...11+7+8+13 on the upper right to lower left diagonal.

you sure that doesn't add up to 37? ;)

Brillig

03-12-2003 01:40 PM

SP1's looks good to me - it's different from mine, but I expected multiple solutions anyway.

5x5 wasn't that difficult at all, I think these are actually easier the bigger the matrix gets...

Bee	03-12-2003 01:42 PM

I got the same one that SP1 has, but he beat me to it. :(

Anrhydeddu

03-12-2003 01:43 PM

Quote:

Originally posted by Bee
you sure that doesn't add up to 37? ;)

Pretty sure (one of my very favorite movie lines).

SplitPersonality1

03-12-2003 01:43 PM

Quote:

Originally posted by Brillig
SP1's looks good to me - it's different from mine, but I expected multiple solutions anyway.

5x5 wasn't that difficult at all, I think these are actually easier the bigger the matrix gets...

I agree and was about to post the same thing. I found a solution for 5x5 in about four minutes.

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