OT - Prime square puzzle

Brillig · 03-12-2003, 12:01 PM

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...

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.

03-12-2003, 12:42 PM	#2
Bee Pro Starter Join Date: Oct 2000 Location: Fairfax, VA	Code: 7 8 3 16 15 9 6 4 2 5 14 13 10 12 11 1 Last edited by Bee : 03-12-2003 at 12:47 PM.

03-12-2003, 01:04 PM	#5
SplitPersonality1 College Benchwarmer Join Date: Jun 2001 Location: Grafton, WI	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 Last edited by SplitPersonality1 : 03-12-2003 at 01:31 PM.

03-12-2003, 01:06 PM	#6
Aylmar High School Varsity Join Date: Mar 2002 Location: Los Angeles	Response to false alarm. __________________ "At its best, football is still football, an amalgam of thought and violence, chess with broken bones and shredded ligaments." -- Dave Kindred Last edited by Aylmar : 03-12-2003 at 01:07 PM.

03-12-2003, 01:22 PM	#8
Bee Pro Starter Join Date: Oct 2000 Location: Fairfax, VA	ok. If I understand it correctly this time... is this correct? Code: 1 2 5 11 6 4 7 12 9 8 10 14 13 3 15 16 Last edited by Bee : 03-12-2003 at 01:22 PM.

03-12-2003, 01:25 PM	#9
Vince Pro Starter Join Date: Aug 2001 Location: Willow Glen, CA	39 isn't prime...11+7+8+13 on the upper right to lower left diagonal. __________________ Every time a Dodger scores a run, an angel has its wings ripped off by a demon, and is forced to tearfully beg the demon to cauterize the wounds.The demon will refuse, and the sobbing angel will lie in a puddle of angel blood and feathers for eternity, wondering why the Dodgers are allowed to score runs.That’s not me talking: that’s science. McCoveyChronicles.com.

03-12-2003, 12:47 PM	#3
Anrhydeddu Resident Curmudgeon Join Date: Oct 2002	34 is a prime number?

03-12-2003, 12:51 PM	#4
Bee Pro Starter Join Date: Oct 2000 Location: Fairfax, VA	Did I misunderstand? I thought the diagonals had to be a prime number, but the rest was supposed to be a normal magic square.

03-12-2003, 01:07 PM	#7
Brillig College Prospect Join Date: Oct 2000 Location: Mountain View, California	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

03-12-2003, 01:40 PM	#11
Brillig College Prospect Join Date: Oct 2000 Location: Mountain View, California	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...

03-12-2003, 01:42 PM	#12
Bee Pro Starter Join Date: Oct 2000 Location: Fairfax, VA	I got the same one that SP1 has, but he beat me to it.

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