10775 - Mystical Matrix

Dmytro Korzhyk · Post by **Dmytro Korzhyk** » Wed Dec 08, 2004 10:59 pm

Can anyone explain an idea how to solve this problem?

.. · Post by .. » Thu Dec 09, 2004 10:31 am

You better first find out the answer of N=9,
it can help you to observe some property of the required matrix.

bugzpodder · Post by **bugzpodder** » Sat Dec 11, 2004 3:12 am

my solution is based on that of the magic square... but i am curious as to the others' approaches since there are possibly literally zillions of ways to generates these monsters

Cho · Post by **Cho** » Sat Dec 11, 2004 12:21 pm

.. wrote:You better first find out the answer of N=9,
it can help you to observe some property of the required matrix.

I know the anwer for N=9 but it doesn't help me to solve the problem.
Base on the solution for N=3, I can generate all solutions for N=3^n. I tried this method but got WA.

.. · Post by .. » Sat Dec 11, 2004 2:24 pm

Code: Select all

N = 3
1 6 8
5 7 3
9 2 4

N = 9
 1  2  3| 16 17 18| 22 23 24
--------+---------+---------
14 15 13| 20 21 19|  8  9  7
--------+---------+---------
27 25 26|  6  4  5| 12 10 11

I find that, if I divide the matrix of N = 9 into 9 parts of 3 numbers, each part will corresponsde to a number in the matrix of N = 3. Because the maximum number in each part is a multiple of the corresponding number in N = 3.

The remaining problem is how to allocate the numbers in each part.
I stop at here to keep the interest of solving this problem

Dmytro Korzhyk · Post by **Dmytro Korzhyk** » Sat Dec 11, 2004 5:15 pm

Thank you, I've got AC

Eduard · Post by **Eduard** » Sat Dec 11, 2004 8:30 pm

Please someone give me answer for N=12.
Thanks

.. · Post by .. » Sat Dec 11, 2004 8:54 pm

Eduard wrote:Please someone give me answer for N=12.
Thanks

.............You better first calculate the column sum for N = 12

Eduard · Post by **Eduard** » Sun Dec 12, 2004 8:23 am

Yes,I see it.

Cho · Post by **Cho** » Sat Dec 25, 2004 8:23 pm

Is it solvable for some N where N is not 3^n?
Is it solvable for N=15?

.. · Post by .. » Sat Dec 25, 2004 9:01 pm

Cho wrote:Is it solvable for some N where N is not 3^n?

Yes

Cho wrote:Is it solvable for N=15?

Yes

You can try to construct the matrix for N = 15 with my hint given before.

Cho · Post by **Cho** » Sat Dec 25, 2004 9:54 pm

I got it, thx a lot.

sjn · Post by **sjn** » Fri Mar 02, 2007 7:32 am

what about N=5?