[wolfgang]

Hello....

We have a keyboard at home to hang our 25 keys, the board is devided into 25 squares,the keys are numbered 1 to 25 and they should be in this arrengement :

1 3 5 7 9

19 17 15 13 11

21 23 25 2 4

14 12 10 8 6

16 18 20 22 24

my brother likes mathmatics,one day he changed the arrengement of the keys ,so that,if we add numbers of each five keys in a raw(vertically.horizontally,or diagonally)will always be the same , but he didn`t notice that my two keys are still in their places!.

which keys are mine?

[Guest]

i come up with keys 11 and 4

but with some manipulation of the square, there could easily be multiple answers.

to support my manipulation theory: "There are 275,305,224 magic 5x5 squares. (Scientific American 1/1976)"

Edited October 16, 2010 by Johnathon

[wolfgang]

i come up with keys 11 and 4

but with some manipulation of the square, there could easily be multiple answers.

to support my manipulation theory: "There are 275,305,224 magic 5x5 squares. (Scientific American 1/1976)"

please write your 5*5 square to compare it with the original one.

[Guest]

i come up with keys 11 and 4

but with some manipulation of the square, there could easily be multiple answers.

to support my manipulation theory: "There are 275,305,224 magic 5x5 squares. (Scientific American 1/1976)"

Do those include magic squares with diagonal sums also equal?

[Guest]

One answer - I think there may be several answer. The rows & columns equal "65" and the top left to lower right diagonal also equal "65". I can't work it so the other diagonal works also. When I figure out how to hide my spoiler, I'll post my grid.

Edited October 16, 2010 by Omega Lion

[Guest]

One answer is "6" and "23". My grid is:

10 20 1 13 21

3 16 24 17 5

8 23 7 12 15

19 4 22 14 6

25 2 11 9 18

[Guest]

Think the hardest part of this puzzle is to find a grid in which two and only two keys do not switch positions. Before I found one - see my solution below - I found grids in which no keys stayed the same, one key stayed the same, and even one grid in which three keys stayed the same - see my non-solution below.

Then I found one in which only two did not switch.

The grid I found is:

11 18 25 2 9

23 5 7 14 16

4 6 13 20 22

10 12 19 21 3

17 24 1 8 15

The keys that don't change positions are 9 and 12.

The grid I found is:

15 3 22 16 9

8 21 20 14 2

1 19 13 7 25

24 12 6 5 18

17 10 4 23 11

The keys that don't change positions are 3, 9, and 12.

[Guest]

please write your 5*5 square to compare it with the original one.

Here's a grid in which Johnathon's answer is correct.

16 14 7 5 23

9 2 25 18 11

22 20 13 6 4

15 8 1 24 17

3 21 19 12 10

[Guest]

the grid that Chuck C. gave which match my answer was the same one that i came up with. i apologize for not having responded sooner, I just returned from a deployment to Iraq and have been spending my time with my family.

[bonanova]

Johnathan, Thank you.