Fill a 5 X 5 grid quiz - Help please

Archived from groups: rec.games.trivia (More info?)

Hi,

i ve got a fill grid quiz that i cant figure out. Any help
given is very much appreciated.


Using all the numbers 1-25 fill in the grid below so that all rows,
columns and diagonals add up to 65.

Number 1 must be in the middle of the grid ( Row 3, Column 3 is 1)


Note: Numbers you can use: 1,2,3,4,5,6,7 ..... 23,24,25

Archived from groups: rec.games.trivia (More info?)

"Top Spin" <ToppSpin@hotmail.com> wrote in message
news:k0dmi0do3lenp6k2lf49a44jnlceb23c18@4ax.com...
> On 22 Aug 2004 20:27:03 -0700, monthly2004@hotmail.com (Robert) wrote:
>
> >Hi,
> >
> >i ve got a fill grid quiz that i cant figure out. Any help
> >given is very much appreciated.
> >
> >
> >Using all the numbers 1-25 fill in the grid below so that all rows,
> >columns and diagonals add up to 65.
> >
> >Number 1 must be in the middle of the grid ( Row 3, Column 3 is 1)
> >
> >
> >Note: Numbers you can use: 1,2,3,4,5,6,7 ..... 23,24,25
>
> This is a very old puzzle. They used to put it in newspapers and
> magazines way back in te 40s and 50s -- maybe before that, but I
> wasn't around then.
>
> There is a simple solution for any NxN grid where N is an odd number
> (1x1, 3x3, 5x5). You simply extend the grid by adding "flaps" on all
> four sides.
>
> I'll do the 5x5 for you. Start with your 5x5 grid. I'm using the
> number "0" to represent a square of the grid:
>
> 00000
> 00000
> 00000
> 00000
> 00000
>
> Now add a triangular flap on each side. I'm using the equal sign (=)
> to represent a blank space:
>
> ====0====
> ===000===
> ==00000==
> =0000000=
> 000000000
> =0000000=
> ==00000==
> ===000===
> ====0====
>
> Now you just start at any of the points and fill in the numbers
> diagonally. The tradiaional method is to start at the left point and
> go diagonally upward. I had to expand the grid to 3 spaces/cell to
> make it readable and align:
>
> =============05============
> ==========04====10=========
> =======03====09====15======
> ====02====08====14====20===
> =01====07====13====19====25
> ====06====12====18====24===
> =======11====17====23======
> ==========16====22=========
> =============21============
>
> The main diagonal of the original grid should now have the middle 5
> numbers, 11,12,13,14,15. You now just take each flap and slide it
> across the grid until it fits in the unfilled spaces:
>
> =03=16=09=22=15
> =20=08=21=14=02
> =07=25=13=01=19
> =24=12=05=18=06
> =11=04=17=10=23
>
> All rows, columns and the diagonals sum to 65.
>
> --
> For email, use Usenet-20031220 at spamex.com

read the question

quote

Number 1 must be in the middle of the grid ( Row 3, Column 3 is 1)

unquote

23 4 7 11 20
6 15 18 24 2
19 22 1 10 13
5 8 14 17 21
12 16 25 3 9


this should fit the bill.

the method that topsin should always give a magic square - but will not
allow you to specify middle square as one.

i do not know a method that will allow a middle square to be specified. but
you can always narrow down the potential possibilities by simple maths. 5
columns and 5 rows and 2 diagonals is 12 time 65 is 780 which must be
equivalent to 4 times the middle square (in this case one) plus 3 times any
square on the diagonals plus two times each of the squares not on the
diagonals.

regards

matthew