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