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
2 answers Last reply
More about fill grid quiz please
  1. Archived from groups: rec.games.trivia (More info?)

    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
  2. 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
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