word problem

[sallyk57]

I don't get how to do this.

Fill in the nine cells of this 3x3 square with the numbers from 1 to 9 so that the sum of the numbers belonging to any given 2x2 square is always the same.

[  1   ][      ][      ]
[      ][      ][  7   ]
[      ][      ][      ]

You can't use the same numbers in the 2x2 square.

 

[stapel]

Since the 2-by-2 sub-squares have to have the same sums, then, looking at the top two sub-squares, and assigning variables as follows:

[  1    ][  a    ][  b    ]
[  c    ][  d    ][  7    ]
[  e    ][  f    ][  g    ]

...we get:

. . . . .1 + a + c + d = a + b + d + 7

. . . . .1 + c = b + 7

. . . . .c = b + 6

[  1    ][  a    ][  b    ]
[ b + 6 ][  d    ][  7    ]
[  e    ][  f    ][  g    ]

Looking at the bottom two sub-squares, we get:

. . . . .(b + 6) + d + e + f = d + 7 + f + g

. . . . .b + d + e + f + 6 = d + f + g + 7

. . . . .b + e + 6 = g + 7

. . . . .b + e = g + 1

. . . . .b + e - 1 = g

[   1    ][   a    ][   b     ]
[ b + 6  ][   d    ][   7     ]
[   e    ][   f    ][b + e - 1]

Now work with other pairings of sub-squares, to obtain further information, and then start doing some guess-n-check to solve the square.

Good luck!

Eliz.