Take one 1, two 2s, three 3s, four 4s, five 5s, six 6s, seven 7s, and eight 8s and place them in a 6-by-6 grid, one digit per square, such that each row, column, and major diagonal sums to 34.

Some careful divide and conquer searching yields tons of solutions; these are a few and more can be had with these via some row permutations.

1,7,7,8,6,5

8,5,3,8,7,3

7,5,8,2,6,6

2,7,6,8,6,5

8,6,3,4,5,8

8,4,7,4,4,7

 

2,5,8,8,3,8

5,8,4,4,8,5

6,6,7,7,5,3

6,7,3,6,6,6

8,1,8,2,7,8

7,7,4,7,5,4

 

2,6,6,6,8,6

5,8,6,5,7,3

8,8,7,3,4,4

4,4,3,7,8,8

7,7,7,6,2,5

8,1,5,7,5,8

 

3,6,1,8,8,8

8,5,5,3,5,8

7,8,8,4,3,4

4,2,7,7,7,7

8,6,6,6,6,2

4,7,7,6,5,5

 

3,7,5,5,7,7

7,6,6,5,2,8

8,4,6,4,8,4

6,8,7,7,1,5

2,6,7,5,8,6

8,3,3,8,8,4

 

3,7,7,7,2,8

3,6,6,5,8,6

5,8,8,4,8,1

8,4,4,5,5,8

8,3,7,7,5,4

7,6,2,6,6,7

 

3,7,7,7,3,7

7,5,4,4,7,7

5,8,6,6,8,1

6,6,4,4,6,8

5,2,8,8,8,3

8,6,5,5,2,8

 

5,3,5,8,8,5

4,8,2,6,8,6

8,4,8,1,5,8

3,7,7,7,7,3

7,6,5,6,2,8

7,6,7,6,4,4

Edited on October 31, 2004, 1:33 am

Edited on October 31, 2004, 1:34 am

Posted by owl on 2004-10-31 01:29:33