2

 

 

 

3

 

 

 

 

 

 

 

 

 

 

4

 

 

3

 

 

 

 

 

 

 

 

 

 

 

6

 

 

1

 

 

 

 

 

 

 

9

 

 

6

 

 

 

 

 

 

 

 

 

 

 

8

 

 

2

 

 

 

 

 

 

 

 

 

 

2

 

 

 

7

 

 

 

n = 12 81 81 k = 8 i = 81 d = 0 quasi-magic(15 2)

*......4..2.....3...3..........1....6.........6....9..........2...8.....7..2....../

A quasi-magic puzzle. The rules are as for standard sudoku but with the additional constraint that the rows, columns and diagonals of the nine 3x3 boxes must sum to any of 13, 14, 15, 16 or 17. So you can think of each box as a kind of quasi-magic square of order 3.

[Hints. (i) Symbols 1 and 2 cannot occur on the same row, column or diagonal of a box; nor can 8 and 9. (ii) The box centres must be 3, 4, 5, 6 or 7. (iii) At most one 3 and at most one 7 can occur as a box centre. (iv) If both 3 and 7 are present as box centres, they must occur in the same row or the same column. (v) A 5 never occurs on the edge of a box; always in the centre or in a corner. See my article in M500 215.]

Tony Forbes.