With the exception of the letter L, each letter of the alphabet is to be placed once in the grid at the lower left. Consecutive letters of the alphabet cannot be adjacent in any direction, not even diagonally. The X has been added to get you started.

Every blue/yellow cell in the upper left grid shows the sum of the numerical values of the letters which appear in the adjoining yellow/blue cells of the lower left grid. So, for example, the 40 in cell 5E, might mean that Z and N (or Y and O) are to be placed in cells 5D and 4E.

The letters and numbers written outside the 5x5 grids serve no purpose, except to identify cells.

1. We can create the following 4 equations since different sums have overlapping cells:

E3-C1=7;  E3-C5=2;  C5-A3=3;  A3-C1=2.

Convert those equations to:

C1+2=A3;  C1+5=C5;  C1+7=E3.

2. Since 16 is the highest number available, C1 can't be higher than 9 (C1+7=E3).

3. C1 can't be 1 because that would make A3=3.

4. C1 can't be 2 or 4 because of the proximity to 3 in B2.

5. C1 can't be 5 because that would make E3=12.

6. C1 can't be 6 or 7 because that would make C5=11 or 12 respectively.

7. C1 can't be 9 because that would make A3=11.

8. C1 must equal 8.

9. So A3=10, C5=13, and E3=15.

10. A1 + B2 = 8, so A1 and B2 must be {1,7} or {2,6}.

11. Neither A1 nor B2 can be 2 (proximity to 3).

12. B2 can't be 7 (proximity to 8).

13. B2 must equal 1.  Thus, A1 must equal 7.

14. D4 + E5 = 16.  The only remaining numbers that sum to 16 are 2 and 14.  D4 can't be 14, so it must be 2.  E5 must equal 14.

15. D2 + E1 = 10.  The only remaining numbers that sum to 10 are 4 and 6.

16. D2 + C3 = 13.  The only remaining numbers that sum to 13 are 4 and 9.

17. Therefore, D2=4, E1=6, and C3=9.

18. It then follows that B4=5 and A5=16.

This provides the same answer as Charlie.

Edited on May 3, 2007, 9:25 pm

Posted by Guest on 2007-05-03 21:23:16