1. Place the numbers 1 thru 9 in a 3x3 grid such that every adjacent pair (excluding diagonals) has a different sum.
2. Your first solution will not use three possible sums. Repeat #1, using these sums.
3. What is the largest possible difference between two adjacent numbers in the grid? Can you find solutions with this difference to satisfy #1 and #2 above?
Source: Original.
Solution: An answer to number 3, with the largest difference of 8 (between 1 and 9) can solve 1 and 2:
 Solution 1:```1 9 7 2 4 8 3 5 6``` Solution 2:```9 1 3 8 6 2 7 5 4```
The first answer doesn't use sums 4, 7, or 17. The second answer (which is simply the complement of the first - subtract each number from 10) doesn't use sums 3, 13, or 16.

Carlos Rivera sent this answer to problem 3 (the unused sums are 4, 6, and 16). Its complement is also shown (unused sums: 6, 14, 16):
 Original:```2 1 6 3 9 8 5 4 7``` Complement:```8 9 4 7 1 2 5 6 7```
Putting the 1 in either the corner or the center, with the 9 adjacent, leads to surprisingly few solutions. Can someone find them all? (Put the 9 in the top center position for comparative purposes if you do this.)

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