Adjacent Sums
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Place the numbers 1 thru 9 in a 3x3 grid such that every adjacent pair
(excluding diagonals) has a different sum.
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Your first solution will not use three possible sums. Repeat #1, using
these sums.
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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.)
Mail to Ken