Fill in each of the boxes with the numbers 1 to 9 so that the three horizontal equations are true.

Each number is used once; no repetition is allowed.

The calculations are done from left to right (i.e., 7-2x3=15, not 1) and may involve only positive numbers (so 5-3-7=-5 is not allowed).

                               _     _     _     _
 _     _     _     _     _    | | - | | x | | = | |
| | x | | x | | = | | + | | + |_| + |_| + | | + |_|
|_| - |_| x |_| = |_| - |_|             - |_|

here is the sequence in order
4 8 1 5 6 9 7 3 6

how i looked into it is that first of all we have to consider that for the longest (center) equation the LHS has to have 2 evens and one odd number.. any other combination will not work.. its a simple question of how evens and odds add up and multiply to leave either even or odd. this can be uniquely determined.

from that point did a brute force.. this lead to what is on the LHS (841) and the rest on the RHS

next looked at the top most equation. with the numbers available the only result that works is 6 and the multiplicand is only 3. the number for subtraction have to leave a difference of 2 (9,7) OR (7,5)..

i dont think this is helping anyone.. i'll just leave it at that :D

cheers!

Posted by zecougar on 2005-09-29 11:18:17