[Prof. Templeton]

This is another old one.

You have nine sacks that are numbered from 1 to 9 arranged in 5 bundles in a row like this...

#7 - #2,#8 - #1,#9,#6 - #3,#4 - #5

So there is one sack, then two sacks together, then three sacks together, then two, then one again. Now we can see that the first single sack (7) when multiplied by the pair next to it (28) equals the three sacks in the center (196). The pair to the right (34) when multiplied by its neighbor (5) does not equal the three in the center (196). Your task is to rearrange the sacks so that when multipling from the left or right the correct product is the number in the middle. There are a few solutions that will satisfy this, but your job is to do it in the fewest moves.

[Guest]

#2 - #7,#8 - #1,#5,#6 - #3,#9 - #4

[Prof. Templeton]

#2 - #7,#8 - #1,#5,#6 - #3,#9 - #4

Looks good. So how many moves does this take?

[bonanova]

Looks good. So how many moves does this take?

Three.

1. Sack 7 to right of sack 2
   
2. Sack 9 to right of sack 3
   
3. Sack 5 to right of sack 1
   

If you need the spacings restored, that will take some more moving.

But you haven't defined a move, exactly?

[Prof. Templeton]

Three.

1. Sack 7 to right of sack 2
   
2. Sack 9 to right of sack 3
   
3. Sack 5 to right of sack 1
   

If you need the spacings restored, that will take some more moving.

But you haven't defined a move, exactly?

I was hoping to keep the grouping the same so it would look more like a valid equation and not a run-on sentence. Either way the line-up given above is the correct answer. In order to retain the groupings you need

5 moves.

There are three other ways to solve but would require more moves.