While checking his supplies, Cy Corncrib noticed something
interesting about his flour sacks. The sacks were
stacked three to a shelf and numbered one through nine.
On shelves one and three, he had a single sack next to a
pair of sacks, while the middle shelf held three sacks
grouped together. Now, if he multiplied the number on the
single sack (7), by the number on the pair next to it (28),
he got 196, the number on the middle sacks. However, if he
tried multiplying the numbers on the third shelf, (34) and
(5), he got 170.
Cy then came up with this problem: How do you rearrange
the sacks, with as few moves as possible, so that
when you multiply each pair by its single neighbor, you
will come up with a product equal to the number on the
middle shelf?
Answer:
On the first shelf exchange sacks (7) and (2). You now have a single sack (2) and a pair (78). Multiplied together we get 156. We then move single sack (5) and exchange it for sack (9) on the middle shelf. The total number on the middle shelf is now 156. Finally, we move sack (9) from the middle shelf down to shelf three, where it takes the place of sack (4) in the pair. Sack (4) is moved to the right, where it becomes the single sack. Now on shelf three we have (39) times (4), which gives us a product of 156. We did this by moving only five sacks.
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