Question

Brown Squirrels can carry 2 acorns at a time. Gray Squirrels can carry 3 acorns at a time. Black Squirrels can carry 5 acorns at a time. Suppose the three squirrels all wanted to store acorns for the winter. Depending on how motivated each squirrel was they would end up with different amounts. For instance, suppose the Brown Squirrel took 4 trips, the Gray Squirrel took 2 trips and the Black Squirrel took 2 trips. The Brown Squirrel would end up with 8 acorns, the Gray Squirrel would have 6 acorns and the Black Squirrel would have 10 . Between them they took every one of the 24 acorns. How Many Ways "Show Them" can the squirrels get all 24 acorns. (One can get all of them, and the others get none

Answer 1

There are five ways in which the squirrels can get all 24 acorns.

Explanation:

The information provided is:

• Brown Squirrels can carry 2 acorns at a time.
• Gray Squirrels can carry 3 acorns at a time.
• Black Squirrels can carry 5 acorns at a time.
• The three squirrels all wanted to store acorns for the winter.
• Between them they took every one of the 24 acorns.

Each squirrel makes at least one trip.

Consider the table for the total number of trips the squirrels make get all 24 acorns:

Brown (2) Gray (3) Black (5) Total no. of acorns

1 4 2 (1 × 2) + (4 × 3) + (2 × 5) = 24

2 5 1 (2 × 2) + (5 × 3) + (1 × 5) = 24

3 1 3 (3 × 2) + (1 × 3) + (3 × 5) = 24

4 2 2 (4 × 2) + (2 × 3) + (2 × 5) = 24

5 3 1 (5 × 2) + (3 × 3) + (1 × 5) = 24

Thus, there are five ways in which the squirrels can get all 24 acorns.