Question

Abigail is using blocks to build a tower. The blocks are 3 inches, 4 inches, and 8 inches tall. She has stack 3 blocks. How many different heights are possible for the tower?

Answer 1

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Answer:

10

Explanation:

Possible tower heights using 3 blocks are ...

{9, 10, 11, 12, 14, 15, 16, 19, 20, 24}

There are 10 different heights possible.

_____

Each block can be used 1, 2, or 3 times.

Using a 3 in block as the smallest, we have ...

3+3+3 = 9

3+3+4 = 10

3+3+8 = 14

3+4+4 = 11

3+4+8 = 15

3+8+8 = 19

Using a 4-in block as the smallest, we have ...

4+4+4 =12

4+4+8 = 16

4+8+8 = 20

And ...

8+8+8 = 24