2017 AMC 10B Problem 6

What is the largest number of solid

2

-in

\times

2

-in

\times

1

-in blocks that can fit in a

3

-in

\times

2

-in

\times

3

-in box?

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Solution

The volume of the large solid object is

3\cdot 3\cdot 2 = 18

and volume of the smaller object is

2\cdot 2\cdot 1=4.

This means we can fit at most

4

of the small objects. We can make this happen by putting

3

of the small objects in a

3 \times 2 \times 2

rectangular prism, and then we have a

3 \times 2 \times 1

space left where we can place one small object. Thus, the correct answer is B .