What is the maximum number of rectangular blocks, each with dimensions 12 centimeters by 6 centimeters by 4 centimeters, that will fi t inside rectangular Box X ? The inside dimensions of Box X are 60 centimeters by 30 centimeters by 20 centimeters.
|show 1 more comment|
Draw a picture!
Pick a bottom for the box, and try to fill that bottom completely. If you can stack the pattern that fills the bottom completely a number of times that evenly divides the height, you've completely filled the box. If you have no leftover space, you've certainly used the maximum number of blocks.
Hint: You can fill the box in your problem completely.
Here's a similar example. Say I had $1 \times 2 \times 3$ blocks and a $2 \times 4 \times 6$ box. Then along the bottom ($2\times4$) of the box, I need to decide if I want the bottom of the blocks to be $1\times2$, $2\times3$, or $1\times3$. I can fill the bottom of the box with 4 blocks by choosing $1\times2$ bottoms. By stacking this pattern twice, I've filled the entire box!