Boxed In

By Kyle Cato-Jacobs

Problem

Luis has 24 boxes to fit into a large carton. Each small box is filled, so they can't fit one inside each other. The post office has 3 large carton size for sale. One is 8 inches long by 8 inches high. The second is 15 inches by 12 inches by 10 inches. The third is 20 inches by 14 by 10 inches.

This is the list of the dimensions of all his small boxes:

8*4*3=96 7*4*6=168 5*5*7=175

8*3*3=72 7*3*3=63 5*3*3=45

8*6*3=144 7*6*3=126 5*6*3=90

8*5*3=120 7*5*3=105 5*4*3=60

8*5*3=120 7*5*3=105 5*4*3=60

8*4*3=96 7*5*4=140 5*5*3=75

8*7*4=224 7*5*4=140 5*5*4=100

8*6*4=192 7*4*5=140 5*4*3=80

ans=1,064 ans=951 ans=685

Question: Which is the smallest carton, of the three Luis has to choose from, that might fit all 24 of the smaller boxes?

The third one