P6 Math: Boxed

 

Solution:

Six of Box A can fit exactly into Box C. We can imagine arrange one by one of Box A into Box C. In the same standing orientation without rotating/flipping it, it can fit six of Box A

--> Box C measurement will be length = breadth = 30 cm and height will be 25 cm.

Now to fit as many Box B as possible into Box C, we can try guessing it first by classical way Volume of Box C divides by Volume of Box B

30 * 30 * 25 

20 * 10 * 8

which is about 14 something. So the answer cannot be bigger than 14.

We do simple spatial analysis to check possible orientation of Box B inside Box C.

Total number of Box B with this arrangement  = 9 + 3 + 1 = 13