Anshul and Balendu have 50 cubes of side 1 cm. They decided to create Rubik's cubes (a larger cube) by joining these smaller cubes. The number of Rubik's cubes (all of different sizes) they can make is
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Solution

Since the side of the smaller cube is 1 cm, its volume will be 1 cubic cm.
Now let us consider the number of smaller cubes required to form different sizes of Rubik's cubes as a number (say p)
This p has to be a perfect cube for the formation of Rubik's cubes. Thus, different values of p will result in Rubik's cubes of different sizes.
We know that the cubes of 1,2,3,4,... are 1,8,27,64...
But Anshul and Balendu have only 50 small cubes, so they can make Rubik's cubes of 3 sizes with the help of 1,8 and 27 smaller cubes.
It should be noted that (50-1-8-27) = 14 smaller cubes will be left unused.

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Anshul and Balendu have 50 cubes of side 1 cm. They decided to create Rubik's cubes (a larger cube) by joining these smaller cubes. The number of Rubik's cubes (all of different sizes) they can make is ___

Anshul and Balendu have 50 cubes of side 1 cm. They decided to create Rubik's cubes (a larger cube) by joining these smaller cubes. The number of Rubik's cubes (all of different sizes) they can make is
___