Question

Cubes are to be stacked in perfectly square layers that can be 5x5 (25 cubes), 4x4 (16 cubes), 3x3 (9 cubes), 2x2 (4 cubes), and 1x1 (1 cube). Each layer above the bottom one must have fewer cubes in it than the layer below it. If you have 54 cubes, and all of them must be stacked, what is the smallest bottom layer you can possibly have?​

Answer 1

25 cubes

Explanation:

Conditions are:

• Each layer must be a perfect square
• The layers must be smaller starting from the bottom layer
• There are 54 cubes and all of them must be stacked

Then the the option is:

• 5*5 + 4*4 + 3*3 + 2*2 =
• 25 + 16 + 9 + 4 =
• 54

So the smallest bottom layer is 5*5 = 25 cubes and the layers from the bottom are:

• 25, 16, 9, 4 cubes