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Ganesh Ujwal April 28th, 2018 11:19 PM

Please explain the solution of this problem.
Find the least number of cuts required to cut a cube into 125 small identical pieces.


Number of cuts = 4+4+4 = 12.

greg1313 April 28th, 2018 11:47 PM

Hint: $5^3=125$.

Ganesh Ujwal April 29th, 2018 01:10 AM

There are 3 dimensions to a cube. It requires 4 cuts per each dimension to get 5 equal sized pieces for each dimension. Thus it takes 12 cuts to get 125 equal sized pieces.

If 4 parts is 5, then 1 part = 5/4

Then 12 parts is , 12 × 5/4 = 15

But answer is 125, how?

romsek April 29th, 2018 01:26 AM

this all depends on what's allowed for a "cut".

If presented with a cube and asked to dice it into 125 equal sized sub-cubes,

I would make 4 cuts, holding the slices in place, rotate it about the y axis 90 degrees, and repeat, then rotate it about the z axis and repeat. This is 12 total cuts.

If you're given an answer of 125 it seems they don't allow that and that a cut must operate on one solid piece only.

So you would cut the cube into 5 square slices with 4 cuts.

Then for each slice you would cut it into 5 rectangular slices with 4 cuts per square slice.

Then for each rectangular slice you would cut it into 5 square pieces using 4 cuts.

This comes to 4 + 5(4) + 25(4) = 124

I don't know where the last cut comes from. I think the answer is 124.

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