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April 28th, 2018, 11:19 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  Please explain the solution of this problem.
Find the least number of cuts required to cut a cube into 125 small identical pieces. Solution: Number of cuts = 4+4+4 = 12. 
April 28th, 2018, 11:47 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond 
Hint: $5^3=125$.

April 29th, 2018, 01:10 AM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1 
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? 
April 29th, 2018, 01:26 AM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,404 Thanks: 1306 
this all depends on what's allowed for a "cut". If presented with a cube and asked to dice it into 125 equal sized subcubes, 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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