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April 29th, 2018, 05:14 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 342 Thanks: 1  Please somebody explain the solution
Find the least number of cuts required to cut a cube into 240 small identical pieces. Solution: 240 = find nearest cube value 216 = 6 is near cube Divide 240 with 6 = 40. 40 mean 8 x 5. Number of cuts = 5 + 7 + 4 = 16. 
April 29th, 2018, 10:34 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,444 Thanks: 946 
Buy a cheese cube and start cutting it...

April 29th, 2018, 10:56 AM  #3 
Senior Member Joined: May 2016 From: USA Posts: 1,184 Thanks: 488 
You have been given the solution. What is it that you do not understand?

April 29th, 2018, 06:28 PM  #4 
Senior Member Joined: Aug 2014 From: India Posts: 342 Thanks: 1 
Why we must take 5 x 8 ? Can I take 2 x 20 or 4 x 10 also?
Last edited by skipjack; April 30th, 2018 at 07:34 AM. 
April 30th, 2018, 07:13 AM  #5 
Senior Member Joined: May 2016 From: USA Posts: 1,184 Thanks: 488  The lengths given are 6 X 8 X 5. That is the relevance of 5 and 8 (and 6, of course, is also relevant). The lengths 10 and 2 and 4 and 20 are not relevant because they are not lengths of the given cube I truly suggest that you follow Denis's advice and ask your mother to show you how to dice an onion. Last edited by skipjack; April 30th, 2018 at 07:33 AM. 
April 30th, 2018, 07:57 AM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,502 Thanks: 2511 Math Focus: Mainly analysis and algebra  
April 30th, 2018, 07:59 AM  #7 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,502 Thanks: 2511 Math Focus: Mainly analysis and algebra  
April 30th, 2018, 09:13 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 19,865 Thanks: 1833  
May 2nd, 2018, 03:28 AM  #9 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
Of all of the integer factorings of 40, 5 and 8 are closest together. That was also the point of finding the nearest cube to 240. Of all possible ways to factor 240 into three factors, 5, 6, and 8 are closest together.


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