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September 4th, 2014, 09:09 AM  #1 
Member Joined: Sep 2013 Posts: 93 Thanks: 2  There are 40 numbers.Can you separate them into 2 groups...
so the sum of the numbers in each group is equal? the numbers are: 1⁶+2⁶+...+40⁶ 
September 4th, 2014, 10:24 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
Yes, there are lots of ways of doing this. One is 40^6 + 38^6 + 35^6 + 33^6 + 30^6 + 29^6 + 27^6 + 26^6 + 25^6 + 23^6 + 21^6 + 15^6 + 12^6 + 11^6 + 10^6 + 9^6 
September 4th, 2014, 10:37 AM  #3 
Member Joined: Sep 2013 Posts: 93 Thanks: 2 
but how do you know that your example is correct? 
September 4th, 2014, 07:18 PM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  

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