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August 13th, 2019, 05:50 AM  #1 
Newbie Joined: Aug 2019 From: India Posts: 3 Thanks: 0  How to do these problems?
1) Given that x = 2a^5 = 3a^2, what is the smallest possible value of x? 2) Suppose 3 distinct numbers are chosen from 1,2,.....,3n with their sum equal to 3n. What is the largest possible product of these numbers? Last edited by skipjack; August 13th, 2019 at 07:53 AM. 
August 13th, 2019, 06:33 AM  #2 
Senior Member Joined: Dec 2015 From: somewhere Posts: 592 Thanks: 87  
August 13th, 2019, 06:44 AM  #3 
Newbie Joined: Aug 2019 From: India Posts: 3 Thanks: 0 
Uh, okay but I mentioned in the second problem that the numbers are distinct; are you sure it's n^3? It would be better if you show me the steps how you got n^3.
Last edited by skipjack; August 13th, 2019 at 07:58 AM. 
August 13th, 2019, 06:50 AM  #4 
Senior Member Joined: Dec 2015 From: somewhere Posts: 592 Thanks: 87 
If they are distinct then the maximum is $\displaystyle (n1)n(n+1)$.

August 13th, 2019, 07:08 AM  #5 
Newbie Joined: Aug 2019 From: India Posts: 3 Thanks: 0 
Do you know how to do the first problem?
Last edited by skipjack; August 13th, 2019 at 08:09 AM. 
August 13th, 2019, 08:02 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
1) 0
