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        riddles >> easy >> Sum of fourth powers
        
(Message started by: NickH on Mar 5^th, 2004, 12:35pm)

Title: Sum of fourth powers
Post by NickH on Mar 5^th, 2004, 12:35pm

If the sum of three numbers is 6, the sum of their squares is 8, and the sum of their cubes is 5, what is the sum of their fourth powers?

[edit]Changed the numbers from (1,15,3) to (6,8,5) to give a more interesting answer.[/edit]

Title: Re: Sum of fourth powers
Post by Barukh on Mar 7^th, 2004, 1:28am

[smiley=blacksquare.gif][hide]
The answer I've got is 0. I used ideas from the Symmetric Expressions (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1068386062) thread.
[/hide][smiley=blacksquare.gif]

Nice riddle, Nick! Are you sure it belongs to easy section?

Title: Re: Sum of fourth powers
Post by NickH on Mar 7^th, 2004, 5:26am

That's the answer I got.

Based on your comment, I'm not sure whether I used the same method. There is a solution that doesn't require a³ + b³ + c³ and a⁴ + b⁴ + c⁴ to be expressed in terms of elementary symmetric expressions. But you may be right; I probably should have placed this puzzle in the medium section!