Intriguing Combinatorics problem

Mathegocart · 2017-02-04 11:23:54

1. How many quintuplets of numbers (a,b,c,d,e) where a,b,c,d and e are either -1,0, or 1 such that a + b^2 + c^3 + d^4 + e^5 = 1? Any quick way to do that? had ~5 mins to do this problem and I don't think I've got all these quintuplets.

Last edited by Mathegocart (2017-02-04 11:24:33)

bobbym · 2017-02-04 12:06:22

Hi;

That is a nice laptop you have there.

Mathegocart · 2017-02-04 12:17:57

nice? quite inelegant but gets the job done.

bobbym · 2017-02-04 12:26:23

I meant your HP-EliteBook-8560p. It has a I7 chip in there and is considered to be a top of the line model. You could blow the doors off my desktop with it.

What did you think of the answer?

Mathegocart · 2017-02-04 15:08:10

What are the specifications of your desktop? I am still currently thinking of the solution(late here), did you use generating functions?

Last edited by Mathegocart (2017-02-04 15:12:49)

bobbym · 2017-02-04 15:21:49

I have a very doggy A8-6410 HP clunker. An i3 can outperform it. I am trying to get an i5 Aspire.

did you use generating functions

First, I programmed it. There is nothing better than a direct count. After that, to make the math types happy I began to look for a math solution to the problem, keep in mind I already had the answer in hand. Working backwards, called in Nevada, "back engineering" is a powerful technique. We work from the answer to a solution. It is much easier to do the math when you only have to fill in the blanks. Once we get the analytical answer and it agrees with the programming we are very, very sure we are right. We invoke probability to say the chance that two different methods came up with the same answer and are both wrong is millions to one against. Those are the kind of odds I like. And yes, my analytical solution is done with a gf.

Mathegocart · 2017-02-04 15:33:44

THat should be enthralling, let me code it tomorrow. ahhahah an A8-6410....

bobbym · 2017-02-04 15:37:10

Yes, I was telling MIF that the older I got the slower my code became. Programming is a game for the young. An A8-6410 is what I deserve...

One more thing about the problem:

Gauss wrote:

I have had my results for a long time: but I do not yet know how I am to arrive at them.

Gauss had discovered the amazing fact that when solving a problem it is often easier to get the answer than to get a method to get the answer. This fact we attempt to exploit everyday.

Mathegocart · 2017-02-05 00:49:18

My code was:

which generated these quintuplets..

thickhead · 2017-02-05 03:00:08

bobbym · 2017-02-05 05:14:30

Hi Mathegocart;

That is very good, how many did you get?

Math Is Fun Forum

#1 2017-02-04 11:23:54

Intriguing Combinatorics problem

#2 2017-02-04 12:06:22

Re: Intriguing Combinatorics problem

#3 2017-02-04 12:17:57

Re: Intriguing Combinatorics problem

#4 2017-02-04 12:26:23

Re: Intriguing Combinatorics problem

#5 2017-02-04 15:08:10

Re: Intriguing Combinatorics problem

#6 2017-02-04 15:21:49

Re: Intriguing Combinatorics problem

#7 2017-02-04 15:33:44

Re: Intriguing Combinatorics problem

#8 2017-02-04 15:37:10

Re: Intriguing Combinatorics problem

#9 2017-02-05 00:49:18

Re: Intriguing Combinatorics problem

#10 2017-02-05 03:00:08

Re: Intriguing Combinatorics problem

#11 2017-02-05 05:14:30

Re: Intriguing Combinatorics problem

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