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        riddles >> medium >> Finger Guages: Sum of consecutive integers
        
(Message started by: sigmashot on Jun 24^th, 2008, 11:11am)

Title: Finger Guages: Sum of consecutive integers
Post by sigmashot on Jun 24^th, 2008, 11:11am

This is a question regarding the method of solving the finger guage problem on the "medium" riddles page. I took a look to see if there was another thread about it, but could not find one. Reply with a link to the thread if this is a dupe.

Basically, the problem is to find the sum of consecutive integers that equal 86, given the integers 1 to 24. Solution follows
[hide] 20+21+22+23[/hide]

I had some success mathematically representing the problem, where
x=the first number in the series
n=the number of integers in the series
z=the target sum (in the first case, 86)

The sum of a string of integers is the product of:
the sum of the first and last digits in the series
and:
half of the number of integers in the series.

(x + (x+n-1)) * n/2 = z

Which can be written:
.5n^2 + ((2x-1)/2)n = z

So, I'm trying to find a way to understand the problem better. It has been almost ten years since I took any higher level math, and the tools I have at my disposal (meaning: the operations I can still remember how to perform) are limited to algebra. Are there any problems that run parallel to this one? What I seem to have is an equation with three variables, so I can use brute force to find all positive integer solutions, etc., but I am looking for another way to look at this.

Title: Re: Finger Guages: Sum of consecutive integers
Post by towr on Jun 24^th, 2008, 12:04pm

There's an older thread here (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=display;num=1037994340;start=10#10).
Note that some of the text there is hidden the old-fashioned way, by giving it the color of the background. So just select any suspicious gaps in text to see if anything's written there.

Title: Re: Finger Guages: Sum of consecutive integers
Post by sigmashot on Jun 24^th, 2008, 1:19pm

Thank You.