Math Is Fun Forum

thinkingoutloud

Member

Registered: 2008-09-30

Posts: 1

Summation problem how to solve without guess and check

I have this problem:
I live on a street where the houses are numbered from 1 up consecutively.  The sum of all the house numbers less than mine is the same as the sum of all the house numbers greater than mine.  My house # is in the 30's.  What is the house # and how many houses are on the street?

I can get the answers of 35 and 49 thru doing the sums of all the possiblilies of the house # being 30 to 39.  But is there a formula?  We aren't allowed to use guess and check.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Summation problem how to solve without guess and check

If your house number is H and there are N houses in the street, then

which simplifies to

Since

The only triangular number that is a perfect square in the range 900–1521 is 1225 = 35[sup]2[/sup], with N = 49.

Last edited by JaneFairfax (2008-09-30 05:57:43)