14Jan/111

## An interesting problem with sums

Check out this brand new video by James Tanton. In it, he tackles a problem I've personally enjoyed solving; determining which positive integers can be written as a sum of consecutive positive integers. For example, 6 = 1+2+3, 7=3+4, but 8 can't be written as a sum of consecutive integers.

The video tackles this problem in Tanton's landmark style, with dots!

And, as usual, there's an extra credit problem.

Enjoy!

JonathanJanuary 17th, 2011 - 09:34

I solve this with a group of seniors each year.

1. We have already (weeks earlier) figured out how to count the number of a factors a number has.

2. I pose the problem and let them experiment with small numbers.

3. I challenge their conjecture and force them to collect more data.

4. I eventually supply the verification (I have gotten some partial stuff from the kiddies, but so far no home runs)

http://jd2718.wordpress.com/2009/11/14/more-puzzle-extension-expressing-n-as-the-sum-of-consecutive-integers/