Braingle: 'Consecutive numbers' Brain Teaser

Consecutive numbers

Math brain teasers require computations to solve.

Puzzle ID:	#14553
Fun:	(2.71)
Difficulty:	(2.72)
Category:	Math
Submitted By:	Gerd

Between 1000 and 2000 you can get each integer as the sum of nonnegative consecutive integers. For example,

147+148+149+150+151+152+153 = 1050

There is only one number that you cannot get.

What is this number?

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Comments

krishnan Sep 01, 2003	Great teaser. Any multiple of an odd number is reachable and that leaves only the powers of two.
pi202 Sep 08, 2003	A really fun teaser, but like a lot of fun teasers, not too difficult if you think about it in the right way.
heyevpos Jan 19, 2004	Thank you, very well done, a great teaching tool.
javaguru Mar 11, 2009	Yes, very cool! I like how that one fell into place with a little thought. Any odd number can be formed by adding two consecutive integers, and any value x * y where x is odd can be formed by centering x consecutive integers on y. That left only even numbers with no odd factors, which are of course the powers of two.

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