25 Sep '11 07:59

The fraternity really likes beer in cans. Over the years they've drunk lots and lots of it. Enough that they don't even remember exactly how many cans they've drunk. They know that there are at least one million empty cans in their backyard, and decide to invest in a new backyard when the number hits two million, but they are not quite there yet. In the meanwhile they decide to tidy up and make a neat pyramid of the cans. After some planning they decide that the pyramid can be "aztec style" with a flat top, high or low as long as it is not just a row of cans, and it can't have a jagged top as that would be "uncool". To get the job done, they pledge to drink no more beer until the job is done.. and try and try.. and finally find out that with the number of cans they have, the job is impossible.

How many cans of beer do they have?

(which, without the flavor text, is the same as, show that there is exactly one integer between 1,000,000 and 2,000,000 that can't be expressed as a sum of two or more consequtive natural numbers and find out what it is.

For example,

1,000,000 = 199,998 + 199,999 + 200,000 + 200,001 + 200,002,

1,000,001 = 500,000 + 500,001

1,000,002 = 333,333 + 333,334 + 333,335

etc.

but going all the way to 2 million by brute force is not elegant and could take a while.)

How many cans of beer do they have?

(which, without the flavor text, is the same as, show that there is exactly one integer between 1,000,000 and 2,000,000 that can't be expressed as a sum of two or more consequtive natural numbers and find out what it is.

For example,

1,000,000 = 199,998 + 199,999 + 200,000 + 200,001 + 200,002,

1,000,001 = 500,000 + 500,001

1,000,002 = 333,333 + 333,334 + 333,335

etc.

but going all the way to 2 million by brute force is not elegant and could take a while.)