## Piles of paper

Posted by Chris on November 19, 2011 – 7:07 pm

Matt has somewhere between 1000 and 2000 pieces of paper he’s trying to divide into piles of the same size (but not all in one pile or piles of one sheet each). He tries 2, 3, 4, 5, 6, 7, and 8 piles but ends up with one sheet left over each time. How many piles does he need?

November 19th, 2011 at 10:24 pm

1681 sheets of paper = 41^2, so 41 piles of 41 sheets each.

November 20th, 2011 at 12:56 am

Wizard of Oz right….

Funny, I just realised (40, 9, 41) -> Pythagorean triple.

November 20th, 2011 at 1:53 am

Well done, Wiz!

November 20th, 2011 at 6:14 am

Hi Wiz. 41 piles of 41 sheets it is. Are you going to show how you did it?

It’s strange tha Aileme spotted the Pythagorean triple. It has nothing to do with the problem, but I nearly posted a problem that did involve that particular triangle.

November 20th, 2011 at 12:03 pm

Number of sheets is a multiple of 2, 3, 4, 5, 6, 7 and 8, plus 1.

Lowest such number is 840, however number of sheets is between 1000 and 2000, so double this to get 1680, then add 1.

1681 is 41^2.

November 20th, 2011 at 12:49 pm

Hi WIz. Fortunately you didn’t use probability