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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?


This post is under “MathsChallenge” and has 6 respond so far.
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6 Responds so far- Add one»

  1. 1. Wizard of Oz Said:

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

  2. 2. Aileme Said:

    Wizard of Oz right….
    Funny, I just realised (40, 9, 41) -> Pythagorean triple.

  3. 3. slavy Said:

    Well done, Wiz!

  4. 4. Chris Said:

    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.

  5. 5. Wizard of Oz Said:

    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.

  6. 6. Chris Said:

    Hi WIz. Fortunately you didn’t use probability ;)

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