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Math Help - Carpets

  1. #1
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    Carpets

    Hello all

    A friend of mine asked me if i could solved a question he was ask at an interview.

    you have a 12 by 9 square and two carpets, one 10 by 10 and the other 1 by 8

    you must fill the square with the two carpets but you many only cut one carpet once, however you can cut it anyway you please.
    Last edited by bobak; January 31st 2008 at 07:38 AM.
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  2. #2
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    Quote Originally Posted by bobak View Post
    Hello all

    A friend of mine asked me if i could solved a question he was ask at an interview.

    you have a 12 by 9 square and two carpets, one 10 by 10 and the other 1 by 8

    you must fill the square with the two carpets but you many only cut on, however you can cut it anyway you please.
    I suppose you can use the smaller piece of carpet, and then cut up the bigger one into multiple pieces? That's the only possible way. The areas add up to 108.
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  3. #3
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    seems harsh that they asked a question that cannot be answered in an interview. he was applying for economics as well, not maths.
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  4. #4
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    Quote Originally Posted by colby2152 View Post
    I suppose you can use the smaller piece of carpet, and then cut up the bigger one into multiple pieces? That's the only possible way. The areas add up to 108.
    he says the interviewer insisted it could be done with one cut only.
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  5. #5
    Forum Admin topsquark's Avatar
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    I don't have time to draw it but cut the larger piece with a right angle cut. If you look at it long enough, you'll see how to do it.

    -Dan
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    Quote Originally Posted by topsquark View Post
    I don't have time to draw it but cut the larger piece with a right angle cut. If you look at it long enough, you'll see how to do it.
    While I agree that is an answer, I must disagree that this should have been the expected answer. How many of us would think of a single cut consisting containing two right angles?
    Donít you agree, at least, the problem should have said that the cuts need not be linear?
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Plato View Post
    While I agree that is an answer, I must disagree that this should have been the expected answer. How many of us would think of a single cut consisting containing two right angles?
    Donít you agree, at least, the problem should have said that the cuts need not be linear?
    (chuckles) I agree with you. Apparently the IQ test people don't: I first saw this question in a book with sample IQ tests.

    -Dan
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  8. #8
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    Quote Originally Posted by Plato View Post
    While I agree that is an answer, I must disagree that this should have been the expected answer. How many of us would think of a single cut consisting containing two right angles?
    Don’t you agree, at least, the problem should have said that the cuts need not be linear?
    Well, the whole point is to see who can think outside the square

    I think "you can cut it anyway you please." is a fair tip off .....

    What should the expected answer be .....?

    Personally, to buy thinking time I'd counter with this question to the interview panel:

    You have ten 12 by 9 squares and two carpets, one 10 by 10 and the other 1 by 8.

    You must fill all ten squares with the two carpets, making as many cuts as you want in any way you please.


    Best case scenario I figure I'll be 1-0 up by the end. Worst case I figure it'll be a 0-0 draw.
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  9. #9
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    I did it the way topsquark did (cut the 10x10 into 8x8, 2x9, 2x8, 1x2) but if I was put on the spot and had to think fast, I'd say cut the 10x10 into 100 1x1 squares, then lay down the 1x8 piece and fill in the empty space as needed :P
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    Quote Originally Posted by angel.white View Post
    I did it the way topsquark did (cut the 10x10 into 8x8, 2x9, 2x8, 1x2) but if I was put on the spot and had to think fast, I'd say cut the 10x10 into 100 1x1 squares, then lay down the 1x8 piece and fill in the empty space as needed :P
    At first, I was a bit baffled by the whole "one cut" scenario.
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  11. #11
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    Hello, bobak!

    This is a classic (very old) puzzle,
    . . and its solution is elusive.


    You have a 12 x 9 floor and two carpets, one 10 x 10 and the other 1 x 8.

    You must fill the floor with the two carpets but you may only cut one carpet once.
    However you can cut it anyway you please.
    Code:
          *---------------------------------------*
          |                                       |
          |                               *-------*       *---*
          |    A                          |       |       |   |
          |                       *-------*       |       |   |
          |                       |               |       |   |
          |               *-------*               |       |   |
          |               |                       |       |   |
          |       *-------*                       |       |   |
          |       |                               |       |   |
          |       *-----------------------*       |       | C |
          |                               |       |       |   |
          |                       *-------*       |       |   |
          |                       |               |       |   |
          |               *-------*               |       |   |
          |               |                       |       |   |
          |       *-------*                       |       |   |
          |       |                               |       |   |
          *-------*                          B    |       *---*
          |                                       |
          *---------------------------------------*

    Code:
          *---------------------------------------*-------*
          |                                       |       |
          |                               *-------*       |
          |    A                          |               |
          |                       *-------*               |
          |                       |                       |
          |               *-------*                       |
          |               |                               |
          |       *-------*-----------------------*       |
          |       |               C               |       |
          |       *-----------------------*-------*       |
          |                               |               |
          |                       *-------*               |
          |                       |                       |
          |               *-------*                       |
          |               |                               |
          |       *-------*                          B    |
          |       |                                       |
          *-------*---------------------------------------*
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