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  1. #1
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    Default A carpenter's problem

    A carpenter working with a circular saw, wishes to cut a wooden cube, three inches on a side, into 27 one inch cubes.
    He can do this easily by making 6 cuts through the cube keeping the pieces together in the cube shape.
    Can he reduce the number of necessary cuts by rearranging the pieces after each cut?


    Greg

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  3. #2
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    I dont think it can be done in less than 6 cuts.

    I might not be thinking outside the square, but I think 6 is it.

  4. #3
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    Default

    There is gonna be lots of one inch cube block sets available on ebay tomorrow. Maybe we should link this question to how to make a tumbler to make nice sanded smooth shapes.
    anne-maria.
    T
    ea Lady

    (White with none)
    Follow my little workshop/gallery on facebook. things of clay and wood.

  5. #4
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    Default

    I don't think it can be done at all unless the carpenter uses a laser circular saw with a 0mm kerf.

  6. #5
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    Default Hi Anne-Maria

    Got your rosewood and camphor slices and a couple of jarrah handle pieces in the car, hope to post tomorrow.
    Don't want a 3" square piece of jarrah as well to cut into squares do you?

    This was posed by a mathematician, they have all manner of tools available, including laser cutters and always cut perfectly straight...... in theory only of course, I mean, they never really cut anything..... but if they did.... what is the minimum number of of theoretical cuts?
    Greg

  7. #6
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    Quote Originally Posted by Greg Ward View Post
    Got your rosewood and camphor slices and a couple of jarrah handle pieces in the car, hope to post tomorrow.
    Don't want a 3" square piece of jarrah as well to cut into squares do you?
    Might just use all 's pine off cuts.
    anne-maria.
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    ea Lady

    (White with none)
    Follow my little workshop/gallery on facebook. things of clay and wood.

  8. #7
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    Default

    If we use a laser cutter can I set up mirrors to redirect the laser and do it in 1 cut or should I ship the job offshore and then who cares how many people or cuts it takes. working on it.

  9. #8
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    Default

    No.

    The central cube must be cut on 6 faces. Doesn't matter how the rest of the cuts are made.

    Cheers,
    Joe
    Of course truth is stranger than fiction.
    Fiction has to make sense. - Mark Twain

  10. #9
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    Default Joe! The US Rules!!!!!

    Joe old mate..... you're correct. (although to be fair, others also correctly stated the answer as '6', but your explanation as to why it is '6' is a beautiful example of mathematical logic)
    Conceptually easy to understand but a nice tidy problem.
    Now what about cutting 4" cube into inch blocks?

    Greg

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    9

  12. #11
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    Default

    I reckon 6 cuts:
    Cut 1 makes 2 x 4x2x4. Move end to end (so effectively 8x2x4)
    Cut 2 makes 4 x 4x1x4. Rotate stacks 90deg
    Cut 3 makes 8 x 2x1x4. Move stacks end to end
    Cut 4 makes 16 x 1x1x4. Put stacks on side
    Cut 5 makes 32 x 1x1x2. Move stacks end to end.
    Cut 6 makes 64 x 1x1x1.

  13. #12
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    Hmm interesting...
    Visit my website at www.myFineWoodWork.com

  14. #13
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    Default Interesting? How about this.

    Cubes of 2 x 2 x 2 and 3 x 3 x 3 are unique in the sense that no matter how the pieces are arranged before each cut (provided each piece is cut somewhere) the former will always need 3 cuts and the latter six to slice into unit cubes.

    Greg

  15. #14
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    I was going to tell you how to do it with 5 cuts but I won't now.
    Visit my website at www.myFineWoodWork.com

  16. #15
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    What's this circular saw business? Give me a decent handsaw and I'll do it in 3!

    Veritas® Variable Gang Saw - Lee Valley Tools

    ---

    Visit my blog The Woodwork Geek to see what I've been up to or follow my ramblings on Twitter

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