August 17, 2010

3x3x3 wooden cube



Imagine a 3x3x3 wooden cube.

How many cuts do we need to break it into 27 1x1x1 cubes?

8 comments:

  1. 6 if you keep the cube togheter after every cut.

    If after the first cut you consider each part a seperate one you'll need 26 cuts

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  2. Five cuts.

    Cut off one third of the cube. Lay that piece horizontally on top of the remaining piece, and cut through both.

    You now have four pieces, a 1x1x3, a 1x2x3, and two 1x3x3's. Lay them flat on the table and arrange them to form a 1x3x9 grid. Cut 1/3rd off lengthwise.

    Now set the one 1x1x1 block aside and arrange the rest to form a 2x13 grid, and cut that in half lengthwise.

    Then, spin all blocks 90 degrees and arrange them into a transposed 13x2 grid, making the final lengthwise cut.

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  3. Just 4 cuts

    two cuts laterally and two cuts horozontally keeping it all together and producing 3x3x3 or...27

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  4. This comment has been removed by the author.

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  5. @ occum then you have 9 stris of 1x1x3

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  6. With anything fewer than 6 cuts, how does the center cube (which as a fresh cut for every surface) get cut free?

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  7. Only 4 Cuts required.

    2 on one side and other 2 on it's perpendicular side, keeping cubes together till final cut..

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