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Slice the Donut

  1. Jul 21, 2004 #1
    One Doughnut
    Two Cuts

    what's the maximum number of pieces you can get?

    and no crazy stuff like "i bought 12 doughnuts and i cut them with my baseball bat and some had like 35 pieces!!!"

    PS> the pieces don't have to be the same size, and the doughnut is standard ring (toroid) shaped
     
  2. jcsd
  3. Jul 21, 2004 #2

    Math Is Hard

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    any folding allowed?
     
  4. Jul 21, 2004 #3

    Gokul43201

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    And the cuts need to be planar !
     
  5. Jul 21, 2004 #4
    yes planar cuts please

    don't fold the doughnuts! Bad!
     
  6. Jul 21, 2004 #5

    Gokul43201

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    I get 5 , but surely you can make more, right ?

    EDIT : I rearranged before the second cut.

    PS : Hey, I just green lights appear - neat ! Have they always been around ?





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    Last edited: Jul 21, 2004
  7. Jul 21, 2004 #6
    yeh the lights have always been around.

    explain how you got 5 :D

    wish we had a chalkboard. this type of problem is way more fun with something to draw with
     
  8. Jul 21, 2004 #7

    Gokul43201

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    I drew a picture, but my posting rules say that I may not post attachments...WHY ???
     
  9. Jul 21, 2004 #8

    Math Is Hard

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    I got 6. (and ruined a perfectly good bagel).
    The only way I can explain it is if you look at it edge on, I made an X shaped cut.(which also you would see if you turned it around and look at the other side).
     
  10. Jul 21, 2004 #9

    Gokul43201

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    Looks like the winner !!
     
  11. Jul 21, 2004 #10

    Math Is Hard

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    wheee! what do I win? A donut?
    actually, I'm expecting Terrabyte to write back any second and post a solution showing how 24 pieces can be made from two strategic cuts... :biggrin:
     
  12. Jul 22, 2004 #11
    You can also get 6 pieces by rearranging between the cuts. Put the donut flat on the table and make a downwards cut through the center.

    That gives you two C shapes. Align one on top of the other and make another downward cut, slicing off the 'prongs'. So you get 4 prong pieces plus 2 attenuated C shapes.

    Obligatory follow-up question. Same rules, but three cuts allowed now. :smile:
     
  13. Jul 22, 2004 #12

    Njorl

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    Damn, I was using a jelly donut! Not only did it restrict how many pieces I could get, it made a real mess.

    Njorl
     
  14. Jul 22, 2004 #13

    NateTG

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    This seems pretty easy considering the other posts: 18.
     
  15. Jul 22, 2004 #14
    yeh, i came up with 6 pieces using the "X" cut as well, but the "C" cuts was a nice surprise. Good thinking!

    Next Question: you have one Labrador Retriever... :surprise:
     
  16. Sep 15, 2004 #15
    If no rearranging is allowed between cuts, I think the maximum with three cuts is thirteen pieces.
     
  17. Sep 16, 2004 #16
    How did you get 13? I get 8...
     
  18. Sep 17, 2004 #17

    NateTG

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    I'll show you how to get more than 8:

    Three cuts:
    If you view the donut from the side, the first cut is from the top left of the hole to the bottom right.
    The second cut is from the top right to the bottom left.
    There should now be six pileces - four wedges, and two C's.

    The third cut is vertical, and slightly off center. It cuts through one of the C's twice, and through all for wedges. That makes for 12 pieces. (Sorry no illustrations.) It's not that hard to get to 13 from there.
     
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