Using 3 slices, how many pieces can a donut be cut into? @MIT 6.00 Intro Co…

Question

Using 3 slices, how many pieces can a donut be cut into?      @MIT 6.00 Intro Co…

anonymous · Answer

I mean, what is the maximum number of pieces a donut can be cut into.

anonymous · Answer

6

anonymous · Answer

nope.

anonymous · Answer

8. Cut the doughnut laterally, then into quarters. That should create 8 pieces.

anonymous · Answer

assuming that the pieces aren't rearranged after each slice, 6

anonymous · Answer

yeah I forgot to say you can rearrange the pieces :-D

osanseviero · Answer

Can it be a curved line?

anonymous · Answer

yeah I forgot to say you can rearrange the pieces :-D

anonymous · Answer

no curved cuts :-D

anonymous · Answer

then 8

anonymous · Answer

infinite no. of pieces?

anonymous · Answer

you can cut it into 12 pieces using 3 slices.

anonymous · Answer

We went over this a couple weeks ago. It's 13. No rearrangement necessary. But I don't know how to do it. http://mathworld.wolfram.com/TorusCutting.html

anonymous · Answer

If you can rearrange the donut each time you cut, the first slice would be in half.  Stack the halves and cut again in quarters, you have 4 pieces.  Stack all 4 pieces and cut again, you get 8 pieces.  

Unless you can somehow fold the donut into quadrants (without breaking it) on the first cut, I can't see how you could get more pieces when done.

anonymous · Answer

13?!? I can't work out how you could possibly end up with an odd number, much less a prime number of pieces. Hmm... upon further reflection (and googling), I suppose you could do some theoretical cutting like in this: http://www.youtube.com/watch?v=drFBhFbRL5E

anonymous · Answer

i can see how you get 12, not 13: you cut it in half then lay the pieces side by side like this: UU then cut horizontal and you have 6 pieces, after that you just line them up and cut them all in half

anonymous · Answer

Like I said, I don't know how to do it, aside from just plugging 3 into their formula and out pops 13.  Maybe I'll go get some donuts and do some research.  You know, for science. ;)

anonymous · Answer

Yes, I need a visual representation of that formula. I googled it but didn't find anything with visual aides.  I'm so glad that dmancine is willing to sacrifice himself like that for science ;)