How to Slice a Donut into 13 Pieces with Only Three Cuts

[terrabyte]

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

 

[Math Is Hard]

any folding allowed?

 

[Gokul43201]

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

And the cuts need to be planar !

 

[terrabyte]

yes planar cuts please

don't fold the doughnuts! Bad!

 

[Gokul43201]

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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[terrabyte]

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

 

[Gokul43201]

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

I drew a picture, but my posting rules say that I may not post attachments...WHY ?

 

[Math Is Hard]

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).

 

[Gokul43201]

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).

Looks like the winner !

 

[Math Is Hard]

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...

 

[ceptimus]

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.

 

[Njorl]

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

Njorl

 

[NateTG]

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.

This seems pretty easy considering the other posts: 18.

 

[terrabyte]

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:

 

[ceptimus]

If no rearranging is allowed between cuts, I think the maximum with three cuts is thirteen pieces.

 

[Learning Curve]

How did you get 13? I get 8...

 

[NateTG]

How did you get 13? I get 8...

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.