# Slice the Donut

1. Jul 21, 2004

### 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

2. Jul 21, 2004

### Math Is Hard

Staff Emeritus
any folding allowed?

3. Jul 21, 2004

### Gokul43201

Staff Emeritus
And the cuts need to be planar !

4. Jul 21, 2004

### terrabyte

5. Jul 21, 2004

### Gokul43201

Staff Emeritus
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 ?

<-----------------------------|

Last edited: Jul 21, 2004
6. Jul 21, 2004

### 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

7. Jul 21, 2004

### Gokul43201

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

8. Jul 21, 2004

### Math Is Hard

Staff Emeritus
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).

9. Jul 21, 2004

### Gokul43201

Staff Emeritus
Looks like the winner !!

10. Jul 21, 2004

### Math Is Hard

Staff Emeritus
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...

11. Jul 22, 2004

### 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.

12. Jul 22, 2004

### 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

13. Jul 22, 2004

### NateTG

This seems pretty easy considering the other posts: 18.

14. Jul 22, 2004

### 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:

15. Sep 15, 2004

### ceptimus

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

16. Sep 16, 2004

### Learning Curve

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

17. Sep 17, 2004

### NateTG

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.