First, my book on creativity, *Did You Spot The Gorilla?*, came out on Kindle in the USA over the weekend. Further details here.

Second, on Friday I posted this puzzle….I like doughnuts. Last week I bought a doughnut and wondered…..what is the largest number of pieces I can create by three straight cuts (and not rearranging the pieces between cuts)?

If you have not tried to solve it, have a go now. For everyone else the answer is after the break.Nine…..

Did you solve it? Any other solutions?

**UPDATE:** Ed has correctly pointed out that the wonderful Tim Hunkin claims 13 pieces! Details here.

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called **PUZZLED** and is available for the **Kindle** (UK here and USA here) and on the **iBookstore** (UK here in the USA here). You can try 101 of the puzzles for free here.

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I got 10. Cut any of the two lines as above, and then horizontally through the doughnut like you would a bagel.

That’s a proper way to think 3-D 🙂

I agree with thinking 3-D = 10

Yup , found both the 2 and 3 D versions…

This is what I did.

Oops. 3 short.

I did get it right. 9 in a minute or two.

10 pieces. Any two of the ones shown plus one horizontal cut through the plane of the doughnut.

The description is of a real three-dimensional doughnut and did not state that the cuts had to be vertical.

Yeah, I went for the 3D option too. It’s a doughnut after all, not a CD.

In fact, in 3 dimensions it is apparently possible to get 13 pieces.

http://www.hunkinsexperiments.com/pages/doughnuts.htm – if your brain is up to visualising it. Mine isn’t.

Nice!

Now I don’t have to spend time trying.

Nice answer. I can visualise 12, but where does that 13th piece come from?

For cutting a torus, the correct answer is 13, but I can get only 12 for the problem here.

Richard’s problem is cutting a doughnut (which is a solid) and is different from a torus (a surface), so 13 may not be a possible answer for the doughnut. Certainly, Richard’s answer is wrong, and the answer is greater (either 12 or 13).

I can find a formula for the torus on the net (in several places) that give the number of pieces N from n cuts as:

N(n) = (n^3 + 3n^2 + 8n)/6

It works for n = 1 and 2 and substituting n = 3 gives 13.

However, I can find no proof nor a picture of the dissection.

The “13th” piece… Ok, the cut pattern gives at first sight 7 pieces, if the cuts where parallel, in a shpere… , however all the cutting planes have a common point. … that results in that the center piece isn not a prism but a pyriamid, and there are two “central” pryramids…

n case of the doughnut there are two small pyramids in the foreground… (and presumably one of them is the 13th piece..)

I hope i was right and it was helpful…

I’m glad Hunkin drew it, so I don’t have to try. I think some of the pieces are called crumbs.

Obviously staying friends with the people with whom you share the itty pieces is a different question. 🙂

I got 10 in a couple of seconds, then spent the next hour pondering how many more it was likely to be when all was revealed. Is it sad or just inevitable when the students are smarter than the teacher?

Yeah I thought “10 but there’s probably more if you do weird things in different planes but I can’t think them through(or afford a test doughnut) so I’ll lazily wait ’til Monday”.

Thanks Ed!

To me, the interesting question is the following:

Q: assuming a 2D donut, does it have to have a minimum “thickness” for this solution to work? Or, in more mathematical language: given two concentric circles A and B such that r(A) > r(B), what is the minimum x such that x=r(A)/r(B) and the area A-B can be divided into 9 different parts by three lines?

Your answers below.

I was so close. Got twelve but didn’t think to vary the angles in more than two dimensions.

So it’s theoretically possible to cut it into 13 pieces.

However, if you were cutting the doughnut in reality with the intention that you and your friends consume it, then assuming you had a knife sharp enough to do the horizontal cut, you’re unlikely to cut it into more than 8 pieces without annoying some of your friends 🙂

I was only working in 2D and I got the 9 pieces solution.

Didn’t we have an almost identical puzzle last year with a pizza?

https://richardwiseman.wordpress.com/2011/06/06/answer-to-the-friday-puzzle-107/#more-4292

In fact, not last year – two months ago!

The Great Wise Man is running out of ideas!

Yes, I enjoyed both a 2D and a 3D solution. Here is a 3D model I made of the 3D solution, to help people visualize it.

http://yfrog.com/kl37x6p

total fail

In my house, donuts do not stay around long enough to be cut into several pieces. They are simply consumed with extreme prejudice. Especially Krispy Kremes.

It is theoretically possible to cut a donut into far more than 13 pieces with three straight cuts. But this method causes the pieces to move around between cuts, and so would not qualify as a valid answer to Richard’s question. Anyway, throw a donut into the air, make three quick slices with a samurai sword and you could end up with many pieces.

I forgot to check yesterday, but I did get the correct answer. However, in all honesty, it took me a good 15 minutes of drawing “doughnuts” on paper, before I was satisfied that I couldn’t break it into more than nine pieces. Thanks for another entertaining puzzle.

I like to receive letters with U.S. commemorative stamps on them; I collect these. How are your letters stampedor are they metered (yech)?