Extreme bagel slicing

[taylweaver]

At Shabbat dinner, AF posed the following challenge: Cut a donut into twelve pieces using only three straight slices. It helps to think of it as a bagel, because donuts come in a broader variety of shapes - but bagels are generally round with a hole in the center. Also, they are less likely to crumble when sliced.

And no, you are not allowed to move the pieces of the bagel - no using the stack and slice strategy that mysticengineer and I both generated independently of each other. There is actually a way to keep the bagel in its original bagel shape and make three straight slices and get twelve pieces.

I know it is possible.

How do I know? Because i just did it.

And it is a rather elegant solution - if a bit difficult to execute, as it requires rather precise cuts. So I must admit that I cheated a bit when making the actual slices, because it is difficult to be precise when using playdough and a plastic knife - so I had to use my fingers to fix the places where the knife went awry - but it worked!

Side note about the playdough: many thanks to lexiefaye and flintknappy for a useful birthday gift - and how appropriate to get it from my "anthropology friends" - because it was maric23, the archaeologist, who suggested trying it out with clay and a wire. Your playdough was the best I had.

So thank you to maric23 for talking it out with me. And thank you to AF for posing the question.

And here is maric23's riddle for the evening (used in the context of a grammar class, if I recall correctly): A man without eyes saw plums on a tree. He neither took plums nor left plums. How can this be?

That one, I did not solve. But that's because it didn't fit my frame of reference.

Comments

[flintknappy.livejournal.com]

See, big kids can use playdoh. :) You have an archaeologist friend J? How do I not know about this? You must tell me about them...

[maric23.livejournal.com]

I'm curious as to what your solution was. My original one I think doesn't work, but during a particularly painfully boring shavuos shiur, a rather simple solution popped into my head; a solution which curiously enough, does say something about learning styles.

I then offered it at lunch, and one person got it instantly. Most humiliating.
-j

[taylweaver.livejournal.com]

My solution is the one I was saying at lunch. But it seems impossible to do it with an actual donut - it crumbles long before the third cut. Try it with clay, like you suggested.

Arrrrgh! AutoCAD!

[mysticengineer.livejournal.com]

Spent a few extra minutes at work yesterday trying to slice the torus on AutoCAD.
I can draw in 3D easily enough, but the program starts to do funny things when I try to use the 'slice' command.
I miss SolidWorks.
Now, maric23, what's your "rather simple solution?"

Re: Arrrrgh! AutoCAD!

[taylweaver.livejournal.com]

tee hee. I hope you were not supposed to be working at the time...

My suggestion: instead of working with a 3-D image, come work with something that is an actual three dimensions - I still have the playdough.