Here's an interesting puzzle given to me by John in
the Azores. I'd been torturing him with several puzzles,
so he retaliated with this:
- You have a two layer ice-cream cake.
The layers are of equal depth, the top
is vanilla, the bottom is chocolate.
- You choose an angle, and cut a regular type
of wedge shaped slice of that angle, remove
the piece, flip it over, and put it back, so
now you have a visible wedge of chocolate.
- Now you rotate the cake by the same angle,
and do it again. And again. And again.
- What happens?
If the angle you've chosen happens to divide exactly
into 360 degrees then after one rotation you've turned
the entire cake upside down, and on the second rotation
you return each piece to its original position.
| One thing to be careful of is that two successive
cut-n-flips of 40 degrees is not the same as a single
cut-n-flip of 80 degrees. The flip doesn't just reverse
top and bottom, it also reverses left and right. |
But what if your chosen angle is, say, 50 degrees? Or
perhaps 75 degrees? Does the cake ever return to its
original state (with extra cuts!)? Or does it just get
more and more complicated?
What does it look like?
Part of the Farrago of Fragments.
Links to this page /
Page history /
Last change to this page
Recent changes /
Edit this page (with sufficient authority)
All pages /
Change password /