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Old 07-01-2010, 03:03 PM   #1
pdurrant
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Cake Cutting Puzzle

  • You have an ordinary, round, fruit cake.
  • You have an ordinary, straight, cake knife.
  • You need to cut the cake into eight equal* pieces.
  • You are only allowed three** cuts with the knife.
No doubt you're thinking that this is another old chestnut of a puzzle. But I'm adding a twist of a new condition:
  • Each of the eight pieces must be as tall as the original cake. So no slicing the cake in half horizontally!
Answers in
Spoiler:
spoiler tags
please.


*So as to avoid arguments as to who's got the biggest piece.
**No, you can't have four cuts. Then we wouldn't have a puzzle!
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Old 07-01-2010, 03:52 PM   #2
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Would something like this be allowed:

Spoiler:
1. Cut the cake in half.

2. Stack the two halves, one on top of the other.

3. Cut the stack into half (so now you have four pieces).

4. Stack the four pieces one on top of the other.

5. Cut in half again.


This is just off the top of my head. No doubt, there's an objection to it somewhere.
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Old 07-01-2010, 04:13 PM   #3
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Quote:
Originally Posted by Mike L View Post
This is just off the top of my head. No doubt, there's an objection to it somewhere.
Sounds reasonable to me. I'm still stumped on the bigger puzzle: why people would willingly wish to consume fruit cake?
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Old 07-01-2010, 04:19 PM   #4
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I'm stumped by ROUND fruit cake! All the fruit cake I've ever seen is rectangular! Perfect for door stops!
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Old 07-01-2010, 04:21 PM   #5
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Is this cheating?

Spoiler:
Cut the cake in half = 1 cut
Stack the 2 pieces and cut in half again = 2nd cut
Stack the 4 pieces and cut in half again = 3rd cut

Or do all pieces have to remain on the same level?
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Old 07-01-2010, 04:55 PM   #6
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Quote:
Originally Posted by Mike L View Post
Would something like this be allowed:

Spoiler:
1. Cut the cake in half.

2. Stack the two halves, one on top of the other.

3. Cut the stack into half (so now you have four pieces).

4. Stack the four pieces one on top of the other.

5. Cut in half again.


This is just off the top of my head. No doubt, there's an objection to it somewhere.
Yes, that's right. I didn't say it was very difficult, just not the usual answer. Congratulations!
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Old 07-01-2010, 04:57 PM   #7
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Quote:
Originally Posted by poohbear_nc View Post
Is this cheating?

Spoiler:
Cut the cake in half = 1 cut
Stack the 2 pieces and cut in half again = 2nd cut
Stack the 4 pieces and cut in half again = 3rd cut

Or do all pieces have to remain on the same level?
Congratulations to you, too. That's a right answer.

Spoiler:
It's not actually necessary to stack the two halves after the first cut; you can just make the second cut at right angles to the first to get the four quarters, and then just do the stacking once.
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Old 07-01-2010, 05:00 PM   #8
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Quote:
Originally Posted by poohbear_nc View Post
I'm stumped by ROUND fruit cake! All the fruit cake I've ever seen is rectangular! Perfect for door stops!
Square fruit cake? The USA is even more strange than I thought!

Although I must admit that I'd much rather have a Victoria Sandwich Cake or a Madeira Cake than a fruit cake. Or Devil's Food Cake.... yum.
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Old 07-01-2010, 05:22 PM   #9
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Spoiler:
Cutting into pieces involves sharing.
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Old 07-01-2010, 06:06 PM   #10
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Quote:
Originally Posted by happy_terd View Post
Spoiler:
Cutting into pieces involves sharing.
A good attempt, but not the right answer
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Old 07-01-2010, 06:38 PM   #11
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[QUOTE=pdurrant;988169]
  • You have an ordinary, round, fruit cake.
  • You have an ordinary, straight, cake knife.
  • You need to cut the cake into eight equal* pieces.
  • You are only allowed three** cuts with the knife.
No doubt you're thinking that this is another old chestnut of a puzzle. But I'm adding a twist of a new condition:
  • Each of the eight pieces must be as tall as the original cake. So no slicing the cake in half horizontally!
Answers in
Spoiler:
spoiler tags
please.

Spoiler:

Cut once lengthwise from the top down. Cut again crosswise from top to bottom. Then cut diagonally from one top edge through the center onto the bottom directly opposite the top cut.
eight pieces, three cuts all equal height and volume.
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Old 07-01-2010, 07:08 PM   #12
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Quote:
Originally Posted by obs20 View Post
Quote:
Originally Posted by pdurrant View Post
  • You have an ordinary, round, fruit cake.
  • You have an ordinary, straight, cake knife.
  • You need to cut the cake into eight equal* pieces.
  • You are only allowed three** cuts with the knife.
No doubt you're thinking that this is another old chestnut of a puzzle. But I'm adding a twist of a new condition:
  • Each of the eight pieces must be as tall as the original cake. So no slicing the cake in half horizontally!
Answers in
Spoiler:
spoiler tags
please.
Spoiler:

Cut once lengthwise from the top down. Cut again crosswise from top to bottom. Then cut diagonally from one top edge through the center onto the bottom directly opposite the top cut.
eight pieces, three cuts all equal height and volume.
I had to go and try it (although not with fruit cake). I'm afraid your solution doesn't work. Your pieces aren't equal. The bottom two pieces on the side you start the cut and the top two pieces on the side you end the cut are full height and equal, but they are bigger than the other four pieces which are only half the height of the original cake.
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Old 07-01-2010, 07:38 PM   #13
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Quote:
Originally Posted by pdurrant View Post
Square fruit cake? The USA is even more strange than I thought!

Although I must admit that I'd much rather have a Victoria Sandwich Cake or a Madeira Cake than a fruit cake. Or Devil's Food Cake.... yum.
Now I really fancy a nice rich fruit cake with apricot jam, marzipan and royal icing

But I'll settle for any cake!
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Old 07-01-2010, 07:44 PM   #14
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Quote:
Originally Posted by pdurrant View Post
I had to go and try it (although not with fruit cake). I'm afraid your solution doesn't work. Your pieces aren't equal. The bottom two pieces on the side you start the cut and the top two pieces on the side you end the cut are full height and equal, but they are bigger than the other four pieces which are only half the height of the original cake.
I realized that it wouldn't work shortly after posting but the correct solution looks like it would make a mess.
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Old 07-01-2010, 10:29 PM   #15
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Spoiler:
From above the cake cut it in half with a vertical cut. Then half these two halves (while they are still in the original position) with a vertical cut from above. Then stack all those four pieces on top of each other vertically, all in the same direction. Cut these four pieces in half with one downward cut. Now there are eight equal pieces.
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