Cake Cutting Puzzle

[pdurrant]

• 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!

[Mike L]

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.

[clarknova]

Originally Posted by Mike L

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?

[poohbear_nc]

I'm stumped by ROUND fruit cake! All the fruit cake I've ever seen is rectangular! Perfect for door stops!

[poohbear_nc]

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?

[pdurrant]

Originally Posted by Mike L

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!

[pdurrant]

Originally Posted by poohbear_nc

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.

[pdurrant]

Originally Posted by poohbear_nc

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.

[happy_terd]

Spoiler:

Cutting into pieces involves sharing.

[pdurrant]

Originally Posted by happy_terd

Spoiler:

Cutting into pieces involves sharing.

A good attempt, but not the right answer

[obs20]

[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.

[pdurrant]

Originally Posted by obs20

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.

[ShortNCuddlyAm]

Originally Posted by pdurrant

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!

[obs20]

Originally Posted by pdurrant

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.

[Javed]

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.