Logic riddle

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Oh no! No! No! No!

Don't feed cake to the dog! Bad! Bad! Bad! Very bad!

If you don't believe me, go ahead and do it. In about ten minutes, you will KNOW why it's bad...

my dog will eat almost anything and he's fine. As long as it's not chocolate cake it's all good Plus watching a dog eat your food is a good lesson in not being a silly whiner.

Third, third, third.

Method to cut a cake into exactly three pieces with only two cuts, without relying on social psychology or knowing what shape the cake is. Requires waxed paper or aluminum foil, a scale, a cutting board, a cooking spoon, some measurable substance to use as a weight, and a knife:

Transfer the cake to the waxed paper or aluminum foil. This is important because one can neglect the weight of aluminum foil, but not the weight of a cake plate.

Weigh the cake, and find something that weighs exactly one-third of that (rice in a bowl should be easy enough). Then put the cake on a cutting board and balance the cutting board on the round handle of a cooking spoon so that the cooking spoon is located exactly at the halfway point of the cutting board. The cutting board should balance across the spoon handle.

Put the weight that weighs one-third of the cake on one end of the cutting board, and the cake on the other end. Move the cake toward the center, keeping the cooking spoon at the center of the cutting board, until the board balances. Cut right across the center of the cutting board. You have now cut exactly one-third of the cake away. Remove this piece.

The two-thirds of the cake remaining can be cut in half by balancing the cake across the middle of the balanced cutting board without the weight present.

(I am, of course, assuming that the amount of cake is judged by density, not size. Cakes of varying density will be cut by weight, not volume.)

Of course, this method has the added bonus of causing the eyes of any non-nerds in the room to glaze over long enough for the nerd to grab the cake and run.

the assertion here is that person 1 would have no incentive to cut the cake fairly without threat of getting a smaller piece himself. most people, out of politeness, would take the smaller piece; so more than likely a shaky cake cutter is going to end up with the bigger piece. therefore, he has incentive to cut the pieces unequally.

and in my world fair or just behavior isn't evoked by fear of consequence but by the lack of desire to impede anyone else's free will. i.e. there is nothing just about a person whose only motive for cutting a cake "fairly" is because he doesn't get first choice of which piece to eat.

so i give the knife freely to any of the three people, and if they want to be a-holes and cheat each other, why am i eating cake with them?

Because you laced the cake with a poison that you already took an antidote for?

It would not be a problem in my family since there is always someone who wants a small piece of cake and someone else who want a big one. I think that it happens a lot in reality.

Anyway, if they are not sure they will cut three pieces of the same size, then they should just invite a fourth person to cut it into four parts since it's easier. Or they could just buy 3 pieces of cake instead of a whole cake.

ok, ok. in all seriousness:

assuming the cake eaters are greedy and all want the biggest piece of cake, and won't cut fairly otherwise.

person 1 cuts the cake into thirds.
person 2 decides which piece person 1 gets.

that way person 1 will cut the cake as evenly as possible knowing that he will get the smallest piece otherwise.

edit: i guess then we have to let person 3 decide on person 2's piece, because person 2 needs a motive for giving away the smallest piece for the rest of it to work out.

there is no difference between there being 2 or 3 or more people.

if the cutter does not get to choose until last, they will cut the cake as equally as they can, as any inequality in the cuts will result in a "smallest piece", and that is the piece the cutter would get.

Of course you could simply use an analog watch in the center and cut out from the 4, 8 and 12 O'clock positions - or you could simply run a string around the circumference and measure and mark 1/3 the total on the string - put back around the cake and cut to the marks - it wouldn't matter in anything that is of equal value throughout. Of course, you are asking this because of perceived inequities in the object being cut...the psychological aspects....or because of other real life situations not being equal and no real way to measure and divide exactly.

So, you could have the 3 agree upon the fairest ways to divide.

One would chose the method to use - he would get second choice...he had the second most control in the solution.

One would do the actual cutting - he would choose last as he has the most control of the solution.

The last one out would choose first as he had the least control over the solution.

All would end up with equal responsibility and control ultimately...and so no right to argue with the result.

You gluttons, you should save some for tomorrow!

but actually...
1 cuts all pieces
2 decides which piece 1 gets
3 takes a piece of his choice
2 takes remainder.

The problem arises when 3 believes that 2 and 1 had colluded ahead of time (conspiracy). A political war can erupt...and in the case of countries, it can mean actual war. If the value is discovered ahead of time by 2 or 1 and a political alliance is formed in order to cheat 3...Hidden minerals later "discovered"...etc....well you can see the problem.

Last edited by Kuma on 19 Aug 2010, 9:14 am, edited 1 time in total.

My version ends like the movie Sleep Away Camp. Cake anyone?

Wow! Now there's an esoteric reference.

BTW, I don't think cakes, being non-biological objects, can have a surprise ending like that.

Hahaha! Yeah but did you see Drag Me to Hell? *shudder* That cake ate that girl's fork. ...and it gave me nightmares.

Btw, I saw Sleep Away Camp kinda by accident when my parents went out one night in 1985 or so and I stayed home alone. An unsuspecting 10 year old, I found the tape so I watched it. I mark that as the end of my childhood. My eyes were stuck like saucers for about a week. No camp for me. Noooo sir.

lol! That brings back memories.
I somehow got my hands on parts 1 and 2 around that time. It was awful trash that we loved. We'd used to sneak-marathon both when we knew our parents wouldn't be around. (Part 3 was too moralizing though--ruined a great franchise.)