Dividing a cake into equal thirds riddle - no not what you think

KingCondanomation

KingCondanomation

New member
3 people are dividing a cake. Each person wants as much cake as possible for himself, but each person thinks that the other two might be colluding. Lets call the three A, B, and C.

A suggests that he will cut the cake into 3 portions, and then C will pick his piece from the 3, and B then would pick his choice from the 2 remaining. and A takes the last piece. B objects to this scheme, saying that A can cut the cake into 1 large piece, and 2 smaller equal pieces. C then would have the largest piece, and B would have to take the smaller piece. In fact, B claims, If A and C were really colluding, this method would allow them to get the entire cake to share among the two of them.

Given this distrusting atmosphere, is there a way to divide the cake so that each person is satisfied? Any proposed method would have to convince each person that he would get his fair share even if the other two were colluding.
 
You could also measure from top to bottom, and cut that into three equal parts. Each taking one of those pieces.
 
How about...

A cuts the cake.
They choose there portions in C,B,A order.
If B is satisfied that his portion is equal to C's then fine. If not then B redivides B's and C's portions and C chooses his portion.

Unless, I am missing something, A could only screw himself.
 
Damocles said:
Cut the cake into 12 equal parts, let each take 4 of the pieces.
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But who cuts and how are the pieces chosen? If A cuts he could cut it into portions of 11 pieces of 1% and one piece of 89%. C takes 92% (1 89% piece and three 1% pieces). B and A would get 4 1% pieces. A and C then split their portions into 2 48% portions. So A gets 48%, B gets 4% and C gets 48%.
 
KingCondanomation said:
3 people are dividing a cake. Each person wants as much cake as possible for himself, but each person thinks that the other two might be colluding. Lets call the three A, B, and C.

A suggests that he will cut the cake into 3 portions, and then C will pick his piece from the 3, and B then would pick his choice from the 2 remaining. and A takes the last piece. B objects to this scheme, saying that A can cut the cake into 1 large piece, and 2 smaller equal pieces. C then would have the largest piece, and B would have to take the smaller piece. In fact, B claims, If A and C were really colluding, this method would allow them to get the entire cake to share among the two of them.

Given this distrusting atmosphere, is there a way to divide the cake so that each person is satisfied? Any proposed method would have to convince each person that he would get his fair share even if the other two were colluding.
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Your first method will work just fine....with one simple stipulation...

After C selects the piece he wants he must devour it before B makes his selection..the same applies to B....problem solved....

Any collusion, by necessity MUST include the one , that does the cutting(A).
If he makes one piece bigger than the others, B will select it and enjoy it before A could join in....
 
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RStringfield said:
But who cuts and how are the pieces chosen? If A cuts he could cut it into portions of 11 pieces of 1% and one piece of 89%. C takes 92% (1 89% piece and three 1% pieces). B and A would get 4 1% pieces. A and C then split their portions into 2 48% portions. So A gets 48%, B gets 4% and C gets 48%.
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They would simply be equal parts. It isn't difficult to check with direct effort of measuring.
 
Damocles said:
Cut the cake into 12 equal parts, let each take 4 of the pieces.
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The number of pieces would be equal, but not the volume of cake.

Each of the 12 pieces would be .08333333 of the whole cake, except for one piece, which would have to be .08333334 to include the entire whole cake. Of course, none of the recipients would be able to tell the difference in a piece of cake .00000001 larger or smaller than the others.
 
Dixie said:
The number of pieces would be equal, but not the volume of cake.

Each of the 12 pieces would be .08333333 of the whole cake, except for one piece, which would have to be .08333334 to include the entire whole cake. Of course, none of the recipients would be able to tell the difference in a piece of cake .00000001 larger or smaller than the others.
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I'm sorry you are so incapable of thought.
 
Dixie said:
The number of pieces would be equal, but not the volume of cake.

Each of the 12 pieces would be .08333333 of the whole cake, except for one piece, which would have to be .08333334 to include the entire whole cake. Of course, none of the recipients would be able to tell the difference in a piece of cake .00000001 larger or smaller than the others.
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I can't understand why the hell you insist on making an ass of yourself when it comes to simple thought.....this has absolutely nothing to do with dividing the decimal numerals, 1 by 3.....nothing at all....
 
bravo said:
I can't understand why the hell you insist on making an ass of yourself when it comes to simple thought.....this has absolutely nothing to do with dividing the decimal numerals, 1 by 3.....nothing at all....
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Some people learned everything they needed to know in life by kindergarten.

Some people learned everything wrong in kindergarten and thats all they ever needed to know.

Some people went on to higher education.

I'll give you one guess as to which one of these describes our resident mathematician.
 
bravo said:
I can't understand why the hell you insist on making an ass of yourself when it comes to simple thought.....this has absolutely nothing to do with dividing the decimal numerals, 1 by 3.....nothing at all....
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I don't understand why the vast majority of this board is so OBTUSE about this fucking ridiculous 1/3 argument, but they goddamn sure are! I learned in the 3rd fucking grade that one divided by three produces a remainder! I also learned that if you continue to carry the remainder and keep dividing it, eventually it becomes assumed as part of the value, no further calculation is required in most cases....we signify this with a little "e" at the end. In high school, I learned in Calculus, that a formula was devised to rectify this remainder when plotting or where critical precise measurement is crucial to an equation. So even goddamn Calculus geniuses recognized that division sometimes produces a repeating remainder, and in order to make their computations work, they needed to develop a means to deal with this problem. I understand it, the calculus geniuses understand it, but it seems that everybody on this particular message board, is clueless about it! How can that be???

I don't know why you think this thread has nothing to do with the 1/3 argument, when it has EVERYTHING to do with it, that is why Dano posted it!
 
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Dixie said:
I don't understand why the vast majority of this board is so OBTUSE about this fucking ridiculous 1/3 argument, but they goddamn sure are! I learned in the 3rd fucking grade that one divided by three produces a remainder! I also learned that if you continue to carry the remainder and keep dividing it, eventually it becomes assumed as part of the value, no further calculation is required in most cases....we signify this with a little "e" at the end. In high school, I learned in Calculus, that a formula was devised to rectify this remainder when plotting or where critical precise measurement is crucial to an equation. So even goddamn Calculus geniuses recognized that division sometimes produces a repeating remainder, and in order to make their computations work, they needed to develop a means to deal with this problem. I understand it, the calculus geniuses understand it, but it seems that everybody on this particular message board, is clueless about it! How can that be???

I don't know why you think this thread has nothing to do with the 1/3 argument, when it has EVERYTHING to do with it, that is why Dano posted it!
Click to expand...

I would go and post comments where you contradicted statements you had made yesterday here, but I'm too lazy.
 
Dixie said:
I don't understand why the vast majority of this board is so OBTUSE about this fucking ridiculous 1/3 argument, but they goddamn sure are! I learned in the 3rd fucking grade that one divided by three produces a remainder! I also learned that if you continue to carry the remainder and keep dividing it, eventually it becomes assumed as part of the value, no further calculation is required in most cases....we signify this with a little "e" at the end. In high school, I learned in Calculus, that a formula was devised to rectify this remainder when plotting or where critical precise measurement is crucial to an equation. So even goddamn Calculus geniuses recognized that division sometimes produces a repeating remainder, and in order to make their computations work, they needed to develop a means to deal with this problem. I understand it, the calculus geniuses understand it, but it seems that everybody on this particular message board, is clueless about it! How can that be???

I don't know why you think this thread has nothing to do with the 1/3 argument, when it has EVERYTHING to do with it, that is why Dano posted it!
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The problem is, you are just plain stupid.

You got one cake, 12 inches long, 4 inches wide. You can slice it every 4 inches and you have EQUAL THIRDS of the cake. It does not f'in matter if a percentage can not represent the equality, they are fuckin equal. 4 inches by 4 inches, each slice, therefore, you fail!
 
Beefy said:
Some people learned everything they needed to know in life by kindergarten.

Some people learned everything wrong in kindergarten and thats all they ever needed to know.

Some people went on to higher education.

I'll give you one guess as to which one of these describes our resident mathematician.
Click to expand...

None of the above. Because it would be an insult to any of them to put them on the same level as ditzie.
 
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