What is the maximum number of slices can you obtain by cutting
a cake with only 4 cuts?
April 17, 2009
Cake cutting puzzle
What is the maximum number of slices can you obtain by cutting
a cake with only 4 cuts?
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12 comments:
I think it should be 16.How?
1st Cut - 2 slices
2nd Cut - 4 Slices
3rd Cut - 8 Slices
4th cut - 16 Slices
Assuming that after each slice cut we are puttin all slice on top of each other i mean together.
The no of slices are..9
Assuming the cuts have to be perfectly straight...
1 slice = 2 pieces
2 = 4
3 = 7
4 = 11 pieces
If the cuts don't have to be perfectly straight, then it's infinite, because you can keep zigzaging and swirling around criss crossing your path with one cut for ever.
Anon2 is correct, assuming that the cake is a convex prism AND that all cuts are made vertically. You can make any number of pieces depending on how complicated the shape of the cake is. It could even have a hole in it like a doughnut.
If you restrict yourself to a regular cake shape (cylinder or rectangular prism) but are permitted to make your cuts anyhow in space, then making them so that they are parallel to the faces of a tetrahedron will give you 15 pieces.
I WOULD THINK
1ST CUT - 2
2ND CUT - 4
3RD CUT - 6
4TH CUT HALF WAY THOUGH THE CAKE YOU WOULD DOUBLE THE SLICES(A HORIZONTAL CUT) MAKING IT 12 SLICES
No because assuming you don't do any horizontal cuts until the last, the second cut would make three pieces.
1) ____________
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|___________|
2) ___________
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|___|______|
3) ___________
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|___|____|__|
Your fourth cut would then go horizontally across leaving you with only six slices. Sorry.
the actual answer is 12.
we have 3 dimensions to make a cut and the no. of slices formed by "n" cuts on any dimension gives "n + 1" pieces.
so we have total allowable cuts as for. so the perfect combination will b 1 + 1+ 2 cuts along the 3 dimensions giving us (1 = 1)(1 + 1)(2 + 1) = 12
no visualisation needed...
god bless.
i would think the answer is 16. 2^4=16. all you would to do is stack the slices or rearrange them to where they are in a row. no matter what you would double the number of slices with each cut.
according to steinr the max pieces for n cuts is C(n) = C(n-1) + n so C(0)= 1 for no slice gives one piece, C(1)=2,...C(4)= 11 which is the maximum
I think we should first agree on the defeinition of a "cut" i would argue that it is to slice from one edge to the other.
so using this definition, on a traditional cake would be 8, however the question leaves so much open space as to how to manipulate the orientation of the cake. so i would have to throw in that based on the question you could have an infinite number of slices.
Lazy caterer sequence says it will be 14
Think of a triangular prism in a sphere. Then the maximum pieces are correspondent to each points lines and sides of the prism, which gives us 4+4+6 and a additional piece, the prism itself, so the final answer is 15
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