Cut the Cake
What is the maximum number of parts you can cut a circular cake by using a knife 4 times. How about maximum number of equal parts?
* Assume your knife only goes in a straight line and you don't move the parts of the cake between the cuts.
* Assume your knife only goes in a straight line and you don't move the parts of the cake between the cuts.
Labels: bcreative, mathemagic, trickofmind
posted by Rajesh Lal at
8:16 AM
22 Comments:
the maximum parts you can get is 14 first by cutting it 3 times making a triangle inear the center and then cutting the cake from edge to edge horizontaly the max equal parts is 12 cutting it in sixths and then spliting on the horizontal
8 pieces. 1:- 2:I 3:\ 4:/
i think it's 16. first you cut the cake in half, then you put one half over the other and cut again. that gives you four pieces with two cuts. then do this two more times and you get 16 pieces :)
paulina....
* Assume your knife only goes in a straight line and you don't move the parts of the cake between the cuts.
for a cylindrical cake yes 8, but this is circular (so I am going to imagine it's 2D cause, well I'm a punk, and I want to be difficult) so I'm going with 6, and now I will try to comprehend the taste of a 2D cake, hmm kinda bland.
um actually I'm going with 7
i guess i have trouble reading the small print.. :)
this time i'll go with 9. two horizontal cuts and two vertical. it would seem somothing like that #
as for the equal parts.. well i'm still working on it
I say 8 for both of them.
for max number of parts, the most i can come up with is 11.
Like someone up above said, make 3 cuts like that create a triangle near the center of the cake.. the cuts overlap near (not at) the outer edge.. this gives you 7 peices so far.. the center triangle, the peice outside each side of the triangle and the peice opposite each angle of the triangle.
Then make one more cut that starts in one of the small peices opposite the one of the angles of the triangle that crosses the adjacent side peice, then croses the center triangle, and finaly the opposite side piece. It's a straight line, but not through the center of the cake.
That las line will divide 4 of the 7 peices giving you 11 peices total.
I don't know how the person up above came out with 14.
For max number of equal peices, i would say 8 peices.. 4 bisecting cuts.
ok so i say the most possible would be twelve...
you use the first 3 cuts to make 6 equal pieces by looking from a top point of view... then you cute the cake through it's side giving you 12 pieces 6 in each layer
the max i came up with is 14 unequals pieces and 12 equal pieces....
Rx
First cut down thru cake about 1/3 way across= 2 pcs
Second cut at a 45* angle from first cut down thru cake about 1/3 across cake= 4 pcs
Third cut at a 45* angle from second cut down thru cake about 1/3across cake= 7 pcs
Fourth cut is perpendicular to others horizontally across middle of cake= 14 pcs
- - - - - - -
Its a nice 3-layer cake!
Cut one is symetrical across top making two equal halves.
Cut two is symetrical 90* to first making four equal quarters.
Cuts three & four are horizontal thru icing between the three layers making twelve equal pieces.
Let's eat!
There are 3 dimensions and 4 cut-plains, so the answer is 2^4 - 1 = 15. It took me a while to figure out how to cut the cake into 15 pieces, but I got there in the end.
Cut the cake with 3 cuts so the top of the cake shows a triangle around the middle. But cut slanted inward, so you have two pyramids in the middle of the cake, pointing at each other. Now cut the cake horizontally from the side at about quarter height, make sure to cap the top off the bottom pyramid. Et voilà, 15 pieces!
As for congruent pieces, I presume 12 is the most you can get, but no mathematical reassurance on that one.
ok i say 12 is the max. make an x across the cake that would be two cuts. then cut down the middle of the x thats six pieces then cut in the middle of the cake to make a bottom and top.
then you have 2 cakes with six cuts.
as for the other part im saying 9.
hope you get that.
11-look
First cut horizontal
2 pieces
Second cut vertical
Four pieces
Now you have a plus sign
Name the quadrants going clockwise-1,2,3,4
Third cut should start in quad one to quad three, passing through quad four.
7 pieces
Fourth cut should start in quad fourpassing over your third cut and ending in quad two.
11 pieces
16 uneven cuts.
Im goin with 11
Im feelin it.
(Open up Paint)
First 3 lines make a triangle in the center of the circle.
The last line should be a little right of the center, but still cutting the top section just a little.
(My cake is thin just btw)
1,563 1/2.3 x 5 to the -3 power.how did i arrive at this answer you ask/ easy: 5 + 30 x 10.3 / 8 - 7.5 x 72 + 5 x 30.70 x pi. pi=3.1415926535897932384626433832795088 this is the first 35 numbers... ...no joke.
how many of you counted the numbers in that pi number thing? i'm guessing 60%
lol at dat to the anonymous directly above me.
fourteen, use crossing lines to create seven unequal lines, since they are all to bisect with each new line bisected all that came before max you can have is 11
2, 4, 7, 11
as each new nies makes a +term amount addition to the one before it. (1 +(1st term) 1+ (2nd term) 2 etc you could use this in a sum equation
but if we assume that this is a regular 3d cake at the 4th term instead of a bisecting line we slice through the middle of the cake height wise getting 14
!, /, \, -
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