how do you cut a cake in to 14 pieces with only 4 cuts of the knife ?

Answer 1

15 pieces are possible (for a 3-dimensional cake).
The progression follows the equation:

p(x) = (x^3 + 5x + 6)/6, where x is the number of cuts.

How to do it:
With the first 3 cuts, divide a cake centered at the origin along the xy ,yz, and zx-planes.
This creates 8 regions.
With the last cut, slice obliquely so that slice cuts 7 of the 8 regions, adding 7 more for 15 total.
Mathematically, the 4 following planes divide space (and more specifically, a cake of suitable size centered at the origin) into 15 regions:
x=0; y=0; z=0; x+y+z=1
If you really needed only 14, modify this last slice so that it cuts only 6 of the 8 regions after 3 slices (the plane x+y=1).

Answer 2

Since you never said the pieces had to be equal do the following:

Cut the cake in half horizontally.
Now use two cuts to vertically cut the cake with an X across the top.
Lastly use your fourth cut to cut the cake through the top so that you do not go through the center of the X you made with the previous two cuts.

You won't have wedge slices of cake, but you will have 14 pieces. Hope this helps.

Answer 3

I am making the assumption that this is a circular cake.

First cut the cake in half horizontally, as if you were cutting it to put jam inside it.

Next, roughly a third of the way across the cake, make a vertical cut across the cake.

Turn the cake 120 degrees and repeat the same cut in the new position.

Turn the cake another 120 degrees and repeat the cut again to make the final cut.

This should leave you with a triangle in the middle of the cake, three triangles with curved edges at the edge of the cake and three trapeziums each with a curved edge.

This makes 7 pieces and, with the horizontal cut you made first, this doubles to 14 pieces.

Answer 4

Easy. Make an 'X' with the first two cuts - that gives you four pieces. Then cut across three of these to cut 'tips' off the existing slices - in the 'X', the top triangle would be in two, and the two side ones. The bottom triangle would be one piece. See? That gives you (counting clockwise) 1-2-3-4-5-6-7 pieces.

Finally, cut laterally across the middle (where the filling would be in a victoria sponge) and voila!

14 pieces. They'd be pieces of different sizes, though. Cutting a cake into equal portions with 4 cuts is, I think, impossible.

Answer 5

first use ur knife twice to cut the cake so that it looks like X then cut with along a straight line on the above part or below part which add s three more to it making it 7 then cut the cake along its body so that u get two halves,which makes it 14.Listen u don't have to slice 14 equal parts of the same cake just make 14 parts that's the trick.

Answer 6

the first three cuts have to be made off-centre so that it forms a triangle in the centre. this way each cut will overlap the other two cuts separately, forming seven pieces. with the fourth cut, cut the cake sideways to make it into two layers. so that's 7 pieces in the bottom layer, and 7 pieces in the top layer, totalling 14 pieces.

Answer 7

Cut it into four by 2 cuts so you 2 cuts left. Gather the four parts and cut it together resulting to eight parts. Cut the six pieces together like the way you cut the four into eight. You'll end up with 12 pieces plus the other two left then that would be 14.

Answer 8

Assuming the cuts are only straight, then you've stumped me. I can only get 6, 9, 10 or 12 pieces with straight cuts. Now, if the cuts don't have to be straight, that's different...

Answer 9

1st cut: cuts cake in half then stack the 2 halves on top of each other ...

2nd cut: with the halves stacked, cut the stack into two equal halves giving you 4 quarters. Stack these 4 slices on top of each other...

3rd cut: with the quarters stacked, cut the stack in half giving you 8 equal slices. Stack the 8 slices on top of each other

4th cut: with the eighths stacked, cut the stack in half giving you 16 slices.

Eat 2 of the slices. That leaves 14 slices of equal size ;)

Answer 10

it is so easy ...cut the cake 2 sides at a 'x' and then hold the cake and cut 2 times sideways at differentt levels then it will give you 14 exact peices.