A cake has 3 raisins inside. Show that it is possible to dissect all three raisins in one cut by knife?

Answer 1

While 2 points define a line, 3 points define a plane. If the midpoint of these raisins act as our points define the plane by the midpoint of the 3 raisins and cut the cake along this plane.

Answer 2

It doesn't matter how the 3 raisins are aligned. If they all are in a single line, then you simply slice throught like the other answer stated.

If they are not in the same line (non-colinear) then there is a theorem that any three non-colinear points determine a plane. You simply cut the knife in the direction of that plane (parallel to the plane, piercing all 3 raisins).

Answer 3

Set up an xyz cartesian coordinate system.
Let the coordinates of the raisins be xi, yi, zi for i = 1, 2, 3.

Solve the equations simultaneously
a xi + b yi + c zi + d = 0, i = 1, 2, 3
(excluding trivial solutions like a = b = c = 0)

The solution for a, b, c, d gives you the equation of a plane. Move the life along that plane and Bob's your uncle.

If the points are collinear then any plane containing that line will do.

Answer 4

make sure all raisins aligned in 1 line so you could cut through them one time and get 'em all