Puzzle | Splitting a Cake with a Missing Piece in two equal portion (original) (raw)

Last Updated : 6 Jun, 2026

Three friends ordered a rectangular cake. One of them was in a hurry, so he cut a rectangular piece from the cake. The piece could be of any arbitrary size(less than the size of the cake) and rotation.

Now the remaining two friends want to divide the remaining cake into two equal portions with a single straight cut.

**Note:

• The single straight cut could pass through the cut-out portion.
• They both need an equal amount of cream and toppings. Therefore, the cut must be made vertically from the top down. You cannot simply slice the cake in half horizontally through its middle (as you would a burger bun).

**Observation:

• All lines in the above diagram divide the rectangle into two equal halves.
• The observation is that,

Check if you were right - full answer with solution below.

**Solution:

• By extending our observation and creating a line such that passes through both the center of the cake as well as the center of the missing piece.
• Such a line would divide the cake into two halves.