Question

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal (45 degree cuts) through any point inside the square?

If you could give an explanation as well as an answer I'd be very grateful! I'd like to learn how to do this, not just get an answer.

Answer 1

Draw a picture of this problem. You'll have 8 pieces, which divides evenly between two people.

http://www.scetv.org/education/ntti/images/2006/funtastic_clip_image006.jpg

Answer 2

Thank you! Just to make sure I'm getting the best answer, here is a hint I was given, if it helps:

The center is an obvious point where it works. What are other obvious points? For a non-obvious point, how could you determine a way to see if the pieces can be divided equally?

Answer 3

Would you try to find the area of each piece? If you found the area of each piece and added them up, I believe this would be a way to tell if the cuts allowed an even amount for each person.