Four math students ordered three pizzas: one large (55 cm diameter), one medium (44 cm diameter) and one small (33 cm diameter).
Upon delivery they decided to divide it fairly between them by cutting the pizzas into the fewest number of pieces.
Ignoring the toppings and assuming uniformity of thickness please provide a solution with less than 6 pieces.

Cut the large pizza in half. 
Using the small pizza as a template placed over the medium pizza with the smaller lies completely over but sharing a "point" along the edge of the crust. From the opposite "point" on the circumference of the medium pizza, make a cut to the edge of the circumference at the opposite "point" of the small pizza, then continue to cut along the circumference of the small to the common "point". The medium pizza will now be 2 pieces of unequal sizes. (If the cut around the small pizza were continued completely around, the pizza would be 3 pieces with the 2 smaller of the pieces being of equal 'volume'.)
Each of two students will get one of the large pizza pieces;
One student will get the larger piece of the medium pizza; and
one student will get the smaller piece of the medium pizza plus the small pizza.

Edited on May 16, 2012, 1:05 pm

Posted by Dej Mar on 2012-05-16 12:10:21