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.

The diameters are in the ratio 3:4:5 which means the areas are in the ratio 9:16:25.  The fact that 9+16=25 makes this problem very convenient:  
The big pizza can be cut in half.
The medium pizza can be cut into two pieces.  The larger of the two must be equal in area to half of the large. 
The smaller piece when added to the small pizza will be of equal area.

This is a two cut (D1) solution which ends up with 5 pieces of pizza. 

You can argue it to be D2 to determine exactly how to cut the medium pizza.

Posted by Jer on 2012-05-16 11:04:00