Tuesday, March 4, 2014

The Sicilian Solution



Sonny and Fredo are finishing a Sicilian pie. Both men are hungry, and there's only one slice left.

Nobody wants any trouble here. By making a single straight-line cut, can you produce two pieces with equal areas and equal ratios of crust to cheese?

2 comments:

jeff said...

The solution that comes to me seems too obvious (Thank you, Dame Insomnia). Still ....

Imagine the pie as a grid of 1x1 boxes. Label the 4 columns A through D; rows are 1 through 6. Starting at the bottom left corner of A5, cut upward at a 45 degree angle, ending at the top right corner of D2.

Each half is a 4x4 right isosceles triangle plus a 4x1 rectangle. Therefore equal areas.

Each piece has 4.5 square inches of crust and 6.5 square inches of cheese. Therefore equal ratios.

(possible to post the image i drew?)

JasonZimba said...

Awesome! I posted your solution in today's follow-up