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?


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