Comments on: A math puzzle about splitting land

By: Sam

Sam — Mon, 29 Nov 2010 09:19:40 +0000

@ Dave: That is actually Celtic inheritance tradition. The youngest son divides the property, then the oldest son selects his section, and subsequent sons take their choices in birth order until the youngest son is left with whichever piece remains.

By: Joe

Joe — Tue, 15 Dec 2009 21:25:31 +0000

I was asked this question during a recent job interview. My way of coming up with a solution was to rephrase the original puzzle by replacing rectangles with circles – i.e., a circle within a circle. When looking at the puzzle in this way, it’s more intuitive to see a line connecting the two centers being the best answer, and then you can extend the analogy to the rectangles.

By: Dave

Dave — Mon, 14 Dec 2009 10:19:44 +0000

Here’s a different take on the question.

The solution provided divides the land equally in terms of area, but realistically there are probably more or less desirable patches on the estate (e.g. fertile soil for farmers, or perhaps more underground oil for oil companies).

A simple and fair (equitable) distribution method would be to have one son divide the land up into 2 pieces, and have the other son choose which piece of land he wants.

By: Presh Talwalkar

Presh Talwalkar — Tue, 17 Nov 2009 09:31:33 +0000

Roman, Jon and Seth: Thanks for the correction to the solution.

By: eye5600

eye5600 — Mon, 16 Nov 2009 18:59:55 +0000

It’s also true the for any point in the interior, there is a line through that point which divides the area. Proof: Pick a point and a line. Note the resulting split. Rotate the line around the point. The split changes in a continuous way, and by the time you have rotated 180 degrees, the spit has reversed. By the mean value theorem, there is one angle which is an even division.