What can be done?
- Please come over at once!
- What’s going on?
- My brother has just served himself a rectangular piece of a rectangular brownie.
- So what?
- I have to divide what remains into two identical pieces for my sister and myself.
- That can’t be too hard.
- You don’t know what you are talking about! The piece he cut is not parallell to the edges of the brownie.
- I see.
- Come over at once. It is an emergency!
Problem source: The Emissary.
May 28th, 2009 at 4:23 am
Cut the brownie in two equal halves at 1/2 its depth. If you start out with a chunk o’ goodness 1″ thick, you’ll end up with two chunks o’ goodness 1/2″ thick.
Another possibility for which a proof would be well beyond my capabilities but seems right to me would be to start at opposing corners of the inner rectangle and create two spirals that follow the contour of the inner rectangle and then go around each other. It seems to me that you would end up with two identical spiral shaped brownies but again – I can’t prove this.
May 29th, 2009 at 1:53 pm
One cuts and the other chooses.
October 18th, 2009 at 5:23 am
Cut along the extended line between the centre of the removed piece and the centre of the original (whole) piece.
Any line passing through the centre of a rectangle divides it into two equal parts. The above cut divide the missing piece into two equal (by area) pieces and the original whole brownie into two equal pieces.
I’m sure that can be stated better.