The brownie problem.

Uncwilly · 2003-12-30, 15:09

This puzzle was shared with me by someone had heard in on NPR.

A woman

decides to make her twin sons (Lucas and Lehmer) a bunch of brownies.

Because they are twins, they share everything 50/50, the brownies are to be shared half/half. The woman bakes the brownies in a rectangular dish and sets it out to cool. Her husband

strolls in and the cad that he is cuts a chunk out for himself and pops it in his mouth.

The wife comes back and sees it.

A clean rectangular hole in cut at a random angle and at a random location.

She is not pleased.

How shall she restore harmony to her house?

She thinks a bit and then pulls out a knife and makes a single, continuous, straight cut. Then she calls the twins

and hands each an equal portion. Happiness is restored!

Your mission is to figure out how she did it.

There are 2 different ways to do it.
PM me with your answers. I will confirm or deny your correctness. After we have the 2 methods in hand, I will have the first person with each correct answer post it here.

Questions are most welcome here as are simple delcarations on "I know".

Included is a handy picture of the brownie.

Uncwilly · 2003-12-30, 15:20

Let's see if this works.

Uncwilly · 2003-12-30, 23:57

There have been 3 replies so far total. 2 for the "math" based solution. 1 for the "practical" type solution.

Uncwilly · 2004-01-02, 14:37

I have let the 2 people that PM'ed me know that they can post the answer already. It is now a free-for-all. Charts graphs and illustrations are most welcome.

Xyzzy · 2004-01-02, 16:33

I would just cut the brownie from the side so you end up with 2 "sheets" of brownie that look the same...

xilman · 2004-01-03, 19:03

Quote:

Originally posted by Uncwilly
I have let the 2 people that PM'ed me know that they can post the answer already. It is now a free-for-all. Charts graphs and illustrations are most welcome.

Draw a line between the center of the two rectangles, extending to the edge of the brownie. Cut.

Paul

tom11784 · 2004-01-04, 04:46

if we can assume that this brownie thing has the same depth at each location, then give each child a "brownie layer" of the same height - 50/50

i.e. if the brownies are 2" high, each child gets brownies that are 1" high - this cut will be continuous through the entire surface of the diagram given above

is this 1 of the 2 you were thinking of?

edit - didn't read xyzzy's close enough

2003-12-30, 15:09	#1
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2·3·7·233 Posts	The brownie problem. This puzzle was shared with me by someone had heard in on NPR. A woman decides to make her twin sons (Lucas and Lehmer) a bunch of brownies. Because they are twins, they share everything 50/50, the brownies are to be shared half/half. The woman bakes the brownies in a rectangular dish and sets it out to cool. Her husband strolls in and the cad that he is cuts a chunk out for himself and pops it in his mouth. The wife comes back and sees it. A clean rectangular hole in cut at a random angle and at a random location. She is not pleased. How shall she restore harmony to her house? She thinks a bit and then pulls out a knife and makes a single, continuous, straight cut. Then she calls the twins and hands each an equal portion. Happiness is restored! Your mission is to figure out how she did it. There are 2 different ways to do it. PM me with your answers. I will confirm or deny your correctness. After we have the 2 methods in hand, I will have the first person with each correct answer post it here. Questions are most welcome here as are simple delcarations on "I know". Included is a handy picture of the brownie.

2003-12-30, 15:20	#2
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2×3×7×233 Posts	Let's see if this works. Attached Thumbnails

2004-01-04, 04:46	#7
tom11784 Aug 2003 Upstate NY, USA 2·163 Posts	if we can assume that this brownie thing has the same depth at each location, then give each child a "brownie layer" of the same height - 50/50 i.e. if the brownies are 2" high, each child gets brownies that are 1" high - this cut will be continuous through the entire surface of the diagram given above is this 1 of the 2 you were thinking of? edit - didn't read xyzzy's close enough Last fiddled with by tom11784 on 2004-01-04 at 04:47

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2003-12-30, 23:57	#3
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 9786₁₀ Posts	There have been 3 replies so far total. 2 for the "math" based solution. 1 for the "practical" type solution.

2004-01-02, 14:37	#4
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 10011000111010₂ Posts	I have let the 2 people that PM'ed me know that they can post the answer already. It is now a free-for-all. Charts graphs and illustrations are most welcome.

2004-01-02, 16:33	#5
Xyzzy "Mike" Aug 2002 8224₁₀ Posts	I would just cut the brownie from the side so you end up with 2 "sheets" of brownie that look the same...