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Minnesota
February 4th 2005, 03:56 PM
The health of China's grand emperor was failing fast, and because he valued each of his four children equally, he decided to divide the country among them, each would have an equal amount of territory to govern. But knowing that the country must have a single ruler, he devised a test to determine which of the four it would be.

Gathering them together, he gave each an outline map of the country, and told them that each must divide the country into four, exactly equal realms, and that each of the realms must border the new royal city, which could be built anywhere they chose. This project, he told them, was to be completed by sundown, and that upon presentation of their maps, they would have to prove that all four of the newly devised realms were, indeed, equal in area. Whoever first and accurately completed the task would be named future emperor of China.

To get an idea of what he had in mind, he also presented them with a sample map of the royal city and four proposed realms (this map fails because the realms are not equal in area).

[attachment]
click to enlarge

Within an hour, Sue Hui Ying returned with her completed map. Looking it over and questioning its accuracy, the emperor was so impressed with his daughter's cleverness and proof, that he not only declared her to be the next ruler of China, but allowed her to take power immediately.

How did Sue Hui Ying do it? (She did not use any advanced math)

technomage
February 4th 2005, 04:00 PM
Ooh! Neat! The solution is probably going to be immensly simple (and I'm probably going to smack myself for not seeing it), but this is a good one!

Justin

Mark_S
February 4th 2005, 04:03 PM
:huh: Hrmmmmm.....

Good one

Mark_S
February 4th 2005, 05:48 PM
Well, I've been thinking about it on and off for almost two hours now. The first solution I came up with (about 2 minutes in) was to draw a grid over the
map and start counting off squares. Quick, dirty, and may come close to accurate, but there has got to be a more exact method.

Mark_S
February 4th 2005, 05:57 PM
Brainstorm....

Make a clay model of the country of uniform thickness.

Break it into 4 chunks roughly the same size

Weigh them

Chip a piece off the heavier ones and add it to the lighter ones until they all weigh the same

Piece each territory together back together like a puzzle

And Whalla

Edited to Add:

forget the clay, just start cutting up the map itself, the material should be heavy enough to weigh.

markporter
February 4th 2005, 06:22 PM
it's not something to do with hanging the map from a point and finding the centre of gravity is it? It's just the kind of thought that naturally springs to mind

Divine_Clarity
February 4th 2005, 06:48 PM
make new borders perfectly strait forming a qudrilateral with each side being equal in length (a square) then divide it equally

Mark_S
February 4th 2005, 07:35 PM
make new borders perfectly strait forming a qudrilateral with each side being equal in length (a square) then divide it equally Make new borders for China?

Minnesota
February 4th 2005, 08:20 PM
Making new borders is a No, No. the kids don't have the power.

guacamole
February 10th 2005, 02:41 PM
powerless children, powerless to :fall: