100th Potpourri

[daniel801]

For #1, what does

[Aarondalf]

It means you have to use one straight cut. as in it cant be a curved line.

[daniel801]

then i think you cant cut the sandwich evenly if the layers are not in layers, i.e. a "wrap"

[Coyote]

Kevin's being pretty generous with the clues here---I think he must want to ensure the donation goes through.

Just do a web-search on 'Ham sandwich theorem'

[NewHere]

Suppose one or more of the ingredients contained an odd numer of quarks...the two halves would not have equal parts, strickly speaking.

[NewHere]

For #11 I have a 14-knight chessboard on which all squares (and knights) are covered. I'll email a jpeg if any wish to see. Does anyone have a smaller solution?

[Coyote]

Note the wording on #11--occupied squares don't necessarily have to be gaurded:











Twelve Knights


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Gravity is a harsh mistress.

[Vanyo]

Haven't seen the "ham sandwich theorem", but the following argument seems intuitive to me.

There must be a point that corresponds to the ham's center of gravity. Any plane through that point divides the ham into two parts with equal mass. There is a similar center of bread gravity, and center of cheese gravity. So the plane that passes through these three points will divide ham, bread and cheese equally in half.

Throw in a fourth ingredient and all bets are off.

[Coyote]

To quote H.E. Dudeney, "Area is one thing, but gravitation is quite another."

Try this experiment: cut a 3 inch x 1 inch rectangle ABCD out of cardboard (with AB as the 3 inch side.) Mark a point E along the AB side 1 inch from A, 2 inches from B. Cut along the line EC so you end up with trapezoid AECD, which consists of a 1 inch square affixed to a right triangle with legs 1 inch and 2 inches. Obviously, both parts are of the same area.

Now tie one end of a string to point E and dangle the trapezoid from the string.

[CookMoominTroll@aol.com]

Re: Potpourri Question 1

I'm confused, are their two sandwiches, one made of melted cheese and one of ham? Maybe I'm thinking too laterally but I need to rule this out before I can focus on the problem.

[Vanyo]

Coyote: I don't see the point of your experiment.

Even if there were two sandwiches, one ham, and one cheese, or even if there were just a bunch of ham slices, cheese slices and bread slices floating in space, there would still be some plane that would divide it all up so that exactlly half the cheese, ham and bread were on one side, and the other half on the other side.

[Ghost Post]

Vanyo-

i think coyote's point was that the plane that splits them in half does not necessarily go through the center of gravity.

[Ghost Post]

coyote's idea seems right... what about the mass of earth's gravitational field? I have heard that "everything has a gravitational effect on everything else to some extent." So how canthe mass of a seemingly infinite force be found?

[This message has been edited by dravid (edited 12-06-2000).]

[Ghost Post]

A plane going through the center of gravity doesn't usually have equal mass on both sides. Imagine that the mass was evenly placed in three dots. The center of gravity would be somewhere between the dots and most planes going through it would have 2 dots on one side and 1 on the other.

[Coyote]

Yeah, those posts above were the idea I was trying to get across. I was a little bit tired last night, which tends to make me a little bit incoherent.

I'm a little tired tonight too--can you tell?

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Gravity is a harsh mistress.

[Vanyo]

Oh, yeah. What the hell was I thinking?