Strange2 (Explaining the three puzzles which defy "common sense."

1. Suppose the earth is a perfect sphere and there is a rope tied tightly around it at the equator.

Now add exactly one foot to the rope's length and support it above ground equally around the globe.

How far is the rope above the ground?

Surprisingly, almost two inches! (1.90985...).

Let's wrap a rope around a orange, then lenghten it by one foot. How far is the gap?

Again, about two inches!

Try a ping pong ball. Same result!

Strangely believe it! The answer is independent of the size of the sphere

Explanation: Let C = the circumference of the earth.
Then C = the original length of the rope and C+1 the extended length.
Let r be the earth's radius and R be the new radius of the rope after extension.
But C = 2 * pi * r and C+1 = 2 * pi * R
and R = (C + 1) / (2 * pi)
and r = C / (2 * pi)
or: R - r = 1 / (2*pi) = 0.159... (feet) or 12 * 0.159 inches.

2. You are on the TV show, "Let's make a deal."

The host shows you three doors and tells you the there is a million dollars behind one and a single dollar behind the other two.

The doors are marked A, B and C. You choose A.

The host then opens door B which reveals a dollar bill.

He then asks you if you want to stay with your first choice, door A, or switch to door C.

What do you do? Well, the odds of winning the million dollars if you stay with A is 1/3. But the odds of winning if you switch to door C is 2/3!

Strangely believe it.

Here are the possibilities:

Original door selected	A	A	A	B	B	B	C	C	C
Location of $1,000,000	A	B	C	A	B	C	A	B	C
Door opened by the host	B/C	C	B	C	A/C	A	B	A	A/B
Do not switch --------	WIN	LOSE	LOSE	LOSE	WIN	LOSE	LOSE	LOSE	WIN
Switch ----------------	LOSE	WIN	WIN	WIN	LOSE	WIN	WIN	WIN	LOSE
So if you DON'T switch, you will win 3 times and lose 6 times, but if you DO switch, you will win six times and lose three. Surf over here for another explanation.

3. According to the book IMPOSSIBLE,

by Julian Havil, in 2003, a Chinese lady named Ma Li Hua, spent six weeks setting up 303,000 dominos. On August 18, 2003, someone knocked over the first. The 303,000th domino was the last to fall, six minutes later.

Does this speed seem credible? How would you test it (without setting up 303,000 dominos)?

(Left to the inginuity of the reader)

John Burgeson

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