Automobile races in the U.K. run clockwise: http://www.youtube.com/watch?v=R63C...

http://en.wikipedia.org/wiki/File:T...

<The players of a card game normally form a circle around a table or other space that can hold cards. The game orientation or direction of play, which obviously is only relevant for three or more players, can be either clockwise or counter-clockwise. It is the direction in which various roles in the game proceed. Most regions have a traditional direction of play, such as:

Counter-clockwise in most of Asia and in South America.

Clockwise in North America and Australia.

Europe is roughly divided into a clockwise area in the north and a counter-clockwise area in the south. The boundary runs between France, Germany, Austria (mostly), the Czech Republic, Poland, Ukraine and Russia (clockwise) and Portugal, Spain, Switzerland, Italy, Slovakia, Hungary, Romania, Turkey (counter-clockwise).

<The players of a card game normally form a circle around a table or other space that can hold cards. The game orientation or direction of play, which...>>

What alarms me is that I've read that page before. In its entirety.

What I *can't* recall is why. It had something to do with a conversation here or on <Kenneth Rogoff>, but I don't remember the particulars.

Here is an idea that occurs to me after thinking some more about the fascinating clockwise-counterclockwise topic introduced to this forum via a stumper by <al wazir>...

And it is the PERFECT sort of experiment to do with a world-side population of experimenters.

Here went my thinking:

1) The unspoken assumption in the clockwise-counterclockwise puzzle is that "everyone knows" that in the Southern hemisphere, water draining from a bathtub will end up spinning clockwise, and water draining from a bathtub in the Northern hemisphere will end up (the last bits, if not before) spinning counterclockwise. Due to inertia of the water. And the direction of spin of the earth. Right?

2) Also, the effect is strongest at the poles, and weakest just off of the equatorial line.

3) This would have been sufficient for a stumper all by itself, since the common knowledge explained in 1) has <been debunked!> For the "Oh Yeah?" crowd: http://www.snopes.com/science/corio...

3) Or has it? Has a real experiment been conducted along the following lines:

a) A normal bathtub is filled with water, all movement is allowed to settle, and the the plug carefully pulled.

b) Direction of spin of the last bits are recorded.

c) Time to achieve maximum apparent rate of spin is recorded (e.g. popcorn--anything smaller and it will probably go down the drain-- floating on the water is watched and its rotations per minute counted) to determine stronger effect toward the poles.

d) Distance N or S of equator is recorded.

e) Dozens of people participate from all continents and pool their results from several trials each.

f) Spreadsheet calculations are used to show a scatter gram analysis to depict true randomness, or <REAL CORIOLIS EFFECT JUST LIKE WITH HURRICANES>!

Anyway, that's what occurred to me. This test hasn't been done. Or has it? Who is a statistician here?

The physics behind this result is elementary. To have a noticeable effect on a rotating gyre, the Coriolis force must be bigger than the gravitational force on a fluid element (32 ft per second per second multiplied by the mass of the element) or the centrifugal force (the square of the velocity times the mass, divided by the radius of the gyre). The Coriolis force due to Earth's rotation, whose frequency is 1 divided by 86,400 (the number of seconds in a day) is proportional to the same mass times that same velocity times that rotational frequency.

Therefore the ratio of the Coriolis force to the centrifugal force is on the order of 1/86,400 times the radius divided by the velocity. For any plausible radius (on the order of 1 ft) and velocity (at most a few feet per second), this is a tiny number, far too small to observe, and the gravitational force is always much bigger. The direction of rotation is determined by small initial fluctuations in the water and so is almost random. The water spins faster as it drains out because of conservation of angular momentum, the same reason a rotating skater spins faster when he draws his arms in to his body.

I suppose you realize this doesn't apply in <∏∏>'s neck of the wabe.

1. Daylight savings and worse

Some countries do not switch to daylight savings during the summer months. That can make nearby neighbors have different times, even within the same time zone. How many "time zones"--or different official clock values--can there be on the earth at any given moment?

a) 24
b) 29
c) 33
d) 40

2. Fastest three days: what is the fastest possible time that a resident of earth could see three consecutive calendar days (western calendar) e.g. Monday, Tuesday Wednesday...(Hint-consider the international date line)

a) About 32 hours
b) 21 hours
c) 8.5 hours
d) None of the above

3. Which country on the planet will never ever have the same time as any other country, including any country next door, or north/south of it?

<kellmano> I did not visit this page for more than a month, and hence my tardy reply to the above. Obviously, it was not like shooting fish in a barrel, because no one gave the correct reply!

<al wazir> was close: he said 6, but the correct expectation value is 5.95 .

"Expectation" has a special meaning in statistics: it means the mean value over a hypothetical infinite series of trials. Thus it is not an integer.

If an integer answer is desired, then perhaps we should ask, "what is the most likely size for the group that you are in?"

The answer is 5, I believe. In order to evaluate the probabilities for each possible group size (from 1 to 100), one would need to calculate the applicable binomial coefficients that appear in the binomial distribution. For such large numbers, that's not trivial because factorials up to 99! appear. I suppose Stirling's formula might be tried. But I'm too lazy even for that, so I used the Poisson distribution, which approximates to the binomial distribution for sufficiently large numbers.

I get the probability for a group of 5 (four other than me) = 0.177195165. For a group of 6, the probability is = 0.175423213.

http://www.itl.nist.gov/div898/hand...

I found the following for the binomial distribution:

Mode p*(n+1) - 1 <= x <= p*(n+1)

For our example p = 0.05, and n = 99, giving:

Mode 4 <= x <= 5

Thus 4 and 5 must be equally likely. Adding 1 (myself), I get that the most likely number of members of my group are 5 or 6, and these are equally likely.

P_m = (99!/m!n!) x (1/20)^m x (19/20)^n, where n = 99 - m.

P_5 = (99x98x97x96x95/5x4x3x2x1) x 0.05^5 x 0.95^94 = 0.18001783.

P_4 = (99x98x97x96/4x3x2x1) x 0.05^4 x 0.95^95 = 0.18001783.

It may seem contradictory that the *expectation* is not the same as the most likely number, but it is easy to understand why this is so. It is true that the expected outcome of an event whose probability is given by the familiar symmetric bell-shaped curve is the same as the number where the curve attains its maximum, but here the probability curve is *asymmetric*: there are 15 possible outcomes where the group is bigger than 5.95, but only 5 where it is smaller.

This result is in fact quite general. Suppose you are one of a total of T people assigned at random to G groups. By the same reasoning as before, the expected number of people besides yourself in your group is m*, where m* = (T-1)/G. The probability that m other people are with you is given by

P_m = (T-1)!/[m!(T-1-m)!] x (1/G)^m x [(G-1)/G]^(T-1-m) = [(T-1)(T-2)x...x(T-m)/m!] x (G-1)^(T-1-m) / G^(T-1), and

P_(m-1)/P_m = m(G-1)/(T-m).

Substituting m = T/G yields