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23 members have voted
Most of you will have heard of the Continetial Divide usually whereby rivers in the US either go West (i.e. towards the Pacific Ocean), East (i.e. towards the Atlantic Ocean). However there's also South (towards the Gulf of Mexico) and North (towards the Arctic Ocean or Hudson Bay etc.). Also for completness there are some areas, e.g. Death Valley, where any water would stay inland - there is a definition that if it flooded where would it go, but that's not the question.
Do you know where the river is whereby water in it could either flow to the Pacific or Atlantic? (If you google it you'll also find a lake with the same idea.)
This question was originally on QI, a TV program on BBC2 which asks questions where the obvious answer is usually wrong. For instance how many moons does the Earth currently have?
Quote: Ace2FL would be knee jerk.Quote: GialmereI'll toss in: Which US state is closest to Africa?
I’ll guess NC. Could even be MA or ME. Might need calculus for this one
Could even be Correct!

Because the earth is a sphere, Maine is the closest state.

If the Wizard wanted to stand on the spot farthest from the center of the earth (in other words closest to outer space), which mountain summit should he climb up to?
You either know the answer or you don’t.
Quote: ksdjdj
Correct!

A few posts back I stated that the earth is a sphere. I'm sorry. I lied. It's technically an oblate spheroid. The centrifugal force of the earth's rotation causes it (and the oceans) to bulge out in the equatorial region, like a pumpkin flattened at the top and bottom. Being literally the size of a planet, this isn't obvious to the human eye, but sea level at the equator is roughly 14 miles farther from the earth's center than at the poles.
A mountain is measured by its height above sea level. Using this criteria Everest is easily #1 but, it's nowhere near the equatorial bulge.
Enter Chimborazo, the highest mountain (a dormant volcano) in Ecuador. You've probably never heard of it. Why would you? From sea level, it's 8,500 feet shorter than Everest. It's not one of the highest 100 peaks in the world. In fact, it's only the 39th tallest mountain in its home range, the Andes. But Chimborazo stands at the top of the bulge, gathering almost every inch of those 14 miles, and that makes all the difference.
You might think that Chimborazo is a poor man's Everest, an easier climb you can make and truthfully say you've stood at the top of the world. Unfortunately, this isn't the case. Everest is certainly no place for beginners but, if you're in good shape, have decent skills and are with a well equipped expedition, the main route up to the summit is essentially a very long hike up a very steep trail.
In contrast, Chimborazo is capped with glaciers, much of it treacherous black ice. Only the most experienced mountaineers should even consider challenging it.

You are a gaming mathematician who has been hired by a foreign country to help set up its national lotto.
The country wants a typical powerball type set up where 5 numbered white balls are drawn from a pool of white balls in a vacuum tube hopper, and a single numbered red powerball is drawn from a pool of red balls in another hopper. To win the jackpot, a ticket must have all 6 numbers picked.
Because it is a small country, you've been asked to set the odds of winning the jackpot at (or as close as possible to) one in 300,000. Note that the ball hoppers can each contain up to 50 balls.
Using this criteria, how many numbered white balls should be placed in one hopper, and how many numbered red powerballs should be placed in the other?
Quote: GialmereAnd now back to our regular programming...
You are a gaming mathematician who has been hired by a foreign country to help set up its national lotto.
The country wants a typical powerball type set up where 5 numbered white balls are drawn from a pool of white balls in a vacuum tube hopper, and a single numbered red powerball is drawn from a pool of red balls in another hopper. To win the jackpot, a ticket must have all 6 numbers picked.
Because it is a small country, you've been asked to set the odds of winning the jackpot at (or as close as possible to) one in 300,000. Note that the ball hoppers can each contain up to 50 balls.
Using this criteria, how many numbered white balls should be placed in one hopper, and how many numbered red powerballs should be placed in the other?
Made a spreadsheet in Excel and got:
Another version could be: both bins must contain the same number of balls. That could probably be solved formulaically
Quote: Ace2Another version could be: both bins must contain the same number of balls. That could probably be solved formulaically
The problem here is, you get a sixth-degree polynomial; if N is the number of balls of each color, the closest value (not necessarily an integer) would be a solution to N N (N-1) (N-2) (N-3) (N-4) - 36,000,000 = 0.