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charliepatrick
charliepatrick
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August 22nd, 2020 at 4:09:28 PM permalink
While we're on the main theme of weird places, here's another teaser about rivers flowing to the ocean.

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?
Gialmere
Gialmere
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August 23rd, 2020 at 5:55:32 PM permalink
Quote: Ace2

Quote: Gialmere

I'll toss in: Which US state is closest to Africa?

FL would be knee jerk.

Iíll 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.
Have you tried 22 tonight? I said 22.
Gialmere
Gialmere
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August 23rd, 2020 at 6:05:44 PM permalink
Here's a tough one...



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?
Have you tried 22 tonight? I said 22.
ksdjdj
ksdjdj
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Gialmere
August 24th, 2020 at 12:58:56 AM permalink
Mount Chimborazo***
***: see >>> link <<< here
Ace2
Ace2
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August 24th, 2020 at 8:55:49 AM permalink
My guess was going to be Kilimanjaro as it was the first mountain near the equator(ial bulge) that came to mind.

You either know the answer or you donít.
Itís all about making that GTA
Gialmere
Gialmere
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August 24th, 2020 at 10:22:53 AM permalink
Quote: ksdjdj

Mount Chimborazo***
***: see >>> link <<< here


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.
Have you tried 22 tonight? I said 22.
Gialmere
Gialmere
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August 24th, 2020 at 10:47:20 AM permalink
And 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?
Have you tried 22 tonight? I said 22.
unJon
unJon 
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Gialmere
August 24th, 2020 at 10:59:44 AM permalink
Quote: Gialmere

And 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:

18 white balls and 35 red balls which has 299,880 combinations so pretty darn close.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
Ace2
Ace2
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August 24th, 2020 at 11:43:33 AM permalink
Since the number of red and white balls are independent variables, I donít think thereís any way to solve this besides trial and error

Another version could be: both bins must contain the same number of balls. That could probably be solved formulaically
Itís all about making that GTA
ThatDonGuy
ThatDonGuy
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August 24th, 2020 at 12:49:28 PM permalink
Quote: Ace2

Another 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.

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