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Monty Hall, we have a PROBLEM

Re: Monty Hall, we have a PROBLEM

The Sicatoka said:
I pulled out the 1/4" grid paper and the circle template and the scale (too lazy to do the math on a Friday afternoon).

Now this is all by eyeball (pencil and paper), but I could see something like a 2.6875' radius working. (I did the two equal right triangles thing as a starting point.)
Click to expand...

The answer, published today, turns out to be r=2.70545. They did use trigonometry in their solution.


It apparently turns out that, whether you line up your semi-circles such that the diameter is along each long side, or whether the diameter is along the diagonal of the rectangle, depends upon the dimensions of the rectangle. In the case of 8' x 4' they used the diagonal of the rectangle for the diameter of the semi-circle.
 
Re: Monty Hall, we have a PROBLEM

ScoobyDoo said:
I'm not going to do the math but if you cut the rectangle into two equal Right Triangles and then make the largest semi circle you can inside the right triangles I believe you will end up with the biggest pieces.
Click to expand...

I was thinking 'just set them opposite each other' but that works too
 
Re: Monty Hall, we have a PROBLEM

FreshFish said:
This problem probably could also be solved empirically....

We were discussing whether the rate of change of length of day was the same throughout the year.

We know that the shape of the earth's orbit is an ellipse. At the "pointier" ends of the ellipse, we have the solstices, and at the "flatter" sides of the ellipse, we have the equinoxes.

I was thinking that the rate of change of the length of day would be greater at the equinoxes and smaller at the solstices: the earth in effect has to slow down more to round the pointier end and speed up more slowly after it rounds the pointier ends, does it not? and it goes through the "flatter" sides more quickly, no?





PS for some reason, I also find it interesting that, even though the summer solstice is the longest day of the year, in this part of the country at least, the earliest sunrise comes before the solstice and the latest sunset comes after the solstice.
Click to expand...

For the general lay person we can say that the length of day is sinusoidal. Now, the sun not being a point-mass and other fun things about spin and orientation changes that. But knowing this, the rest is an application of calculus taken appropriately
 
Re: Monty Hall, we have a PROBLEM

No fair looking up the answer on the internet, memory only...

Among the so-called major 4 US pro sports leagues (MLB, NFL, NBA, NHL), six sets of teams have the same mascot. (sort of like in college, how U Washington and U Connecticut are each "The Huskies"). Which ones are they?
 
Re: Monty Hall, we have a PROBLEM

FreshFish said:
No fair looking up the answer on the internet, memory only...

Among the so-called major 4 US pro sports leagues (MLB, NFL, NBA, NHL), six sets of teams have the same mascot. (sort of like in college, how U Washington and U Connecticut are each "The Huskies"). Which ones are they?
Click to expand...
Jets
Rangers
Kings
Sox

ETA: Oh, and Giants
 
Re: Monty Hall, we have a PROBLEM

FreshFish said:
No fair looking up the answer on the internet, memory only...

Among the so-called major 4 US pro sports leagues (MLB, NFL, NBA, NHL), six sets of teams have the same mascot. (sort of like in college, how U Washington and U Connecticut are each "The Huskies"). Which ones are they?
Click to expand...

Texas MLB - New York NHL
St. Louis MLB - Arizona (via St. Louis) NFL
New York NFL - San Francisco (via New York) MLB
and... um...
Carolina NFL - Florida NHL
I can't think of any others.

Edit: Oh, Christ: New York NFL - Winnipeg NHL I'm an idiot.
 
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Re: Monty Hall, we have a PROBLEM

Kepler said:
Texas MLB - New York NHL
St. Louis MLB - Arizona (via St. Louis) NFL
New York NFL - San Francisco (via New York) MLB
and... um...
Carolina NFL - Florida NHL
I can't think of any others.
Click to expand...

Yeah, I completely blanked on the Panthers.

Panthers
Cardinals
Giants
Kings
Rangers
Jets

So, six teams.
 
Re: Monty Hall, we have a PROBLEM

For the record, no MLS team shares a nickname with any of the other major sports league teams (closest would be Real Salt Lake and the Royals).

On that note, if we add MLS to the "Major" list, which two cities are the only ones to win a championship in all 5 leagues?
 
Re: Monty Hall, we have a PROBLEM

Jimjamesak said:
For the record, no MLS team shares a nickname with any of the other major sports league teams (closest would be Real Salt Lake and the Royals).

On that note, if we add MLS to the "Major" list, which two cities are the only ones to win a championship in all 5 leagues?
Click to expand...

My guess would be Chicago and Los Angeles: If memory serves correctly the LA Raiders won a Super Bowl during their brief foray in LA.
 
Re: Monty Hall, we have a PROBLEM

Jimjamesak said:
For the record, no MLS team shares a nickname with any of the other major sports league teams (closest would be Real Salt Lake and the Royals).

On that note, if we add MLS to the "Major" list, which two cities are the only ones to win a championship in all 5 leagues?
Click to expand...

Seattle and LA?

*edit* Nevermind. Mariners are terrible. Gotta be Chicago and LA then.
 
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Re: Monty Hall, we have a PROBLEM

Chicago and LA would be the answer. Seattle is short a World Series, New York and Boston are short an MLS Cup.

Of course don't let that distract you from the fact that the Revolution have lost 4 Finals...
 
Jimjamesak said:
Chicago and LA would be the answer. Seattle is short a World Series, New York and Boston are short an MLS Cup.

Of course don't let that distract you from the fact that the Revolution have lost 4 Finals...
Click to expand...

But back in the day, the Cosmos won the NASL. Does that count?
 
joecct said:
But back in the day, the Cosmos won the NASL. Does that count?
Click to expand...
That's actually interesting conversation to have regarding soccer history in this country. I would consider an NASL (1968-1984) Title as equivalent but some don't. It's kind of in the same realm of including pre-Super Bowl NFL Titles (or AFL Titles).
 
Re: Monty Hall, we have a PROBLEM

Jimjamesak said:
That's actually interesting conversation to have regarding soccer history in this country. I would consider an NASL (1968-1984) Title as equivalent but some don't. It's kind of in the same realm of including pre-Super Bowl NFL Titles (or AFL Titles).
Click to expand...

NASL and Pre-Super Bowl NFL titles should count.

The AFL... that's tricky. My instinct is no, you only count the top league in the sport in a given year (e.g., the WHA can suck it.)
 
What's the better deal?

A 6 inch slice of pizza cut at a 60 degree angle for $1.30...

Or a 7 inch slice of pizza cut at a 45 degree angle for $1.60?
 
Re: Monty Hall, we have a PROBLEM

Are that pie squared?

7*7 = 49*3.14 = 153.86. You're getting 1/8th of that pie, so 153.86/8 = 19.2325 in^2

6*6 = 36*3.14 = 113.04. You're getting 1/6th of that pie, so 113.04/6 = 18.84 in^2

19.2325/1.6 = 12.02
18.84/1.3 = 14.19

You get more pizza per dollar with the 6" pizza that gives you a full radian of the pie, but you get slightly more pizza with the 45-degree slice of the 7" pie.
 
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