Riddle ;)
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 Audio Lead Emeritus
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 Joined: Fri Jul 25, 2003 1:52 pm
 Location: Cincinnati OH, USA
long long ago .....
i don't know if it's right but :
obvious the solution is not 25mph
say the car runs for an hour with 30mph in one direction and than with 20mph in the other (which needs 1.5hours) so
1h * 30mph + 1.5*20mph = 60miles,
the car has gone 60miles in 2.5 hours, so the average speed was 24mph.
plz, don't laugh, it's really long ago
i don't know if it's right but :
obvious the solution is not 25mph
say the car runs for an hour with 30mph in one direction and than with 20mph in the other (which needs 1.5hours) so
1h * 30mph + 1.5*20mph = 60miles,
the car has gone 60miles in 2.5 hours, so the average speed was 24mph.
plz, don't laugh, it's really long ago
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Can COWs fly?
Can COWs fly?
24 mph
Edit: oops. Next time i should make sure I read the entire thread...
So, here's my solution.
Let d be the (unspecified/unimportant) distance
v1 the velocity for one route (30 mph), v2 the route back (20 mph)
So it takes t = D/v1 + D/v2 time in total for the whole trip. The average speed therefor is v = 2D/t = 2D/(D/v1 + D/v2).
Multiply numerator and denominator with 1/D => v = 2/(1/v1 + 1/v2)
Edit: oops. Next time i should make sure I read the entire thread...
So, here's my solution.
Let d be the (unspecified/unimportant) distance
v1 the velocity for one route (30 mph), v2 the route back (20 mph)
So it takes t = D/v1 + D/v2 time in total for the whole trip. The average speed therefor is v = 2D/t = 2D/(D/v1 + D/v2).
Multiply numerator and denominator with 1/D => v = 2/(1/v1 + 1/v2)
Ghetto rig all three lamps to turn on with only one of the switches. Problem solved.

Here is one of my favorite 'riddles' :
Say that a certain game show has a feature where a contestant is presented with three doors. A worthwhile prize is behind only one of the doors. The contestant is instructed to pick one of the three doors. Afterwards, the host always opens one of the remaining doors that does not have the prize behind it, and then questions the contestant about whether they want to remain with their chosen door or switch to the remaining door.
The question  What is the rule of thumb that provides a higher 'statistical' chance of winning?
sorry, I'm just a stats junkie

Here is one of my favorite 'riddles' :
Say that a certain game show has a feature where a contestant is presented with three doors. A worthwhile prize is behind only one of the doors. The contestant is instructed to pick one of the three doors. Afterwards, the host always opens one of the remaining doors that does not have the prize behind it, and then questions the contestant about whether they want to remain with their chosen door or switch to the remaining door.
The question  What is the rule of thumb that provides a higher 'statistical' chance of winning?
sorry, I'm just a stats junkie
In germany the show was/is called "Geh auf's Ganze".
At the moment, i'm too lazy to do the math, but the contestant is wise if he always change his mind. He should always chose the door, which the host left in the game.
But the the german show, those steps were changed Now, the contestant has also to chose which of the left doors, the host should open. this way the likelyhood is always the same.
At the moment, i'm too lazy to do the math, but the contestant is wise if he always change his mind. He should always chose the door, which the host left in the game.
But the the german show, those steps were changed Now, the contestant has also to chose which of the left doors, the host should open. this way the likelyhood is always the same.
Press any key to continue or any other key to cancel.
Can COWs fly?
Can COWs fly?
He should switch doors. I forget the specifics, but it comes down to the probability given the host has selected one of the remaining two doors, making the other one more likely to contain a prize than the original door picked by the contestant.Pink wrote:The question  What is the rule of thumb that provides a higher 'statistical' chance of winning?
When he did the first choice, he had a 1/3 chance of picking the right door. The secound time one of the false doors are eliminated so he has 1/2 chance of picking the right door if he changes. It is either the door he took from the beginning or the other one. But it's still only 1 in 3 that the first door he choosed has the prize.
Well, as with most of the german shows, the original is a show from the US. Forgot the name, though. And in this show there were 2 Goats and 1 Price...
And here is a different proof that the chance of winning is 2/3 if you switch doors:
Let's assume that the winning door is A, then depending on the door you chose first, the way to win is:
If you chose A, stay.
If you chose B, switch.
If you chose C, switch.
(keep in mind that after the moderator opened a door with a goat, there are only 2 left)
So, in 2 of 3 cases, switching is better.
And if you still don't believe it, think of it in this way: Just assume that you have 1000 doors instead of 3. Only 1 win, 999 blanks. After you chose one door, the hosts openes 998 doors with blanks.
Do you still believe that you got lucky in the first guess and have chosen correctly (chance 1:1000), or do you think the remaining door holds the price?
And here is a different proof that the chance of winning is 2/3 if you switch doors:
Let's assume that the winning door is A, then depending on the door you chose first, the way to win is:
If you chose A, stay.
If you chose B, switch.
If you chose C, switch.
(keep in mind that after the moderator opened a door with a goat, there are only 2 left)
So, in 2 of 3 cases, switching is better.
And if you still don't believe it, think of it in this way: Just assume that you have 1000 doors instead of 3. Only 1 win, 999 blanks. After you chose one door, the hosts openes 998 doors with blanks.
Do you still believe that you got lucky in the first guess and have chosen correctly (chance 1:1000), or do you think the remaining door holds the price?

 Creative Contributor
 Posts: 1060
 Joined: Sun Jun 29, 2003 12:40 am
 Location: Tucson, Arizona USA
Another alalogy, a bag with 2 Black and 1 white marble. Reach in and take out a marble and keep it in your fist without looking at it. A Blck Marble is then removed from the bag, do you switch the one in your hand with the one remaining in the bag to get the white marble?
Fear is the Mind Killer  Frank Herbert Dune