Some cool puzzles

Game show puzzle:

Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the other two doors are goats. You pick a door and the host (who knows where the car is) opens door #3 which has a goat. The host will always open a door with a goat.

He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?

The answer is:

Yes; you should switch

I love this puzzle because people always say that it doesn't matter and you have a 50/50 chance. Truth is you have a 66% chance by switching.

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Candy problem

Suppose you have 3 bags of candy. They are labeled mixed (red & green), red, green. You know that ALL the bags are labeled wrong. How do you determine which bag has which flavors by only opening up one bag and taking out ONE piece of candy?

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Hey Bio, I didn't know red and green were a flavor?

I have heard of the first one and with that answer. I still am not sure I agree though.

Haven't heard of the second one. Thinking on it.

I wasn't sure if I should have posted the answer. Maybe I should remove it so people can guess. The answer does seem illogical at first, but when you think about it and finally understand it, it becomes so clear.

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Answer to puzzle 2 here:

It's actually very easy, if you write it down (can't do that on a gameshow, though)

http://www.thefastlanetomillions.com...html#post61117

-Russ H.

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Runum,

Here is a way to think about this problem/solution that will make it clear that this is the correct way to optimize EV:

In the original problem, you have three doors, you pick one, the game show host (who knows which door the prize is behind) eliminates another, and you have the choice to switch or stay. It seems like the chances are the same whether you stay or switch, but they're not.

To better see why, imagine that the same game show offers a game where you have 1 million doors. You are asked to pick a door. You do. It should be clear that your chance of picking the correct door is 1 in a million, right?

Now, let's say the game show host eliminates doors one-after-another (though again, he knows where the prize is, and never eliminates that one). Eventually, he eliminates 999,998 other doors, leaving the one you picked and one other.

He asks if you'd like to keep your door or switch to the other door...what do you do?

Does your door have a 50/50 chance of being the right door just because there are two left? No, it should be obvious that your door is still a 1 in a million long-shot, and the other door most likely has the prize.

Does that make more sense?

The key to this puzzle is that the game show host knows where the prize is, and will never eliminate that particular door...it's easier to get a feel for the math when you take the puzzle to a logical extreme...

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J Scott
http://www.reistartup.com

Great explanation, JScott.

Has anyone here every seen the movie "21"? They actually have a little part in the beginning about this puzzle in the beginning.

My favourite brain teaser:

You are driving down a road in the forest which suddenly splits in two, forming a fork. There aren't any signs or other indications which fork leads you to your destination. There is a house beside the fork in the road in which two sisters live. One sister always lies, and one always tells the truth. If you can only ask a single question to either one of the sisters, what would you ask in order to find out which way is the right way?

This is a cool one :-)

I love these things, keep posting!

"Which way would your sister tell me to go to get to my destination?"

Then go the other way...

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J Scott
http://www.reistartup.com

This is what first came to my mind while reading the post as well!

That was a pretty cool demonstration during his class in the movie.

-Alex

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Nice work, J :-)

Three men, and they go to this hotel. There, the manager tells them that there is only one room left. The three people share that room for $30 so each person pays $10.

Later the manager found out that the room is only $25. He calls the bell boy and tells them to give them $5 back the bell boy decides that since you cannot divide $5 by 3 people, so he takes $2 for himself and returned to $1 each person.

So now each person paid $9 and the bell boy has a $2.

$9 * 3 = $27 plus the bell boy's $2 is $29 dollars.

Where is the extra dollar?

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The government?

I always liked this one. 30-3=27 minus his 2 equals 25.

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#1 If you take 2 apples from 3, how many do you have?

#2 You have 5 straight lines with 4 dots in each line. Several dots can be used in more than one line Draw 5 lines with only 10 dots.

Ex: 2 lines with only 7 dots.
.
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. . . .

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