May 05, 2006
Bored? Tired of Politics? Tired of Liberals? Try These.
I enjoy brain teasers because they, unlike liberals, can be logically explained. If you want to take a rest from politics and liberals, try these puzzles that I enjoyed:
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Imagine that the set of Monty Hall's game show Let's Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does.The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn't hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors.
After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the car if she stays with her first choice? What if she decides to switch?
Should the contestant keep the original door that she picked or switch? It's one thing to know the answer, but quite another to know why it is correct. Well, you should always switch from the door you originally picked. Why? To better understand the probabilities, try this exercise.
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Three men go to stay at a motel, and the man at the desk charges them $30.00 for a room. They split the cost ten dollars each. Later the manager tells the desk man that he overcharged the men, that the actual cost should have been $25.00. The manager gives the bellboy $5.00 and tells him to give it to the men. The bellboy, however, decides to cheat the men and pockets $2.00, giving each of the men only one dollar.Now each man has paid $9.00 to stay in the room and 3 x $9.00 = $27.00. The bellboy has pocketed $2.00. $27.00 + $2.00 = $29.00 - so where is the missing $1.00?
Hint: It didn't go for taxes. Go to the bottom of the problem's link for the solution--but, only after you've tried to answer it.
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This puzzle allows you to pick one number out of a jumbled set, and the character in the game will guess your number. Well, if that doesn't make sense, just play the game and you will understand it. Click on the above link which will take you to the quiz, and advance each page by clicking on the guy at the bottom right "thumbing a ride."
How does it work? In the third grade, I learned a math concept called "casting out nines" to check my math. There's your hint. If you understand the concept, you can impress your friends by guessing their numbers.
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Wasn't that fun and a nice diversion from the worries of the world? If you didn't cheat and looked ahead at the solutions, these could keep you busy for hours--years if you're a liberal. Okay, back to work.
Posted by Woody M. at May 5, 2006 09:20 PM | TrackBack#1 - switch. I don't know why and I can't explain it but I know that the odds of choosing the right one increase by switching.
#2 - There's no math problem there. It's just worded to be confusing.
#3 - My brain is already smarting too much. I never learned how to cast nines.
Posted by Oyster at May 6, 2006 07:55 AM
Oyster, on the first one, the odds of being right with the first pick are only 1 in 3 (there are three doors when selecting) while the odds of being right on the second one is 1 in 2 (with only two doors when selecting). Just because you eliminate one of the doors in the process does not change the original odds on the first pick, which is a longer shot.
You're right about the second one. This is like the word problems in grammar school where you had to pick out what information is important and what information is given to throw you off.
The last one is much easier than you thought and can be solved in your head very quickly if you understand casting out nines, which takes about two minutes to grasp. Those techniques bought me many a "100" on arithmetic tests. I gave a talk to some businessmen and used this trick to show how "brilliant" I am with numbers. One smart-alec in the group also understood casting out nines and blurted out how I did it right in the middle of the presentation--ruining the fun illustration. Thanks a lot, buddy.
Posted by Woody at May 6, 2006 01:13 PM
Chestnuts, my precious.
But you may gets lots of mail insisting you're wrong on the first one. You're not, of course, but because the numbers are so small it seems counterintuitive to people.
Posted by Assistant Village Idiot at May 6, 2006 06:13 PM