Thursday, May 1, 2008

Puzzlers

A friend of mine passed along some puzzlers, and now I pass them on to you. The answers will be in the comments, so you needn't spoil yourself by accident.

1. You're on the old TV game show "Let's Make a Deal." Monty Hall presents you with a choice of three doors. Behind one of the doors is a shiny new car. Behind each of the other doors is a goat. You choose Door Number One. Monty Hall, knowing which door conceals the car, opens Door Number Three and reveals one of the goats. Then he asks if you would like to switch your choice to Door Number Two. If you changed your choice, would you be more likely or less likely to win the new car, or would your chances stay the same?

2. There is three things wrong with this sentance. What are they?

3. You're sailing on a small, closed lake when you throw a 50-pound anchor over the side, and it sinks right to the bottom. Does the water level rise, go down, or stay the same?

4. You're driving over a steep hill. The uphill side is one mile long, and the downhill side is one mile long. Going uphill, your average speed is 30 miles per hour. What speed must you average on the downhill side to have an average speed of 60 miles an hour going up and down?

4 comments:

Robbie F. said...

ANSWERS: 1. You are 16% more likely to win the car if you switch your choice. Why? Because when you guessed Door #1, you had a 33:66 chance of winning the car. But if you choose Door #2 now, you have a 50:50 chance of winning.

2. There is no answer; it is a paradox. Unless you count "three" as a mistake, there are only two mistakes. But if you count "three," it is no longer a mistake.

3. The water level goes down when you throw the anchor in, because the weight of the anchor (inside the boat) displaces more water than the volume of the anchor (outside the boat). So, theoretically, if the lake was full of boats and they all weighed anchor at the same time, they could cause a flood.

4. It is impossible to average 60 mph over a 2-mile hill after averaging 30 mph on the first mile. Why? Because you would have to cover an average of 1 mile per minute, and having taken 2 minutes to travel the first mile, your time is already up.

Joseph said...
This comment has been removed by the author.
Feresto said...

i got the first three correct. however the 4th one was not explained properly. all you would have to do to achieve an average speed of 60 mph over the hill would be to go very fast downhill. you would have 30 seconds to get down the hill, that would mean going at a speed of 120mph

by my calculations.. it can be done

Robbie F. said...

Sorry, Feresto. If you averaged 30 mph on the first mile, it took you 2 minutes to get to the top of the hill. To average 60 mph over all, you have to cover both miles in 2 minutes. Therefore, you would have to cover the 2nd mile at infinite speed, which is, needless to say, impossible.