• ### Quick! A car drove up a hill at 20 mph and down the hill at 30 mph, what was its average speed for the entire trip?

No, I'm not going to tell you how far it is up or down the hill. Who can get the correct answer first, along with an explanation?
No, I'm not going to tell you how far it is up or down the hill. Who can get the correct answer first, along with an explanation?
6 answers · Mathematics · 3 years ago
• ### Find the two numbers...?

The following question came off the Mensa Puzzle Calendar for 2007. "The square of the first number plus the second number equals 7. And the square of the second number plus the first number equals 11." There's an obvious trivial solution, but there are also three other real solutions. I'm most interested in the 3 other... show more
The following question came off the Mensa Puzzle Calendar for 2007. "The square of the first number plus the second number equals 7. And the square of the second number plus the first number equals 11." There's an obvious trivial solution, but there are also three other real solutions. I'm most interested in the 3 other solutions. Answers must be provided in radical form, *not* as decimal approximations. Are you up to the challenge?
• ### How do I keep myself motivated to answer questions if there is no level 8?

I'm not really answering questions to get points, but now that I have reached the top milestone I'm reevaluating why I answer questions here. I feel I've help a lot of people, especially in Mathematics, but now I'm realizing I don't feel the same "enjoyment" I used to feel in helping people out. Anyone get feelings... show more
I'm not really answering questions to get points, but now that I have reached the top milestone I'm reevaluating why I answer questions here. I feel I've help a lot of people, especially in Mathematics, but now I'm realizing I don't feel the same "enjoyment" I used to feel in helping people out. Anyone get feelings like this after answering lots of questions? Can anyone give me a fresh perspective on answering questions and remind me of that enjoyment. Do you have suggestions on how I can get motivated again?
• ### Puzzle: How can you save the 100 prisoners from execution?

The warden of a jail goes to the 100 prisoners in the jail and tells them he has a problem with overcrowding. He devises the following test where he will put a hat, either white or black, on the head of each of prisoner. There will be at least one hat of each color, but beyond that there is no limit to the number of hats of each color. The... show more
The warden of a jail goes to the 100 prisoners in the jail and tells them he has a problem with overcrowding. He devises the following test where he will put a hat, either white or black, on the head of each of prisoner. There will be at least one hat of each color, but beyond that there is no limit to the number of hats of each color. The prisoners can see everyone else's hat, but their own. After the test commences, they will not be able to signal or otherwise communicate other than to say 'WHITE' or 'BLACK'. He also says that the test will be all pass or all fail. So everyone must state their hat correctly, but if any one person states incorrectly, all 100 prisoners will be executed. The prisoners are given 20 minutes to discuss the situation and then will have the hats placed on their heads. So they go and discuss for some time. And after they come back, the warden starts the test. Interestingly, each of them answers correctly and hence all are released. How?
• ### This question will be rhetorical once I ask it... will I lose a level?

I just made level 5 and am at 5002 points. If I ask a question I understand I'll lose 5 points, but will I drop down to level 4 also?
I just made level 5 and am at 5002 points. If I ask a question I understand I'll lose 5 points, but will I drop down to level 4 also?