I have ten or more daughters. I have less than ten daughters. I have at least one daughter. If only one of these statements is true, how many daughters do I have?

SEE ANSWER

I have three envelopes, into one of them I put a $20 note. I lay the envelopes out on a table in front of me and allow you to pick one envelope. You hold but do not open this envelope. I then take one of the envelopes from the table, demonstrate to you that it was empty, screw it up and throw it away. The question is would you rather stick with the envelope you have selected or exchange it for the one on the table. Why? What would be the expected value to you of the exchange?

Answer:- The answer might seem a little counter intuitive at first but we'll see... The short answer is that it is in your advantage to exchange. But why? Well initially there was a 1/3 chance that you were holding the envelope with the note in it and a 2/3 chance that the note was on the table. This is still the case after one of the envelopes on the table has been removed, there is still a 1/3 chance that you have the note and a 2/3 chance of it being on the table. If this is confusing then it may help to think that the questioner knows which envelope the $20 note is in, though in practice it doesn't actually matter. The questioner would always be able to demonstrate that the note was not in one of the envelopes on the table regardless of where the note was, so the fact that he was able to do this changes nothing. Consider a different example.... Say there are a 1000 envelopes on the table, 1 with a note inside. You pick 1 envelope, the chance that this has the note in it is clearly 1/1000, where as the chance that it is still on the table is 999/1000. Odds are its on the table. Now the questioner could, assuming he can remember where the note is demonstrate to you that the note is not in 998 of the envelopes on the table. In this case nothing would have happened to change the fact that there is only a 1/1000 chance of you having the note. That is why you exchange. What is the value of the exchange? Simply before the exchange you have 1/3 of $20 and afterwards you will have 2/3 of $20, ie the advantage to you is about $6.66

I have three feet but can't walk; I tell you things but can't talk; Sometimes I bend but I'm mostly straight. I'm like a scale but can't tell your weight. What am I?

Answer:- A yardstick.

I have three USA coins. They are not a quarter, dime or penny and they add up to 60 cents. What are the coins?

Answer:- A 50 cent piece and 2 nickels.

I hit the tall miss the small. In a flash I am gone. What am I?

Answer:- Lightning.

I know what my job is, The point has been made. You say I have a big head, And you're right, I'm afraid. Put me in my place, And then leave me alone. What I need most, Is someone to drive me home. What am I?

Answer:- A Nail!

I lead the way into the unknown, and bring strength where there is fear. I am the creator of invention, and the maker of all adventure. What am I?

Answer:- I am curiosity!

I like indigo but not blue, I like onions but not turnips, I like forms but not shapes. According to the same rule, do I like tomatoes or avocados?

Answer:- Avocadoes - I like all things that start with a preposition.