This is a blog assignment. Title the post "My Super Brain." Each of these questions is worth 2 points. So in order to get full credit, you must get 5 correct. If you get all seven correct you will get extra credit.
1) What's the largest number of U.S. coins you can have without having even change for a dollar (how many and what coins)?
You have three boxes of fruit. One contains just apples, one contains just oranges, and one contains a mixture of both. Each box is labeled -- one says "apples," one says "oranges," and one says "apples and oranges." However, it is known that none of the boxes are labeled correctly. How can you label the boxes correctly if you are only allowed to take and look at just one piece of fruit from just one of the boxes?
3) You have a jug that holds five gallons, and a jug that holds three gallons. You have no other containers, and there are no markings on the jugs. You need to obtain exactly seven gallons of water from a faucet. How can you do it?
Second Problem: You need exactly four gallons. How do you do it?
4) Mary's mum has four children.
The first child is called April.
The second May.
The third June.
What is the name of the fourth child?
5) Cathy has twelve black socks and twelve white socks in her drawer.
In complete darkness, and without looking, how many socks must she take from the drawer in order to be sure to get a pair that match?
6) A frog is at the bottom of a 30 meter well. Each day he summons enough energy for one 3 meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?
Note: Assume after the first leap that his hind legs are exactly three meters up the well. His hind legs must clear the well for him to escape.
7) You are trapped in a room with two doors. One leads to certain death and the other leads to freedom. You don't know which is which.
There are two robots guarding the doors. They will let you choose one door but upon doing so you must go through it.
You can, however, ask one robot one question. The problem is one robot always tells the truth ,the other always lies and you don't know which is which.
What is the question you ask? What will the other robot say is the certain death door? The liar robot will tell you a lie about the truth. The truth robot will tell you the truth about a lie. That is the door that you go in.