What is both possible and impossible at the same time?

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

One is to three as three is to five and five is to four and four is the magic number.
What is the pattern?

You have two buckets - one holds exactly 5 gallons and the other 3 gallons. How can you measure 4 gallons of water into the 5 gallon bucket?

(Assume you have an unlimited supply of water and that there are no measurement markings of any kind on the buckets.)

Below the four parts have been reorganised. The four partitions are exactly the same in both arrangements. Why is there a hole?

A man and a dog were going down the street. The man rode, yet walked. What was the dog’s name?

I’m orange, I wear a green hat and I sound like a parrot. What am I?

You along with your friend are standing in front of two houses. Each of those houses inhabits a family with two children.

Your friend tells you the below two facts:
1) On your left is a family that has a boy who likes accounts but the other child loves science.
2) On the right is a family with a seven-year-old boy and a newborn baby.

You ask him, "Does either of the family have a girl?"

To this, he replies, "I am not quite sure. But can you guess that? If you are right, I will give you $500."

Which family do you think is likely to have a girl?

You see me once in June, twice in November, and not at all in May. What am I?

I hide my treasure in the ground, my tail is big and fluffy. If you spot me in a tree, please don’t call me scruffy. What am I?