Some short puzzle collections

Click on questions for hints. Kindly bear with the terse hints.

1. If 6 cats can kill 6 rats in 6 minutes, how many cats will be needed to kill one rat in one minute ?
   Different answers are possible - not just 6.
   
2. An angry commander ordered 10 soldiers to stand in 5 rows of 4 each. Explain?
   A star
   
3. How to divide a regular hexagon into eight identical parts ?
   First divide it into 24 parts.
   
4. Tell me whether the following statement is true or false - "This statement is false."
   Neither true nor false
   
5. A man born in the first half of the 19th century was x years old in the year x^2. Which year was he born in?
   1806
   
6. If two people want to divide a pie but do not trust each other, they can still ensure that each gets a fair share by using the technique that one person cuts and the other person chooses. Generalize this technique to more than two people. Take care to ensure that no one can be cheated by a coalition of the others.
   Hmm ....
   
7. An Arab sheikh tells his two sons to race their camels to a distant city to see who will inherit his fortune. The one whose camel is slower will win. The brothers, after wandering aimlessly for days, ask a wise man for advise. After hearing the advice they jump on the camels and race as fast as they can to the city. What does the wise man say?
   Swap them
   
8. You have four pieces of a broken chain each with three links intact. For repairing the chain, opening and joining each link costs Rs 10. How to make it circular by joining all pieces together and spending not more than Rs 30 ?
   Dissemble one piece.
   
9. Four bugs are placed at the corners of a square. Each bug walks always directly towards the next bug, at any instant, in the clockwise direction. How far do each bug walk before they meet ? (All bugs walk with same speed)
   Equal to the side.
   
10. You want to send a valuable object to a friend. You have a box which is more than large enough to contain the object. You have several locks with keys. The box has a locking ring which is more than large enough to have a lock attached. But your friend does not have the key to any lock that you have. How do you do it? Note that you cannot send a key in an unlocked box, since it might be copied.
    Lock and send it. Your friend will put one more lock and send it back to you.
    
11. Start with a half cup of tea and a half cup of coffee. Take one tablespoon of the tea and mix it in with the coffee. Take one tablespoon of this mixture and mix it back in with the tea. Which of the two cups contains more of its original contents?
    None.
    
12. A uniformly and infinitely elastic rubber band is attached to a wall at one end and to a car at the other end. The car is moving at 1 m/sec while a bug on the band, starting from wall, is only moving at 1 cm/sec towards car. Will the bug ever reach the car?
    It will.
    
13. Make the following equation to be correct by adding only one straight line. The symbol "does not equal" does not belong to solution. 5+5+5 = 550
    Make a "4" out of a "+"
    
14. Two boxes are labeled "A" and "B". A sign on box A says "The sign on box B is true and the gold is in box A". A sign on box B says "The sign on box A is false and the gold is in box A". Assuming there is gold in one of the boxes, which box contains the gold?
    Box B
    
15. Find a number ABCDEFGHIJ such that A is the count of how many 0's are in the number, B is the number of 1's, and so on. There is only one such number. (Can we generate this number?)
    6210001000
    
16. Suppose I place a rupee coin and a five rupee coin on the table, and make you the following offer: If you make a true statement, I will give you one of the coins. If you make a false statement, I will give you neither coin. What statement can you make that will force me to give you the five rupee coin?
    You will not give me that rupee coin. Or You will either give me (a) a million rupees plus at least one of the coins, or (b) neither of the coins ... !?