daily life puzzles

lion bait puzzle

A sheep sits in the middle of a field surrounded by n lions . Any lion can eat the sheep but, as each lion knows, it would become so tired that it would be as defenseless as a sheep itself–easy prey for another hungry lion who would in turn become tired and defenseless. The lions are all hungry , rational, but not suicidal. Would any lion eat the sheep? 

The solution is based on the number of lions in the circle – if it’s odd or even.

Start with the most basic case  – if there is one lion and one lamb the lamb get’s eaten – there is no threat for lion  after getting a little tired. If there are two lions and one lamb, the lamb is safe because the act of attacking the lamb puts the first lion  at risk of being eaten.

Now extend that to three lions. One lion will eat the lamb and the other two will look at each other and realize that they don’t want to be eaten by the other so that lion  in the middle is now safe

This can then be extended to any n quantity of lions

You have a bucket of jelly beans. Some are red, some are blue, and some green. With your eyes closed, pick out 2 of a like color. How many do you have to grab to be sure you have 2 of the same?

ANS :

To be sure, to pick atleast 2 marbles of a same color we need to grab at least 4 marbles, since the worst case is that three of them are different, the fourth marble has to be a repetition of one of three colors.

Q I have 2 coins. One of them is a two-headed coin, and the others are normal coins. I pick a coin, and then I flip that coin two times; each time is heads. What is the probability that the coin is two-headed?

• 1/2 chance of getting a double headed coin (so would get head both times)
• 1/2 *1/2*1/2 chance of getting a normal coin and two heads

  So, Probability is (1/2)/(1/2 + 1/8)=4/5