A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?

There are 20 people in an empty, square room. Each person has full sight of the entire room and everyone in it without turning his head or body, or moving in any way (other than the eyes). Where can you place an apple so that all but one person can see it?

All of you like to eat me. I am a five-lettered word. Remove the first two and I turn into an infamous animal. Remove just the first and I become a heinous crime. Remove the first and the last and you can groove on me.

Can you guess who am I?

15 caves are arranged in a circle at the temple of doom. One of these caves has the treasure of gems and wealth. Each day the treasure keepers can move the treasure to an adjacent cave or can keep it in the same cave. Every day two treasure seekers visit the place and have enough time to enter any two caves of their choice.

How do the treasure seekers ensure that they find the treasure in the minimum number of possible days?

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 ?

There is a jar in which there are two types of candies.
20 blueberries and 16 strawberries. You perform the following steps:
1) You take out two candies.
2) If the two candies are of the same flavour, you add a blueberry one otherwise, you add the strawberry one.

You repeat these two steps till there is just one candy remaining in the jar. Which flavoured candy will be left?

There are two guys standing face to face in a room. On a wall, there is a clock. One of those is a prophet. He tells the other guy that he will be stabbed in the back in five minutes.

Shocked to hear that, the other guy stares at the clock. Just after the five minutes, he is stabbed on the back. Can you tell what happened?

Replace the question mark with the correct number.

2 + 2= 4
3 + 3= 18
4 + 4= 48
5 + 5= ?

In a box, there is a jumble of 7 red balls, 6 blue balls, 5 green balls, and 4 yellow balls. What is the minimum number of balls, will you have to pick up so that you have at least 4 balls of the same colour?

What is the next number in the series?

15 29 56 108 208 ?