In a supermarket, there is an intelligent glass pane before a refrigerating unit. This glass pane allows cherries and apples through it but does not allow grapes and Orange to pass through it.

Can you identify the rule that the glass pane is following?

Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

What does the following represent?

N N N N N N N

A A A A A A A

C C C C C C C

In the image given, you can find several triangles. Can you count them all?

You have two jars of chocolates labelled as P and Q. If you move one chocolate from P to Q, the number of chocolates on B will become twice the number of chocolates in A. If you move one chocolate from Q to P, the number of chocolates in both the jars will become equal.

Can you find out how many chocolates are there in P and Q respectively?

We have arranged an array of numbers below. What you have to do is use any kind of mathematical symbol you know excluding any symbol that contains a number like cube root. You can use any amount of symbols but you have to come up with a valid equation for all of them.

0 0 0 = 6
1 1 1 = 6
2 + 2 + 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

Do you know who was buried in John's tomb?

Can you count the number of seconds in a year?

Clue: You need to bother about calculation.

Consider this: Arnold Schwarzenegger has a big one. Michael J. Fox has a small one. Prince doesn’t have one. The Pope has one but never uses it. Bill Clinton has one and uses it all the time. What is it?