You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?

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?

When we see 2 but call 10?

I am the beginning of the end, and the end of time and space. I am essential to creation, and I surround every place. What am I?

Every words stands for unique digit that makes the arithmetic equation true

SEVEN + SEVEN + SIX = TWENTY.

What are the digits ?

You are given with the following sum. Each of the letters can be decoded as a digit. If we tell you that D = 5, then can you solve it entirely?

DONALD
+GERALD
=ROBERT

What does this mathematical rebus means ?

100 prisoners are stuck in the prison in solitary cells. The warden of the prison got bored one day and offered them a challenge. He will put one prisoner per day, selected at random (a prisoner can be selected more than once), into a special room with a light bulb and a switch which controls the bulb. No other prisoners can see or control the light bulb. The prisoner in the special room can either turn on the bulb, turn off the bulb or do nothing. On any day, the prisoners can stop this process and say "Every prisoner has been in the special room at least once". If that happens to be true, all the prisoners will be set free. If it is false, then all the prisoners will be executed. The prisoners are given some time to discuss and figure out a solution. How do they ensure they all go free?

When Jack was six years old he hammered a nail into his favourite tree to mark his height. Ten years later at age sixteen, Jack returned to see how much higher the nail was. If the tree grew by five centimetres each year, how much higher would the nail be?

Find the next number in the series below

21 32 54 87 131 ?