Find the next number in the series below

21 32 54 87 131 ?

Twenty frogs are sitting on a log floating on the surface of a river. Two of them decide to jump off into the water.

How many frogs are there on the log at this moment?

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 ?

A finger goes in me. You fiddle with me when you're bored. The best man always has me first. What am I?

Which Number is the odd one out?

A) 7145
B) 2716
C) 5321
D) 4135

In a guessing game, five friends had to guess the exact numbers of apples in a covered basket.
Friends guessed 22, 24, 29, 33, and 38, but none of the guesses was correct. The guesses were off by 1, 8, 6, 3, and 8 (in random order).

Can you determine the number of apples in a basket from this information?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

How many triangles are there in the picture below?

What always comes into a house through the keyhole?

There is one thing that goes round the house and also inside the house but never even share a brief touch. What is it?