Find the next number in the sequence

1, 2, 6, 21, 88, __?

Prove that the below maths equation is true.

8 + 8 = 91

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equal to 1/3.

(You can use one number only once)

P is the father of Q and S is the son of R. T is the brother of P and has a daughter U. If R is the sister of P, then what is the relation between U, Q and S?

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different. How do you measure 45 minutes?

A sundial has the fewest moving parts of any timepiece. Which has the most?

A girl rode into a tourist spot out of the city on Thursday. She loved the place and decided to stay for a few days. She stayed for four days and then she left for back home on Thursday.

How can this be possible?

In a science lab, a petri dish hosts a healthy colony of yeast for an experiment. Now every minute, all the yeast cells divide into two. At noon, there was just a single cell of yeast and at 1:22, the Petri dish was half full. Can you calculate when the dish will be full of yeast?

If I put in one bird per cage, I have one bird too many. If I put in two bird per cage, I have one cage too many. How many cages and birds do I have?

Can you count the number of squares in the figure below?