Find the next number in the sequence

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

What is the word or phrase?

What is the fewest number of coins that would be required in order to make sure each and every coin touches exactly three other coins?

You have to fill the below given grid in a manner that every row and column contains the digits 1 to 6. Also, make sure that the squares that are connected with each other must contains the same digit.

Today, I celebrated my 32nd birthday but I was born in 1972.
How is this possible?

It is always ahead of me yet I can never see it. What is it?

A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 3 hours to fill the tank with the large inlet pipe. On the other hand, it takes 6 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 9 hours.

What fraction of the tank (initially empty) will be filled in 0.64 hours if all three pipes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).

There's one "sport" in which neither the spectators nor the participants know the score or the leader until the contest ends.

What is it?

A time long back, there lived a king who ruled the great kingdom of Trojan House. As a part of the renovation of the kingdom to meet future security needs, he asked his chief architect to lay down a new play in a manner that all of his 10 castles are connected through five straight walls and each wall must connect four castles together. He also asked the architect that at least one of his castles should be protected with walls. The architect could not come up with any solution that served all of King's choices, but he suggested the best plan that you can see in the picture below. Can you find a better solution to serve the king's demand?

It is a 5 letter word if you take away first letter it is something you get from sun, if you remove second letter you will get something to eat, if you remove third letter you get a word you use in pointing at and if you remove the fourth letter you get something to drink. What is it?