Find the next number in the sequence

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

A man lives on the fifteenth floor of an apartment building. Every morning he takes the elevator down to the lobby and leaves the building. In the evening, he gets into the elevator, and, if there is someone else in the elevator, or if it was raining that day, he goes back to his floor directly. Otherwise, he goes to the tenth floor and walks up five flights of stairs to his apartment. Can you explain why he does this?

The day after tomorrow will be three days before Tuesday. Can you find out what is today?

I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?

Remove two matchsticks to make the below equation correct.

The host of a game show offers the guest a choice of three doors. Behind one is an expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

Count the number of triangles in the below picture?

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

With the help clues provided in the image, can you find the 5 digit key?

If an electric train is travelling south, then which way is the smoke going?