2, 3, 5, 9, 17, _ What is the next number in the sequence?

I hide my treasure in the ground, my tail is big and fluffy. If you spot me in a tree, please don’t call me scruffy. What am I?

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

I cannot talk, but I always reply when spoken to. What am I?

I welcome the day with a show of light, I stealthily came here in the night. I bathe the earthy stuff at dawn, But by noon, alas! I'm gone.

Can you find the 09 errors in the picture below?

2 ladies and 2 girls need to cross a river in a boat big enough for 1 LADY or 2 girls. How do they do it?

If a shopkeeper can only place the weights on one side of the common balance. For example, if he has weights 1 and 3 then he can measure 1, 3 and 4 only. Now the question is how many minimum weights and names of the weights you will need to measure all weights from 1 to 1000? This is a fairly simple problem and very easy to prove also.

Decode below three cipher riddles:

26 L of the A
7 D of the W
1000 Y in a M

There are 2 people near the river and both of them want to get on the other side. The boat can only take one of them. But they got across.
How?