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

In a kingdom, King George did not allow any citizen to visit the world outside. Also, only a person with proper paperwork was allowed to enter or he was sent back. A wooden bridge was what connected the kingdom to the world. The king had appointed a sharpshooter who would check the every five minutes on the bridge to check. After checking, he would go back to his hut and return exactly after five minutes again. The bridge took 9 minutes to cross.

A merchant was able to escape the kingdom without harming the shooter. How?

The following "Brain Bat" means Slow Down.
S
L
O
W

Using the same logic, can you tell us what does the following Brain Bat means ?
E
V
I
G

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

Four men were in a boat on the lake. The boat turns over, and all four men sink to the bottom of the lake, yet not a single man got wet! Why?

A thief is convicted in Mexico. He gets the death penalty. The judge allows him to say the last sentence to determine how the penalty will be carried out. If the thief lies, he will be hanged, if he speaks the truth he will be beheaded. The thief tells the last sentence and to everybody's surprise some minutes later he is set free because the judge cannot determine his penalty. What did the thief say?

As easy as you can get into me, it is as hard to get out of me.

Do you know what I am?

12345 a famous South Indian actor
567 is a path in jumbled form
8 & 10 are same letters
9 is one among the first six alphabets.
WHO AM I?

Can you count the number of quadrilaterals in the picture below?

Can you solve the photo plexer logic ?