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

Two-person want to cross a river. Only one boat is present on the riverside that can carry only one person at a time.

However, they still manage to cross the river. How is it possible?

Suppose we lay down two cups in front of you. One of the cups is filled with tea and the other one with coffee. Now we ask you to take a spoonful of tea and mix it with the coffee. At this moment, the coffee cup has a mixture of tea and coffee. You have to take that mixture (spoonful) and add it back to the tea.

Can you now tell if the cup of coffee has more tea or the cup of tea has more coffee?

Can you find the next number in the below sequence
3 , 7 , 10 , 11 , 12 , 17 ?

A number can be multiplied by multiple of nine
i.e 9 18 27 36 45 ...

and the resulting number consist of only one digit.

Can you identify the number ?

What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller than 9?

In the given figure, move three matchsticks so that the resulting figure contains two rectangles.

What does this Rebus Picture means ?

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?

Can you identify the direction in which this bus is moving; left or right?

Hint: The bus is moving on the roads of London.