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

In the given figure, you can see that four match sticks are used to form a square. Can you form five squares by using six matches?

I am thinking of a five-digit number such that:
The first and last digits are the same, their submission is an even number and multiplication is an odd number and is equal to the fourth number. Subtract five from it and we obtain the second number. Then divide into exact halves and we get the 3rd number.

What number I am thinking of?

If nine thousand, nine hundred nine dollars is written as $9,909,
how should twelve thousand, twelve hundred twelve dollars be written?

In the Wild West, you are challenged into a death match by two bounty hunters nicknamed Golden Revolver (GR) and Killer Boots (KB). You accept the challenge. None of you want to waste any of the bullet and so a certain rules are laid down:

1) All of you will shoot in a given order till the last man standing.
2) Each of you shoots only once upon his turn.
3) If any one of you is injured, the other two will finish him off with an iron rod.
4) The worst shooter of all (which is you) shoots first and the best one shoots at the last.

Now, how will you plan things if you know that you hit every third shot of yours, KB hits every second shot and GR hits every shot ?

Is the statement valid that it does not matter how much older a sibling is, eventually the younger one will be half as old as the older one?

By moving exactly three matchsticks can you make the below equation true.It can be solved by 3 ways.

John can fit six large chocolate boxes or nine small chocolate boxes into a carton. How many cartons will he require to put sixty-six chocolate boxes into?

There’s a girl who has a large family. She has an equal amount of brothers and sisters, but each brother only has half as many brothers and sisters. What’s the correct amount of brothers and sisters?

A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?