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Complete the missing letters of the given word.

When I get multiplied by any number, the sum of the figures in the product is always me. What am I?

You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?

I am 5 letters long.
My first two tell you who I am
My first 3 could be a medicine
My last three reversed could be a young boy.
My 4th, 3rd and 2nd in that order could be a fruit drink.
If you have me you may hang me round your neck
WHAT AM I ?

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

We know that the number 7 is the prime followed by a cube. Which next number is also a prime followed by a cube?

The person who makes it has no need for it. He who purchases it does not use it. The person who does use it does not know they are. What is it?

Two boys wish to cross a river. The only way to get to the other side is by boat, but that boat can only take one boy at a time. The boat cannot return on its own, there are no ropes or similar tricks, yet both boys manage to cross using the boat.

How?

John asked Jack, "The time right now is 7 pm. Can you tell me what will be the time 23, 999, 995 hours later ?"

While Bella does not know the answer, do you ?

A Detective reviewed the information they had on the case so far.

A lady named 'Caterina' was found shot and they already had a list of suspects - Ankit, Tarun, Harish, Manoj and Manish.
The killer is a fan of challenges him by leaving notes ad various places.
* The first was found in a toilet room.
* The second was found in an art room.
* The third was in a restroom.
* the fourth in an underwater room.
* The fifth at the no-smoking room.

All of the notes read the same thing, 'The clues are where you find the notes.' Yet, nothing was found at any place the notes were.
Detective the genius, immediately solved the case.
Who was the killer?