why number 8549176320 is one of a kind?

You are presented with three boxes. One of them has a red ball inside and the other two have a black ball inside each of them. You are asked to pick up the one with red ball and you pick one. Now, one of the other boxes is opened and it is found to have a black ball.

You are presented with a chance to change your box with the one that is left closed. Will you change your box? Why or why not?

Three fair coins are tossed in the air and they land with heads up. Can you calculate the chances that when they are tossed again, two coins will again land with heads up?

Find the Odd One Out?
84129
32418
47632
36119
67626
72927

Find the next number in the series below

21 32 54 87 131 ?

There are 20 people in an empty, square room. Each person has full sight of the entire room and everyone in it without turning his head or body, or moving in any way (other than the eyes). Where can you place an apple so that all but one person can see it?

There are five people. One of them shot and killed one of the other five.
We know following clues:
1. Dan ran in the NY City Marathon yesterday with one of the innocent men.
2. Mike consider being a farmer before he moved to the city.
3. Jeff is a top notch computer consultant and wants to install Ben new computer next week.
4. The murderer had his leg amputated last month.
5. Ben met Jack for the first time six months ago.
6. Jack has been in seclusion since the crime.
7. Dan used to drink heavily.
8. Ben and Jeff built their last computers together.
9. The murderer is Jack's brother. They grew up together in Seattle.

Consider yourself to be a famous detective "Sherlock Homles", Can you find the killer?

A farmer went to a market and bought a wolf, a goat, and a cabbage. On his way home, the farmer came to the bank of a river and rented a boat. But crossing the river by boat, the farmer could carry only himself and a single one of his purchases: the wolf, the goat, or the cabbage. If left unattended together, the wolf would eat the goat, or the goat would eat the cabbage. The farmer’s challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it?

There are seven sisters in a house in a village where there is no electricity or any gadget.

Sister-1: Reading Novel
Sister-2: Cooking
Sister-3: Playing Chess
Sister-4: Playing Sudoku
Sister-5: Washing clothes
Sister-6: Gardening

what is Sister-7 doing ?

A spy was in Canada trying to steal insider information on how to set up new Maple Syrup factories in their country. He was introduced to the operations manager of the biggest factory in Canada. However, the manager was suspicious and decided to test him with a question before he trusted him. So he asked, “What would you be sure to find in the middle of Toronto?” The spy thought fast and came up with an answer for the manager. What was his answer?