why number 8549176320 is one of a kind?

An inspection by the superintendent of St. Joseph School was scheduled on the next day. The class teacher Jenifer knew that he would be asking questions from her class and she would have to choose a pupil to answer. To offer a perfect impression over him, the teacher explained certain instructions to the students to maximise the chances of getting correct answer every time.

What did she say to the students?

A mathematician couple was having a Frappuccino in Starbucks sitting opposite to each other. Suddenly the guy noticed the text written on the paper in front of them and exclaimed that it was wrong. The girl denied it and said it is appropriate. Both are correct. What is written on the paper?

Can you identify the famous TV character from the rebus below?

A man is walking down a road with a basket of eggs. As he
is walking he meets someone who buys one-half of his eggs
plus one-half of an egg.
He walks a little further and meets another person who buys
one-half of his eggs plus one-half of an egg.
After proceeding further he meets another person who buys
one-half of his eggs plus one half an egg. At this point, he
has sold all of his eggs, and he never broke an egg.
How many eggs did the man have to start with?

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?

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?

You have to fill the below given grid in a manner that every row and column contains the digits 1 to 6. Also, make sure that the squares that are connected with each other must contains the same digit.

Four children having five rocks each were playing a game in which they had to throw the rock at a particular solid area in the water. Child 1- Succeeded in throwing three rocks at a solid area but one of the rocks sunk. Child 3 - His aim was so bad that all rocks got sunk. Child 4- He was awesome and none of the rocks got sunk. Child 2 - Was the winner but was struck by a rock in the head and died. Who killed Child 2?

Replace the question mark with the number below given a simple math problem.