Can you fill the blank with the correct number?

6 30 870 756030 _____

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

There is an ancient kingdom where every married woman keeps information regarding the fidelity of other men. However, what they don't know is the fidelity of their own husbands. Also, there is an ancient belief that they don't tell each other about the fidelity of their husbands.

On a certain day, the queen of the kingdom declares that she has identified at least one unfaithful man in the kingdom. She allows the wives to identify and gives them authority to kill their husbands if they are unfaithful at midnight.

How will the wives manage it?

A farmer and his neighbour once went to Emperor Akbar"s court with a complaint. "Your Majesty, I bought a well from him," said the farmer pointing to his neighbour, "and now he wants me to pay for the water."
"That"s right, your Majesty," said the neighbour. "I sold him the well but not the water!"?
The Emperor asked Birbal to settle the dispute. How did Birbal solve the dispute?

How can you tell a raw egg from a hard-boiled egg?

Can you find the 09 errors in the picture below?

There are two beautiful yet remote islands in the South Pacific. The Islanders born on one island always tell the truth, and the Islanders from the other island always lie.
You are on one of the islands and meet three Islanders. You ask the first which island they are from in the most appropriate Polynesian tongue, and he indicates that the other two Islanders are from the same island. You ask the second Islander the same question, and he also indicates that the other two Islanders are from the same island.
Can you guess what the third Islander will answer to the same question?

Can you name three consecutive days without using the words Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday?

What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first two, and the last is three times the second?

Why is it very easy to weigh a fish?