Birthdate together

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?




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

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In a certain bank, a man deposits a certain amount. According to the bank policies, the amount will be doubled up in a year but as the service charge, they will also deduct Rs. 65 by the end of every year.

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Can you find out the next digit in the following series ?

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How many triangles are there on the puzzle below?

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Amazing Facts

Challenging

There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.