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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what one word does the below rebus identifies?

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Three cars are driving on a track that forms a perfect circle and is wide enough that multiple cars can pass anytime. The car that is leading in the race right now is driving at 55 MPH and the car that is trailing at the last is going at 45 MPH. The car that is in the middle is somewhere between these two speeds.
Right now, you can assume that there is a distance of x miles between the leading car and the middle car and x miles between the middle car and the last car and also, x is not equal to 0 or 1.
The cars maintain their speed till the leading car catches up with the last car and then every car stops. In this scenario, do you think of any point when the distance between any two pairs will again be x miles i.e. the pairs will be x distance apart at the same time ?

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While preparing the table for dinner, wife came up with an idea to tease his mathematician husband. She asked her husband to pick nine toothpicks and make ten without breaking any toothpick.

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What does this rebus riddle means ?

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I always drive my customer away.

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There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
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No Solution

In 2007, a puzzle was released and $2 million prizes were offered for the first complete solution. The competition ended at noon on 31 December 2010, with no solution being found. Wiki