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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Replace the question mark with the correct number below.

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On one occasion, A Boy collects 71 rupees in form of 20 paise and 25 paise. He collects a total of 324 coins.

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One fine day, an intellectual man came to the emperor's court with the aim of testing Birbal's wittiness. In order to do this, he challenged Birbal to answer his question and hence prove that he was as intelligent and witty as he was said to be.
He asked Birbal, Do you want me to ask one difficult question or a hundred easy ones?
Since both Akbar and Birbal had had a tough day and were eager to leave, Birbal hastily told the intellectual to ask him a single difficult question.
Intellectual: OK. Tell me what came first into the world, the egg or the chicken?
Of course, the chicken, Birbal replied with a smile.
This time with a note of victory in his voice, the intellectual asked Birbal, How will you demonstrate that?
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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