maths Maths Puzzle

What is the minimum number of times a fair die must be thrown for there to be at least an even chance that all scores appear at least once?

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maths Other Question

Player A has one more coin than player B. Both players throw all of their coins simultaneously and observe the number that come up heads. Assuming all the coins are fair, what is the probability that A obtains more heads than B? What is the expected number of times a fair die must be thrown until all scores appear at least once?