Two New Variations
Variation 1 (fairly easy if you can do the orignial variation)
The manager of a movie theatre announces that a free ticket will be given to the first person in line whose birthday and birth hour is the same as someone else who has already purchased a ticket. You can get in line at any time. The birthdays and hours are distributed uniformly at random over 365 days and 24 hours. Which position in line should you take?
Variation 2
(Hard. I don't think there is a closed form expression for the answer, but maybe good approximations exist.)
The manager of a movie theatre announces that a free ticket will be given to the first person in line whose random number is the same as someone else who has already purchased a ticket. You can get in line at any time. The random numbers are uniformly distributed integers ranging from 1 to N. Which position in line should you take? (The answer is a formula which depends on N.)
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