By the pigeonhole principle, the solution to this problem is 100% when n = 366 or more.
Sevast'yanov showed that an approximate answer of "1.2 times the square root of c over 2k plus one" resolves the "almost" variant of this problem. Schemes named after this problem work by storing values and their associated inverse images, and then checking to see if any of the stored values are the same; such schemes become impractical when n, or the number of stored values, is greater than 160, though those schemes named after this problem are still used to (*) brute-force cryptographic hashes. The generalized form of this problem was modeled using multinomial theory by Levin. In Martin Gardner's original formulation of this problem, for n = 30, the solution to this problem is approximately 70%. By the pigeonhole principle, the solution to this problem is 100% when n = 366 or more. For 10 points, name this problem from combinatorics that asks for the probability that at least 2 people in a group are born during the same day.
Sevast'yanov showed that an approximate answer of "1.2 times the square root of c over 2k plus one" resolves the "almost" variant of this problem.
birthday paradox or problem 