An authentication system accepts passwords that are composed of lowercase letters from a to z and digits from 0 to 9. Prove that, in this system, given any set of 3000 passwords, there must be at least three passwords that begin with the same pair of characters (in the same order), for example, st4fk7 and std3gy37.
2026-03-25 18:24:43.1774463083
proof by letters with characters
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Create a bin for every possible beginning of a password, from "aa", "ab" all the way to "99". Then throw each of the present passwords into its bin.