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MathNet 2016-part-02 — 184 problems (EN–VI) Question 141

Math Olympiad Vault · MathNet 2016-part-02 — 184 problems (EN–VI)

Question 141

From $100$ tickets numbered $00, 01, 02, 03, \ldots, 97, 98, 99$, whenever any $k$ tickets are chosen, among the chosen tickets there are always $4$ tickets whose tens digits are pairwise distinct and whose units digits are also pairwise distinct. Find the smallest possible value of $k$.