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Alice has a deck of 36 cards, 4 suits of 9 cards each, game with Bob

Source: Tournament of Towns, Junior A-Level Paper, Spring 2020 , p6

June 10, 2020
combinatoricsgame

Problem Statement

Alice has a deck of 3636 cards, 44 suits of 99 cards each. She picks any 1818 cards and gives the rest to Bob. Now each turn Alice picks any of her cards and lays it face-up onto the table, then Bob similarly picks any of his cards and lays it face-up onto the table. If this pair of cards has the same suit or the same value, Bob gains a point. What is the maximum number of points he can guarantee regardless of Alice’s actions?
Mikhail Evdokimov