Problem #PRU-98583

Problems Algebra and arithmetic Arithmetic operations. Number identities Set theory and logic Theory of algotithms Game theory Game theory (other)

Problem

On a table there are 2022 cards with the numbers 1, 2, 3, ..., 2022. Two players take one card in turn. After all the cards are taken, the winner is the one who has a greater last digit of the sum of the numbers on the cards taken. Find out which of the players can always win regardless of the opponent’s strategy, and also explain how he should go about playing.