(Originais Teachy 2024) - Question Hard of Mathematics

Consider a board game where, in each round, a player rolls two dice and moves their piece on the board according to the sum of the points obtained in the rolls. For example, if the dice show 3 and 4, the player will move a total of 7 spaces. The first player to reach or exceed space number 100 wins. Player A has achieved a sequence of rolls that placed them on space number 95. Now, to determine their next move, they must mentally calculate whether the number 95 is even or odd and, based on that, roll only one die. If the number is even, they will use the die result to advance; if it is odd, they must disregard the result and their turn ends. Player B, an expert in quick calculations, claims that the number 95 is even and that the next die roll will result in 3, which will place them exactly on space number 100 to win the game. Based on knowledge of algorithms and logical reasoning: 1. How can Player A determine if the number 95 is even or odd without performing division? 2. Is Player B correct in their claim? Explain the mental calculation process that Player A must follow to decide if the number 95 is even or odd and how this influences their decision to use the die in the next turn.