Question 2 (1 point) Consider the following sequence: aj = 2, and 2a,-1 + 1, for n > 1. an What is the value of as?

Whoever must play, cannot play def subtract_square(queries): Two players play a game of "Subtract a square", starting with a positive integer. On their turn to play, each player must subtract some square number (1, 4, 9, 16, 25, 36, 49, ...) from the current number so that the result does not become negative. Under the normal play convention of these games, the player who moves to zero wins, leaving his opponent stuck with no possible moves. (In the misère version of the game that has otherwise identical rules but where you win by losing the original game, these definitions would be adjusted accordingly.) This and many similar combinatorial games can be modelled with recursive equations. This game is an example of an impartial game since the moves available to both players are exactly the same, as opposed to “partisan games” such as chess where each player can only move pieces of one colour. A game state is therefore determined by the remaining number alone, but not by which player has…

Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Let S= (1, 2, 3, 4, 5). Select all the 3-combinations of S. (Check all that apply.) ? 123, 124, 125, 134, 135 145, 234, 235, 245, 345 ? 145, 234, 225, 245, 315 ? 231, 252, 125, 142, 213

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