Game With Numbers

Two players take turns selecting numbers from the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Each number can be selected at most once. The player who first selects a subset of their chosen numbers that sums to exactly 15 wins. If all numbers are selected and no player has reached a sum of 15, the game ends in a draw.

This game is isomorphic to tic-tac-toe played on a 3x3 magic square. Both players play optimally. Since tic-tac-toe always ends in a draw with optimal play, determine whether the first player can force a win from the empty board. Return false if the game is a draw.

Examples
Input: 15
Output: false
Hints

Game With Numbers

Two players take turns selecting numbers from the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Each number can be selected at most once. The player who first selects a subset of their chosen numbers that sums to exactly 15 wins. If all numbers are selected and no player has reached a sum of 15, the game ends in a draw.