The Snowflake Game is played on a board that consists \(9\) circles. There is \(1\) circle in the centre of the board, with \(4\) line segments through it, and a circle at the end of each line segment.
Two players alternate turns placing discs numbered \(1\) to \(9\) in the circles on the board. Each number can only be used once in any game. The object of the game is to be the first player to place a disc so that the sum of the three numbers along a line segment through the centre circle is exactly \(15.\)
Alex and Blake play the game. Alex goes first. Show that Alex has a winning strategy if she places a \(6\) in the centre circle on her first turn. That is, show that if Alex places a \(6\) in the centre circle on her first turn, then no matter which numbers Blake plays, Alex can always win the game.
Theme: Computational Thinking