Problem Set 9 Now I know that the three numbered squares do not contain mines. Furthermore, each number indicates how many squares adjacent to that number do contain mines (Two squares are adjacent if they share an edge or a corner )Lete c s be the event that the configuration of mines is consistent with this numbering Describe all outcomes in the event E Solution here is the board with some squares labeled for discussion: We can divide all the outcomes in E into three groups based on the distribution of mines among the squares labeled a, b, c, d, and e and the 49 blank squares of mines a b d e other of configurations 100126()((()((6) 010036(()()()(3)(6) 001027()6)(6)(6)(②)() (c)On the next move, I must click an unnumbered square. If that square contains a mine, I lose the game! The squares marked a and y in the diagram below look like reasonable choices� �� �� �� �� �� � � �� �� �� �� �� � � �� �� �� �� �� � 10 Problem Set 9 1 1 3 Now I know that the three numbered squares do not contain mines. Furthermore, each number indicates how many squares adjacent to that number do contain mines. (Two squares are adjacent if they share an edge or a corner.) Let E ⊆ S be the event that the configuration of mines is consistent with this numbering. Describe all outcomes in the event E. Solution. Here is the board with some squares labeled for discussion: a b c d e a 1 1 3 e a b c d e We can divide all the outcomes in E into three groups based on the distribution of mines among the squares labeled a, b, c, d, and e and the 49 blank squares: # of mines a b c d e other # of configurations 3 49 1 2 0 2 0 2 1 3 2 1 0 0 1 2 6 0 1 0 0 3 6 0 0 1 0 2 7 6 3 0 2 1 2 0 2 0 3 3 49 6 3 0 2 0 2 1 2 0 3 2 49 7 (c) On the next move, I must click an unnumbered square. If that square contains a mine, I lose the game! The squares marked x and y in the diagram below look like reasonable choices