Question 10
Ten-dig is a game for two players. They try to make a $10$-digit number with all its digits different. The first player, A, writes any non-zero digit. On the right of this digit, the second player, B, then writes a digit so that the $2$-digit number formed is divisible by $2$. They take turns to add a digit, always on the right, but when the $n$th digit is added, the number formed must be divisible by $n$. The game finishes when a $10$-digit number is successfully made (in which case it is a draw) or the next player cannot legally place a digit (in which case the other player wins).
Show that there is only one way to reach a draw. [5 marks]
Investigation. Show that if A starts with any non-zero even digit, then A can always win no matter how B responds. [4 bonus marks]
The original Investigation is retained under this question; its four bonus marks are separate from the paper's 35 base marks and from the 5-point main rubric.
Show that there is only one way to reach a draw. [5 marks]
Investigation. Show that if A starts with any non-zero even digit, then A can always win no matter how B responds. [4 bonus marks]
The original Investigation is retained under this question; its four bonus marks are separate from the paper's 35 base marks and from the 5-point main rubric.