Can you win the game if a) the other player has reached the total of 6 and it is your turn? b) the other player has reached the total of 7 and it is your turn? c) the other player has reached the total of 8 and it is your turn?
Can you win the game if the other player has reached the total of 6 and it is your turn?
Yes, add 2 to reach 8. Then whatever the opponent plays (1 or 2), add the complement to reach 10 and win.
Can you win the game if the other player has reached the total of 7 and it is your turn?
Yes, add 2 to reach 9. Then whatever the opponent adds (1 or 2), you can add the remaining amount to reach 10 and win.
Can you win the game if the other player has reached the total of 8 and it is your turn?
Yes, add 2 to reach 10 and win the game immediately.
Explanation
(a) Position 8 is a winning position because from 8, you can reach 10 in one move. (b) Position 9 is a winning position because from 9, you need only 1 or 2 to reach 10. (c) From position 8, adding 2 reaches the target of 10 directly.