Race To 80
Dan and Sam play a game in which the first to start says the number 1, the next says 2, and the one who's next must say an integer number strictly between the number previously said and its double (not including the endpoints).
For example, Dan begins saying 1; then Sam says 2 and then Dan can say whichever number he wants between 2 and 4; as the only integer between 2 and 4 is 3, he must say 3. Then, Sam can choose any number between 3 and 6; that is, he can say either 4 or 5.
The game finishes when someone reaches 80 (who is the winner). If Dan begins, who will win? In other words, who has a winning strategy?
This is the second problem of the set Winning Strategies .
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1 solution
Since we need to reach 80 , the first person to say 41 or any greater number loses , as his enemy can just say 80 in the next turn.
That means the person who reaches 40 first wins, as his opponent has to say a number greater than or equal to 41 .
Using the same logic as above the first person to say 20 wins . And following that , first to 10 wins and thus first to 5 wins , which must be Sam