In a two-player strategy game, the first player says “January 1”, and then players after that say, on their turn, any date later in the year than the previous one by changing either the month or the day forward. For example, the first player since January 1, and then the second player might say January 5 (changing the day), Then the first player might respond April 5 (changing the month). The game continues in this manner until someone wins by saying December 31. If I start the game by saying January 1, you can guarantee you'll win by the following with:
a) January 29.
b) January 28.
c) January 20th.
d) October 1.
e) November 1.
If you have the opportunity to say Dec 31, you win.
If you have the opportunity to say Nov 30, you win. That's because:
I can then only say Dec 30. You then say Dec 31 and win.
If you have the opportunity to say Oct 29, you win. That's because:
If I then say Oct 30, you then say Nov 30 and win.
If I then say Oct 31, you will say Dec 31 and win.
If I then say Nov 29, you will say Nov 30 and win.
If I then say Dec 29, you will say Dec 31 and win.
If you have the opportunity to say Sep 28, you win. That's because:
If I then say Sep 29, you will say Oct 29 and win.
If I then say Sep 30, you will say Nov 30 and win.
If I then say Oct 28, you will say Oct 29 and win.
If I then say Nov 28, you will say Nov 30 and win.
If I then say Dec 28, you will say Dec 31 and win.
If you have the opportunity to say Aug 27, you win. That's because:
If I then say Aug 28, you will say Sep 28 and win.
If I then say Aug 29, you will say Oct 29 and win.
If I then say Aug 30, you will say Nov 30 and win.
If I then say Aug 31, you will say Dec 31 and win.
If I then say Sep 27, you will say Sep 28 and win.
If I then say Oct 27, you will say Oct 29 and win.
If I then say Nov 27, you will say Nov 30 and win.
If I then say Dec 27, you will say Dec 31 and win.
If you have the opportunity to say Jul 26, you win. That's because:
If I then say Jul 27, you will say Aug 27 and win.
If I then say Jul 28, you will say Sep 28 and win.
If I then say Jul 29, you will say Oct 29 and win.
If I then say Jul 30, you will say Nov 30 and win.
If I then say Jul 31, you will say Dec 31 and win.
If I then say Aug 26, you will say Sep 28 and win.
If I then say Sep 26, you will say Sep 28 and win.
If I then say Oct 26, you will say Oct 29 and win.
If I then say Nov 26, you will say Nov 30 and win.
If I then say Dec 26, you will say Dec 31 and win.
If you have the opportunity to say Jun 25, you win. That's because:
If I then say Jun 26, you will say Jul 26 and win.
If I then say Jun 27, you will say Aug 27 and win.
If I then say Jun 28, you will say Sep 28 and win.
If I then say Jun 29, you will say Oct 29 and win.
If I then say Jun 30, you will say Nov 30 and win.
If I then say Jul 25, you will say Jun 26 and win.
If I then say Aug 25, you will say Aug 27 and win.
If I then say Sep 25, you will say Sep 28 and win.
If I then say Oct 25, you will say Oct 29 and win.
If I then say Nov 25, you will say Nov 30 and win.
If I then say Dec 25, you will say Dec 31 and win.
If you have the opportunity to say May 24, you win. That's because:
If I then say May 25. you will say Jun 25 and win.
If I then say May 26, you will say Jul 26 and win.
If I then say May 27, you will say Aug 27 and win.
If I then say May 28, you will say Sep 28 and win.
If I then say May 29, you will say Oct 29 and win.
If I then say May 30, you will say Nov 30 and win.
If I then say May 31, you will say Dec 31 and win.
If I then say Jun 24, you will say Jun 25 and win.
If I then say Jul 24, you will say Jul 26 and win.
If I then say Sep 24, you will say Sep 28 and win.
If I then say Oct 24, you will say Oct 29 and win.
If I then say Nov 24, you will say Nov 30 and win.
If I then say Dec 24, you will say Dec 31 and win.
If you have the opportunity to say Apr 23, you win. That's because:
If I then say Apr 24, you will say May 24 and win.
If I then say Apr 25, you will say Jun 25 and win.
If I then say Apr 26, you will say Jul 26 and win.
If I then say Apr 27, you will say Aug 27 and win.
If I then say Apr 28, you will say Sep 28 and win.
If I then say Apr 29, you will say Oct 29 and win.
If I then say Apr 30, you will say Nov 30 and win.
If I then say May 23, you will say May 24 and win.
If I then say Jun 23, you will say Jun 25 and win.
If I then say Jul 23, you will say Jun 26 and win.
If I then say Aug 23, you will say Aug 27 and win.
If I then say Sep 23, you will say Sep 28 and win.
If I then say Oct 23, you will say Oct 29 and win.
If I then say Nov 23, you will say Nov 30 and win.
If I then say Dec 23, you will say Dec 31 and win.
If you have the opportunity to say Mar 22, you win. That's because:
If I then say Mar 23, you will say Apr 23 and win.
If I then say Mar 24, you will say May 24 and win.
If I then say Mar 25, you will say Jun 25 and win.
If I then say Mar 26, you will say Jul 26 and win.
If I then say Mar 27, you will say Aug 27 and win.
If I then say Mar 28, you will say Sep 28 and win.
If I then say Mar 29, you will say Oct 29 and win.
If I then say Mar 30, you will say Nov 30 and win.
If I then say Mar 31, you will say Dec 31 and win.
If I then say Apr 22, you will say Apr 23 and win.
If I then say May 22, you will say May 24 and win.
If I then say Jun 22, you will say Jun 25 and win.
If I then say Jul 22, you will say Jun 26 and win.
If I then say Aug 22, you will say Aug 27 and win.
If I then say Sep 22, you will say Sep 28 and win.
If I then say Oct 22, you will say Oct 29 and win.
If I then say Nov 22, you will say Nov 30 and win.
If I then say Dec 22, you will say Dec 31 and win.
If you have the opportunity to say Feb 21, you win. That's because:
If I then say Feb 22, you will say Mar 22 and win.
If I then say Feb 23, you will say Apr 23 and win.
If I then say Feb 24, you will say May 24 and win.
If I then say Feb 25, you will say Jun 25 and win.
If I then say Feb 26, you will say Jul 26 and win.
If I then say Feb 27, you will say Aug 27 and win.
If I then say Feb 28, you will say Sep 28 and win.
If I then say Feb 29 (leap year), you will say Oct 29 and win.
If I then say Mar 21, you will say Mar 22 and win.
If I then say Apr 21, you will say Apr 23 and win.
If I then say May 21, you will say May 24 and win.
If I then say Jun 21, you will say Jun 25 and win.
If I then say Jul 21, you will say Jul 26 and win.
If I then say Aug 21, you will say Aug 27 and win.
If I then say Sep 21, you will say Sep 28 and win.
If I then say Oct 21, you will say Oct 29 and win.
If I then say Nov 21, you will say Nov 30 and win.
If I then say Dec 21, you will say Dec 31 and win.
If you have the opportunity to say Jan 20, you win. That's because:
If I then say Jan 21, you will say Feb 21 and win.
If I then say Jan 22, you will say Mar 22 and win.
If I then say Jan 23, you will say Apr 23 and win.
If I then say Jan 24, you will say May 24 and win.
If I then say Jan 25, you will say Jun 25 and win.
If I then say Jan 26, you will say Jul 26 and win.
If I then say Jan 27, you will say Aug 27 and win.
If I then say Jan 28, you will say Sep 28 and win.
If I then say Jan 29, you will say Oct 29 and win.
If I then say Jan 30, you will say Nov 30 and win.
If I then say Jan 31, you will say Dec 31 and win.
If I then say Feb 20, you will say Feb 21 and win.
If I then say Mar 20, you will say Mar 22 and win.
If I then say Apr 20, you will say Apr 23 and win.
If I then say May 20, you will say May 24 and win.
If I then say Jun 20, you will say Jun 25 and win.
If I then say Jul 20, you will say Jul 26 and win.
If I then say Aug 20, you will say Aug 27 and win.
If I then say Sep 20, you will say Sep 28 and win.
If I then say Oct 20, you will say Oct 29 and win.
If I then say Nov 20, you will say Nov 30 and win.
If I then say Dec 20, you will say Dec 31 and win.
Answer: January 20.
me: Oct 1
you: Nov 1 or Oct x
me: Nov 30 or Nov x
you: Dec 1 or Dec x
me: Dec 31
To determine the answer, we need to analyze the game and find the winning strategy.
First, let's consider the rules of the game. The players can change either the month or the day forward relative to the previous date. The game ends when a player says December 31.
Now, let's analyze the options:
a) January 29: If the first player chooses January 29, the second player can change it to either January 30 or February 29, depending on whether it's a leap year or not. Either way, the second player will win before reaching December 31.
b) January 28: Similar to option a), the second player can choose January 29 or February 29 (leap year), ensuring their victory before December 31.
c) January 20th: In this case, the second player can select any date after January 20th and win before reaching December 31. Therefore, this option does not guarantee a win for the second player.
d) October 1: If the first player selects October 1, the second player can respond by choosing either October 2 or November 1. In either case, the second player will not reach December 31, so the first player wins.
e) November 1: In this case, the second player can select any date after November 1 and win before reaching December 31. Therefore, this option does not guarantee a win for the second player.
Considering the analysis above, the only option that guarantees a win for the second player is option (d) October 1.
Therefore, the correct answer is d) October 1.