Claim the Last FlagDate: 10/25/2002 at 13:02:43 From: Cathy Williams Subject: Survivor Challenge: be the one to choose last I saw a challenge on tv last night that had two teams facing a field of 21 flags. The challenge was this: the teams took turns choosing 1, 2, or 3 flags at each turn. The team that was able to claim the last flag won. I know I saw a show about this problem a few months back. There's an equation of sorts for how to win. Any help? Thanks! Date: 10/25/2002 at 14:54:02 From: Doctor Achilles Subject: Re: Survivor Challenge: be the one to choose last Hi Cathy, Thanks for writing to Dr. Math. If there are 1, 2, or 3 flags left when it's my turn to choose, then I can win easily. If there are 4 flags left when it's my turn to choose, then no matter what I do, my opponent will be left with 1, 2, or 3 flags, and can win easily. So I want to make sure that I can leave my opponent with 4 flags on his/her turn. How can I do that? Well, if there are 5, 6, or 7 flags left on my turn, then I can easily leave my opponent with 4 flags. But I have to be careful. If there are 8 flags left on my turn, then I have to give my opponent 5, 6, or 7 flags and s/he will be able to leave me with 4 on my next turn and make me lose. So I want to make sure that I can leave my opponent with 8 flags on his/her turn. How can I do that? Well, if there are 9, 10, or 11 flags left on my turn, then I can easilty leave my opponent with 8 flags. But I have to be careful. If there are 12 flags left on my turn, then I have to give my opponent 9, 10, or 11 flags and s/he will be able to leave me with 8 flags on my next turn and make me lose. So I want to make sure that I can leave my opponent with 12 flags on his/her turn. How can I do that? See the pattern? - Doctor Achilles, The Math Forum http://mathforum.org/dr.math/ |
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