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My street hockey team plays three games each week.  My team lost all $9$ games in the first three weeks. Then, my team won one game and lost two games in the fourth week, bringing our record to $1$ win and $11$ losses. Each week after that, my team won one game and lost two games.  My team first wins at least $60\%$ of all its games by the end of the first $n$ weeks.  What is $n$?

 Aug 25, 2024
 #1
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Well, let's note something about this problem really quickly. 

So, throughout the first 12 games, you have 1 win and 11 losses, which is 1/12, or about 8% win rate. 

After that, you win 1 game and lose 2 games, which is 1/3 or about 33% win rate. 

 

However, in order to achieve a 60% win rate, you must win more games than you lose. 

Since you ALWAYS lose more than you win, it's not possible you have a 60% win rate. 

 

Thanks! :)

 

~900 answers

 Aug 26, 2024
edited by NotThatSmart  Aug 26, 2024
edited by NotThatSmart  Aug 26, 2024

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