MATHEMATICAL MUSICAL CHAIRS
Number Theory
Level
4
2014 people stand in a circle. The 1st person says 'yes', the 2nd 'no', 3rd 'yes' and so on. All the people saying 'no' are are eliminated from the game. At last, what numbered person will remain?
2013
1981
1113
1007
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1 solution
You can truncate the problem by testing reduced forms of this, instead of trying to deal with 2014. From that you can see, relative to the prime factors of the number, how close the last one is to the end number. Thus you can tell that the answer has to be a 33 away from 2014 meaning that it is 1981.