Players, Boys and Girls

Difficulty: Hard · Topics: Discrete Mathematics, Sets, Word Problems

In a group where everybody plays the guitar or the violin, the number of guitar players, the number of violin players and the number of men are all equal, and twice the number of people who play both the guitar and the violin.

The number of girls who play the guitar plus the number of men who play the violin is 10, and the number of girls who play the violin is twice the number of girls who play the guitar.

If 6 men play both the guitar and the violin, how many men in this group play only the guitar?