The numbers 2, 3, 4 are written on the board. At each step, we choose two of them ($a$ and $b$) and replace the third number with $a+b-1$.

1) Can we obtain the numbers $6, 9, 14$?
2) Can we obtain the numbers $2011, 2012, 2013$?
3) Can we obtain the numbers $2011, 2013, 2015$?
1) Yes: we replace 2 with 6, then 3 with 9, and finally 4 with 14.
2) We see that the sum of the numbers on the board remains odd \((a+b+(a+b-1)=2(a+b)-1)\). Since \(2012+2012+2013\) is even, we will not be able to obtain the numbers 2011, 2012, 2013.
3) We see that the number of odd numbers on the board is an invariant: we will therefore not be able to obtain the numbers 2012, 2013, 2015.