
Input (m,n) output...
Starting with the input (m,n), Machine A gives the output (n,m)
Starting with the input (m,n), Machine B gives the output (m+3n,n)
Starting with the input (m,n), Machine C gives the output (m2n,n)
Starting with the pair (0,1) which of the following is impossible to obtain after using the machines any number of times ?
A. (2009,1016)
B. (2009,1004)
C. (2009,1002)
D. (2009,1008)
E. (2009,1032)
Thank you in advance

None are possible as stated.
Machine A (0,1) will always yield (1,0).
If you entered (0,1) several million times you expect (1,0) to result.
Do you intend for the output of machine A to be the input for machine B?
Machine B output to be the input for machine C & machine C output to be the input for A?
Or
Is the output of machine A supposed to be the input for the next cycle of machine A?
It is not clear.
Actually, it looks like a trick question.

So for example with (0,1) I use machine B
(0,1)
= (3,1)
Then I use machine A
(3,1) becomes (1,3).