There are 13 which, 15 black, 16 red hats on a table. In one step, you may chose two hats of different colors and replace each one by a hat of the third color. After how many steps this can be reached?  Pick one:
A) 2  B) 7  C) 3  D) 9  E) 1
Let the initial number of hats are (a, b, c). In one step the hats color may change into one of the following (a+2, b-1, c-1), (a-1, b+2, c-1), (a-1, b-1, c+2). In each of these cases, difference between any two colored hats should be divisible by 3 to reach mono chromatic stage. ie., a + b + c should also be divisible by 3.   In this case sum is not divisible by 3 so the final stage cannot be reached.   Answer:3
<result>C</result>
There are 13 which, 15 black, 16 red hats on a table. In one step, you may chose two hats of different colors and replace each one by a hat of the third color. After how many steps this can be reached?