Solution:

Step5 is Wrong.

Explanation:
We divided the two sides by (A-B).Since A = B which indicates that (A - B) = 0 and we cannot divide by zero.

Solution:

-3 -1 1

Explanation:
-3 * 1 * -1 = 3(prime)
-1 - (-3) = 1 -(-1) = 2

Solution:

The answer is 'R'

It represents the gear stick. The number 1-5 represents gears and the last one thus should be reverse i.e. R.

Solution:

Since the knife was in her hand which implies that she was planning to kill her husband "Inspector Montalbano".

Solution:

The stranger said that he thought the room was his. If so, he must have had the keys to the room and thus he must not have knocked.

Solution:

The last marble will be yellow.

Since marbles can only be taken out in pairs and you started off with an odd number of yellows there is always going to be one yellow left over that you'll keep putting back in the box until it's left on it's own.

Solution:

7, 4, 6, 5, 8

Solution:

The competition was held on 11 November 2013. The logic is simple. In America, the dates are mentioned as Month/Day/Year and in Britain, dates are written as Day/Month/Year. But on 11 November 2013, the date and month will be the same. And thus both will write in the same manner i.e. 11/11/2013. If it would have been any other date, the evaluators would have been able to identify it.

Solution:

Pages 19, 20, 23, 37, 38, & 42 will also be missing

Solution:

The clerk said that every day the password is CHANGED. Changed is the password.

Solution:

192 021

If you look at it as two-digit numbers you'll see:10 11 12 13 14 15 16 17 18 19 20 21