what does it mean by smudges?
It's a method of hacking a passcode by examining the screen for the smudges left on the screen above the digits by oily fingers. The idea is that when the legitimate user taps in the passcode, the digits he touched will be smudged. So that reveals which digits are in the passcode, therefore narrowing down the possible combinations.
.
+2666 In the question, the word "smudges" is referring to a mark.
The question is trying to ask: If you knew that 4 distinct numbers were used in the 4 digit passcode, how many passcodes would be possible?
