There is a numeric lock which has a 3-digit PIN. The PIN contains digits 1 to 7. There is no repetition of…
There is a numeric lock which has a 3-digit PIN. The PIN contains digits 1 to 7. There is no repetition of digits. The digits in the PIN from left to right are in decreasing order. Any two digits in the PIN differ by at least 2. How many maximum attempts does one need to find out the PIN with certainty?
6
8
10
12
Solution
Digits are from 1-7, distinct, decreasing left to right, with any two differing by at least 2. If the rightmost digit is 1: 531, 631, 731, 641, 741, 751 (6 cases). If it is 2: 642, 742, 752 (3 cases). If it is 3: 753 (1 case). The rightmost digit cannot exceed 3. Total = 6 + 3 + 1 = 10.