Question

A number lock has 3 rings and each ring has 9 digits 1, 2, 3, ......, 9. Find the maximum number of unsuccessful attempts that can be made by a thief who tries to open the lock without knowing the key code.

Answer 1

The lock has 3 rings.

Each ring can be set to any one of the digits from 1 to 9.

Therefore, there are 9 possible choices for each ring.

The total number of possible combinations for the lock is the number of ways to set each of the 3 rings independently.

Since each ring has 9 possible choices, the total number of combinations is: 

9 × 9 × 9 = 9³ = 729

If a thief doesn't know the key code, they could attempt to open the lock by trying different combinations.

The thief can try all combinations except the correct one, which means the maximum number of unsuccessful attempts is the total number of possible combinations minus 1 (for the correct code).

Maximum number of unsuccessful attempts = 729 − 1 = 728

Thus, the maximum number of unsuccessful attempts the thief can make is 728.