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A Dubai based gangster Chhota Vakil is in Switzerland. He wants to rob a bank there, whose locker code according to his information is an odd number between 50 and 450. He also knows that the numbers are from the set: 0, 1, 2, 3, 4, 5}. How many maximum trials he has to take to unlock the locker?

Question

A Dubai based gangster Chhota Vakil is in Switzerland. He wants to rob a bank there, whose locker code according to his information is an odd number between 50 and 450. He also knows that the numbers are from the set: 0, 1, 2, 3, 4, 5}. How many maximum trials he has to take to unlock the locker?

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Solution

The problem can be solved by considering the following steps:

  1. The locker code is an odd number between 50 and 450. This means the code could be a two-digit number (from 51 to 99) or a three-digit number (from 101 to 449).

  2. The digits of the code are from the set {0, 1, 2, 3, 4, 5}. This means each digit of the code can be one of these 6 numbers.

  3. For the two-digit codes, there are 6 options for the tens place and 3 options for the units place (1, 3, 5 to make the number odd), giving us 6*3 = 18 possibilities.

  4. For the three-digit codes, there are 5 options for the hundreds place (it can't be 0), 6 options for the tens place, and 3 options for the units place (1, 3, 5 to make the number odd), giving us 563 = 90 possibilities.

  5. Adding these together, the maximum number of trials Chhota Vakil would have to take to unlock the locker is 18 + 90 = 108 trials.

This problem has been solved

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