QUESTION

CSAT

Easy

Maths

Prelims 2022

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?

Select an option to attempt

Explanation

To solve this question, let’s go through the conditions:

The PIN has 3 digits chosen from the numbers 1 to 7, with no repetition of digits.
The digits are in decreasing order from left to right.
Any two digits differ by at least 2.

We’ll look for all possible 3-digit combinations that meet these requirements.

Starting with 7 as the leftmost digit: Possible combinations: 753, 752, 751, 742, 741, 731

Starting with 6 as the leftmost digit: Possible combinations: 642, 641, 631

Starting with 5 as the leftmost digit: Possible combinations: 531

Adding these up, we find 10 unique combinations that meet the conditions.

Therefore, the maximum number of attempts required to guarantee finding the PIN is 10.

Answer: 10

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