Solve this DILR Question on Security Scan from CAT 2017. You are expected to answer the questions that follow, based on the constraints given. Some constraints could be specific to each question. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands. When an employee first joins the lab, her fingers are scanned in an order of her choice, and then when she wants to re-enter the facility, she has to scan the five fingers in the same sequence.

The lab authorities are considering some relaxations of the scan order requirements, since it is observed that some employees often get locked-out because they forget the sequence.

Question 4: The lab has now decided to require six scans in the pass sequence, where exactly one finger is scanned twice, and the other fingers are scanned once, which can be done in any order. For example a possible sequence is TIMTRL.

Suppose the lab allows a variation of the original sequence (of six inputs) so that input in the form of scanned sequence of six fingers is allowed to vary from the original sequence by one place for any of the fingers, as long as the finger originally scanned twice is scanned twice and other fingers are scanned once. How many different sequences of scans are allowed if the original sequence is LRLTIM?

- 8
- 11
- 13
- 14

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**Detailed Explanation**

We can follow an approach similar to the one we saw for the 2nd question.

Variants where only one pair is switched – RLLTIM, LLRTIM, LRTLIM, LRLITM, LRLTMI

Variants where only two pairs are switched

With the first two fingers being swapped – RLTLIM, RLLITM, RLLTMI

We can follow an approach similar to the one we saw for the 2nd question.

Variants where only one pair is switched – RLLTIM, LLRTIM, LRTLIM, LRLITM, LRLTMI

Variants where only two pairs are switched

With the first two fingers being swapped – RLTLIM, RLLITM, RLLTMI,

With the first finger is in the same position but the 2nd and 3rd are swapped – LLRITM, LLRTMI

First two positions are intact – LRTLMI

We cannot have a scenario where first three are intact.

Beyond these, we can have a scenario where 3 pairs are swapped – RLTLMI.

So, we have a total of 5 + 3 + 2 + 1 + 1 variants. Added to the original LRLTIM, this gives a total of 13 possibilities.

The question is **"How many different sequences of scans are allowed if the original sequence is LRLTIM?"**

Choice C is the correct answer.

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