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 2: The lab has decided to allow variations of the original sequence so that input of the scanned sequence of five fingers is allowed to vary from the original sequence by one place for any of the fingers. Thus, for example, if TIMRL is the original sequence, then ITRML is allowed, but LIMRT is not. How many different sequences are allowed for any given person's original scan?

- 7
- 5
- 8
- 13

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**Detailed Explanation**

Let us approach this by trial and error. First up, let us say that only two finger’s positions are swapped, then we will move to the others.

If the original were TIMRL, we could have ITMRL, TMIRL, TIRML and TIMLR.

Now, let us swap 2 pairs. We can have ITRML, ITMLR and TMILR.

We cannot swap more than 2 pairs. So, we have a total of 8 possibilities – original + 4 variants where one pair is swapped + 3 variants where 2 pairs are swapped.

The question is **"How many different sequences are allowed for any given person's original scan?"**

Choice C is the correct answer.

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