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  • 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 sca

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 :  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 also allowed, but LIMRT is not.How many different sequences are allowed for any given Person's original scan?

Option: 1

7


Option: 2

5


Option: 3

8


Option: 4

13


Answers (1)

best_answer

The question asks us to find how many different sequences are allowed for any given person's original scan, given that 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.

We can use the following cases to solve the problem:

Case 1: Only a set of two consecutive numbers are interchanged.

Case 2: Two sets of two consecutive numbers are interchanged.

For Case 1: We can choose any two consecutive numbers in the original sequence in (25?) =10 ways.

For Case 2: There are two ways to do this:

We can interchange the first two numbers, and then the last two numbers.

We can interchange the second two numbers, and then the first two numbers.

Therefore, the total number of sequences in Case 2 is 2.

Therefore, the total number of allowed sequences is 10+2=12?

Here is a table that summarizes the two cases:

Case

Number of sequences

Only a set of two consecutive numbers are interchanged

10

Two sets of two consecutive numbers are interchanged

2

Total

12

 

Posted by

manish painkra

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