TMRLI
(CAT 2017)
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.
Questions
1.
The lab has decided to allow a variation in the sequence of scans of the five
fingers so that at most two scans (out of five) are out of place. For example,
if the original sequence is Thumb (T), index finger (I), middle finger (M),
ring finger (R) and little finger (L) then TLMRI is also allowed, but TMRLI is
not.
How
many different sequences of scans are allowed for any given person’s original
scan?
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 also allowed, but LIMRT is not.
How
many different sequences are allowed for any given person’s original scan?
(A) 7
(B) 5
(C) 8
(D) 13
(A) 7
(B) 5
(C) 8
(D) 13
3.
The lab has now decided to require six scans in the pass key sequence, where
exactly one finger is scanned twice, and the other fingers are scanned exactly
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) where at
most two scans (out of six) are out of place, 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 for any given person’s original
scan?
4.
The lab has now decided to require six scans in the pass key sequence, where
exactly one finger is scanned twice, and the other fingers are scanned exactly
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 scan sequence is
LRLTIM?
(A) 8
(B) 11
(C) 13
(D) 14
(A) 8
(B) 11
(C) 13
(D) 14
For Answers click here.
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