The Angry Cinemagoer

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The Angry Cinemagoer

• An Investigation

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The Angry Cinemagoer
gangway
The above diagram shows the arrangement of
seating in one row in a cinema. Suppose that
(i) the
row is fully occupied
(ii) you are sitting in seat A 1
(a) If you get up to go to the toilet, how many
people will you disturb? (b) If the person
next to you does the same, how many people will
he/she disturb? (c) If each person in the
row gets up once during the film, how
many disturbances are there altogether?
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2. Consider the following arrangement of seating-
gangway
Has the total number of disturbances been
reduced by moving the gangway? Is this the best
arrangement (as far as disturbance is concerned)
for the 12 seats with 1 gangway?
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The cinema management decide to introduce 2
gangways (by removing ONE of the 12 seats in a
row). Find the arrangement that gives the least
overall disturbance.
If there are N seats and 2 gangways find the best
arrangement? If there are N seats and M gangways
find the best arrangement?