ECS 101 Problem 1.6 Solution

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ECS 101 Problem 1.6 Solution

• Example of Problem Solving Methodology

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Problem Statement

• Joe Flannery had a week off from his trucker's
  job and intended to spend all nine days of his
  vacation (Saturday through the following Sunday)
  sleeping late. But his plans were foiled by some
  of the people who work in his neighborhood. On
  Saturday, his first morning off, Joe was wakened
  by the doorbell it was a salesman of magazine
  subscriptions who was "working his way through
  college. On Sunday, the barking of the
  neighbor's dog as the paperboy tried to deliver
  the paper abruptly ended Joe's sleep. On Monday,
  he was again wakened by the persistent salesman
  but was able to fall asleep again, only to be
  disturbed by the garbage men. In fact, the
  salesman, the garbage men, and the neighbor's dog
  that barked at the paper boy combined to wake Joe
  at least once each day of his vacation, with one
  exception. The salesman woke him on Wednesday
  the garbage men on the second Saturday the dog
  on Wednesday and the final Sunday. No one of the
  three noisemakers was quiet for three consecutive
  days but yet, no pair of them made noise on more
  than one day during Joe's vacation-for example,
  the salesman and the garbage men both woke Joe on
  Monday but did not both wake him up on any other
  day. On which day of his vacation was Joe able to
  sleep late?

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Find the clues

• On Saturday, his first morning off, Joe was
  wakened by the .. salesman
• On Sunday, the barking of the neighbor's dog as
  the paperboy tried to deliver the paper abruptly
  ended Joe's sleep.
• On Monday, he was again wakened by the persistent
  salesman but was able to fall asleep again, only
  to be disturbed by the garbage men.
• In fact, the salesman, the garbage men, and the
  neighbor's dog that barked at the paper boy
  combined to wake Joe at least once each day of
  his vacation, with one exception.

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Find the clues

• The salesman woke him on Wednesday the
  garbage-men on the second Saturday the dog on
  Wednesday and the final Sunday.
• No one of the three noisemakers was quiet for
  three consecutive days
• But yet, no pair of them made noise on more than
  one day during Joe's vacation-for example, the
  salesman and the garbage-men both woke Joe on
  Monday but did not both wake him up on any other
  day.

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What is the Problem?

• On which day of his vacation was Joe able to
  sleep late?

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Create a Table from Clue Facts
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Analyze the Clues and the Chart

• The only possible solutions are Tuesday, Thursday
  or Friday.
• Clue d tells us there are no other things that
  disturbed Joe, and there is only one solution.
• So we have to use Clues f and g and deduce which
  of the three days is correct.

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Analyze the Clues Using the Chart

• From clue f, at least once in three consecutive
  days, we need
• Barking on Thursday, Friday or 2nd Saturday.
• Salesman on Friday or 2nd Saturday.
• Garbage men on Wednesday or Thursday

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Consider Alternatives

• Consider alternatives for Garbage men on
  Wednesday or Thursday
• If we put garbage men on Wednesday there will be
  a salesman - garbage men pair that already exists
  for Monday, and clue g says this cannot happen.
• Therefore the garbage men must be a disturbance
  on Thursday.

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Update the Table from Conclusion
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Consider Alternatives

• Consider alternatives for Salesman on Friday or
  2nd Saturday
• If we choose the 2nd Saturday, this will form a
  salesman - garbage men pair which cannot exist by
  clue g and Monday.
• Therefore the salesman comes on Friday.

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Update the Table from Conclusion
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Consider Alternatives

• Consider alternatives for barking on Thursday,
  Friday, or 2nd Saturday
• If barking occurred on Friday there would be a
  barking-salesman pair, but by clue g that cannot
  be because there already is on Wednesday.
• Therefore barking occurs on Thursday or 2nd
  Saturday. This will form a barking - garbage men
  pair on either day that is acceptable by rule g.

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Update the Table from Conclusion
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Solution

• This leads to a solution that Tuesday is the day
  Joe was able to sleep late.

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For Completeness

• Now why didnt we try Thursday or the 2nd Sunday
  of the salesman or Tuesday or Friday for garbage
  men? Any of these choices would not solve the
  problem created by clue f. But even so lets look
  at each case
• Salesman on Thursday - This would form a salesman
  - garbage men pair that cannot exist by rule f
  and Monday.
• Salesman on 2nd Sunday - This would form a
  salesman - garbage men pair that cannot exist by
  rule f and Monday.
• Garbage men Tuesday - There would be no solution
  to problem which violates clue d.
• Garbage men Friday - This would form a salesman -
  garbage men pair that cannot exist by rule f and
  Monday.

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Issue of Uniqueness

• What if the problem asked show a complete chart
  of what disturbs Joe on what day except the day
  he can sleep late.
• There would not be a single solution, because
• On Thursday there can be barking and this is a
  solution
• Or on 2nd Saturday there could be barking, and
  this also is a solution.