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ECS 101 Problem 1.6 Solution

ECS 101 Problem 1.6 Solution . Example of Problem Solving Methodology . Problem Statement.

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ECS 101 Problem 1.6 Solution

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  1. ECS 101 Problem 1.6 Solution Example of Problem Solving Methodology

  2. 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?

  3. 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.

  4. 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.

  5. What is the Problem? • On which day of his vacation was Joe able to sleep late?

  6. Create a Table from Clue Facts

  7. 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.

  8. 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

  9. 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.

  10. Update the Table from Conclusion

  11. 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.

  12. Update the Table from Conclusion

  13. 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.

  14. Update the Table from Conclusion

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

  16. For Completeness • Now why didn’t 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.

  17. 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.

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