Instructions Can you solve this puzzle? Give it a try and then compare your answ
ID: 2908645 • Letter: I
Question
Instructions Can you solve this puzzle? Give it a try and then compare your answers with those of classmates. Remember your communicative skill:s! Puzzle Khalili, McCain, Middleton, Porter, and Quintaro teach at Oklahoma City University Each gets two weeks of vacation a year. Last year, each took his or her first week in the first five months of the year and his or her second week in the last five months. If each professor took each of his or her weeks in a different month from the other professors, in which months did each professor take his or her first and second week? Here are the facts: McCain took her first week before Khalili, who took hers before Porter; for their second week, the order was reversed. The professor who vacationed in March also vacationed in September. Quintaro did not take her first week in March or April. Neither Quintaro nor the professor who took his or her first week in January took his or her second week in August or December. Middleton took her second week before McCain but after Quintaro. 1. 2. 3. 4. 5.Explanation / Answer
We'll frist provide all the possible solutions for every professor and then using the given constraints arrive at a unique solution.
1.) So using first constraint, possible solutions for professors are:
(Here months before ',' correspond to first leave month and those after ',' correspond to second leave month)
McCain: Jan Feb Mar, Oct Nov Dec
Khalili: Feb Mar Apr, Sep Oct Nov
Porter: Mar Apr May, Aug Sep Oct
2.) Using second constraint:
We denote this unknown professor as Prof2
Prof2: Mar, Sep
3.) Using third constraint:
Quintaro: Jan Feb May, ?
4.) Using fourth constraint:
Quintaro: Jan Feb May, Sep Oct Nov
We denote the second unknown professor as Prof4: Jan, Sep Oct Nov
5.) Using fifth constraint:
Middleton: ?, Oct Nov
Since variables are too many we take a guess for Prof2. We assume Prof2 is Khalili
Our solution so far:
McCain: Jan Feb Mar, Oct Nov Dec
Khalili: Feb Mar Apr, Sep Oct Nov
Porter: Mar Apr May, Aug Sep Oct
Quintaro: Jan Feb May, Sep Oct Nov
Middleton: ?, Oct Nov
Now Khalili: Mar, Sep
So we delete Mar and Sep elsewhere
McCain: Jan Feb, Oct Nov Dec
Porter: Apr May, Aug Oct
Quintaro: Jan Feb May, Oct Nov
Middleton: ?, Oct Nov
First leave order: McCain < Khalili < Porter
Second leave order: Porter < Khalili < McCain
and Quintaro < Middleton < McCain
So from second leave order we deduce that McCain took his second week off at the last i.e. Dec
So McCain: Jan Feb, Dec
Revised solution:
Khalili: Mar, Sep
McCain: Jan Feb, Dec
Porter: Apr May, Aug Oct
Quintaro: Jan Feb May, Oct Nov
Middleton: ?, Oct Nov
Middleton took her second leave after Quintaro so:
Middleton: ?, Nov
Quintaro: Jan Feb May, Oct
Khalili: Mar, Sep
McCain: Jan Feb, Dec
Porter: Apr May, Aug
From constraint 4. we know that the professor who took his or her first week in Jan did not take his second week in Aug or Dec. So McCain cannot be that professor, Revised Solution:
Middleton: ?, Nov
Quintaro: Jan May, Oct
Khalili: Mar, Sep
McCain: Feb, Dec
Porter: Apr May, Aug
Constraint 4 also says that Quintaro didn't take his first week in Jan, So revised solution with Quintaro: May and removing May from any other Professors
Middleton: ?, Nov
Quintaro: May, Oct
Khalili: Mar, Sep
McCain: Feb, Dec
Porter: Apr, Aug
? is Jan
Final Solution:
Middleton: Jan, Nov
Quintaro: May, Oct
Khalili: Mar, Sep
McCain: Feb, Dec
Porter: Apr, Aug