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Town Trends (Posted on 2014-03-19) Difficulty: 3 of 5
In a certain town- the supermarket, the department store, and the bank are open together on one day each week.
  1. Each of the three places is open precisely 4 days a week
  2. On Sunday all of these places are closed.
  3. None of the three places is open on three consecutive days.
  4. On six consecutive days:
    • the department store was closed on the first day
    • the supermarket was closed on the second day
    • the bank was closed on the third day
    • the supermarket was closed on the fourth day
    • the department store was closed on the fifth day
    • the bank was closed on the sixth day.
On which one of these seven days do all the three places in the town remain open?

No Solution Yet Submitted by K Sengupta    
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Solution Solution Comment 1 of 1

Let's consider the six consecutive days described in the problem. 

The department store was closed on the 1st and 5th days.  If the first day was Monday or Tuesday, this would mean the department store was open three days in a row (TWT or WTF, respectively), which violates one of the conditions. 

The bank was closed on the 3rd and 6th days.  If the first day was Wednesday or Thursday, this would mean the bank was open three days in a row (TWT or WTF, respectively).

The supermarket was closed on the 2nd and 4th days.  If the first day was Friday or Sunday, this would mean the supermarket was open three (or four) days in a row (TWTF or TFS, respectively).

Thus the first day of the six consecutive days was Saturday.

The department store is closed on Wednesday, Saturday, and Sunday.

The bank is closed Monday, Thursday, and Sunday.

The supermarket is closed Tuesday, Thursday, and Sunday.

They're all open together on Friday. 


  Posted by tomarken on 2014-03-19 14:43:16
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