SOLUTION: Some years ago, the dates of three Sundays in a particular month were odd numbers. On which day of the week was the 12th day of the month?

Question 1173768: Some years ago, the dates of three Sundays in a particular month were odd numbers. On which day of the week was the 12th day of the month?
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
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Some years ago, the dates of three Sundays in a particular month were odd numbers.
On which day of the week was the 12th day of the month?
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SOLUTION

Let me start the solution by noticing that if today' Sunday is an odd date, then the next Sunday is an even date.


It implies that the "odd date Sundays" are alternated with the "even date Sundays".


So, our Sundays go in this sequence in this particular month


       1) odd date Sunday ;

       2) even date Sunday;

       3) odd date Sunday ;

       4) even date Sunday;

       5) odd date Sunday .


In this way, 5 Sundays of this month span 7 + 7 + 7 + 7 + 1 = 29 days.


So, there are not so many possibilities,  and the first Sunday must be one of these dates


        (a) the 1st day of the month   (making the fifth Sunday the 29th day of the month)

        (b) the 2nd day of the month   (making the fifth Sunday the 30th day of the month)

        (c) the 3rd day of the month   (making the fifth Sunday the 31th day of the month)


From here, it is not difficult to determine that the 12th day of this month is either

        Thursday,  or  Wednesday,  or  Tuesday,


in accordance with the possibilities a), b) or c) above.

Solved.

--------------

As you see, the answer is NOT a unique day.

            But had the problem said that that month was February of a leap-year,
            then we would be in position to state definitely, that the 12th day of that February was Thursday . . .

So, if you change the problem formulation ACCORDINGLY, you will get a   P R O B L E M   as sweet as a cookie.

/\/\/\/\/\/\/\/

As soon as you complete reading my post, send IMMEDIATELY your deepest "THANKS" to me for my teaching . . .

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