Nine Dates

You are looking at a printed calendar for a given month. The weeks are in rows. Each day is a square on the calendar. You draw a three-by-three square around nine dates. You notice that the sum of these 9 dates is divisible by 13. What is the date in the lower-right corner of your three-by-three square?


Source: mathcontest.olemiss.edu 8/27/2012

SOLUTION
There are eleven three-by-three squares that contain 9 dates.
1\quad\;\;\;2\quad\;\;\;3
8\quad\;\;\;9\quad\;10
15\quad 16\quad\;17
Sum =81. NO, not divisible by 13.

2\quad\;\;\;3\quad\;\;\;4
9\quad\;10\quad\;\;11
16\quad 17\quad\;18
Sum =90. NO.

5\quad\;\;\;6\quad\;\;\;7
12\quad 13\quad\;14
19\quad 20\quad\;21
Sum =117. YES, divisible by 13. The lower-right corner number is 21.

None of the eight remaining sums 126,135,144,153,180,189,198,207 is divisible by 13.

Answer: 21.

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About mvtrinh

Retired high school math teacher.
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