Problem 1 · 2018 Math Kangaroo
Easy
Logic & Word Problems
clock-calendar
The diagram shows the calendar page of a certain month, but ink has run across parts of the page. Which day of the week does the 27th of that month fall on? (The weekday columns read Mon, Tue, Wed, Thu, Fri, Sat, Sun.)
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Answer: A — Monday
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Hint 1 of 2
Read the two visible dates to figure out which weekday column the month starts in.
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Hint 2 of 2
Once you know the weekday of the 1st, count forward 26 days using remainders mod 7.
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Approach: anchor the calendar, then step the weekday forward by a multiple of 7
- The clear cells show Thursday is the 2nd and Friday the 3rd, so the 1st falls on Wednesday.
- The 1st, 8th, 15th and 22nd are all Wednesdays.
- From the 22nd, five more days (23,24,25,26,27) land on Monday.
- So the 27th is a Monday.
Mark:
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