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2010 Math Kangaroo

Problem 17

Problem 17 · 2010 Math Kangaroo Medium
Logic & Word Problems clock-calendar

In one month, three Tuesdays fall on even days. Which day of the week is the 21st of the month?

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Answer: E — Sunday
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Hint 1 of 2
Consecutive Tuesdays are 7 days apart, and 7 is odd, so their dates flip between even and odd.
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Hint 2 of 2
For three Tuesdays to be even, fix the first Tuesday's date, then locate the 21st.
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Approach: parity of Tuesday dates
  1. Since 7 is odd, Tuesday dates alternate even, odd, even, ...
  2. Three even Tuesdays force the Tuesdays onto the 2nd, 9th, 16th, 23rd and 30th.
  3. The 21st is 5 days after Tuesday the 16th, which is a Sunday.
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