Problem 6 · 2018 Math Kangaroo
Medium
Logic & Word Problems
work-backward
A big spot of ink covers most of a calendar page for a certain month. On which day of the week does the 25th of that month fall? (In the calendar the weekday columns are labelled Mo, Di, Mi, Do, Fr, Sa, So — Monday through Sunday.)
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Answer: D — Saturday
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Hint 1 of 2
Use the few dates you can still read at the edges of the blot to lock down the weekday pattern.
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Hint 2 of 2
Dates a week apart fall on the same weekday; step by sevens from a known date to reach the 25th.
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Approach: anchor on a visible date and jump in steps of 7
- A calendar repeats weekdays every 7 days, so the 25th shares a weekday with the 18th, 11th, and 4th.
- Reading a date that the ink did not cover fixes that column's weekday.
- Stepping by sevens to the 25th gives Saturday.
Mark:
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