2006 AMC 10B Problems/Problem 16
Problem
Leap Day, February , , occurred on a Sunday. On what day of the week will Leap Day, February , , occur?
Solution
There are days in a year, plus extra day if there is a Leap Day, which occurs on years that are multiples of (with a few exceptions that don't affect this problem).
Therefore, the number of days between Leap Day and Leap Day is:
Since the days of the week repeat every days and , the day of the week Leap Day occurs is the day of the week the day before Leap Day occurs, which is .
Solution 2 (Feasible Shortcuts)
Since every non-leap year there is one day extra after the weeks, we can deduce that if we were to travel forward amount of non-leap years, then the answer would be "Sunday + " days.
However, we also have leap-years in our pool of years traveled forward, and for every leap-year that passes, we have two extra days after the 52 weeks. So we would travel "Sunday + " days.
Mixing these two together, we get leap years , and non-leap years. We thus get "extra days" after Sunday. Since seven days are in a week, we can get , and six days after Sunday is .
- Note how we did not require any complex or time-consuming computation, and thus it will save crucial time, especially during a test like the AMC 10.
See Also
2006 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.