2005 PMWC Problems/Problem I8
From AoPSWiki
Problem
Some people in Hong Kong express 
as 8th Feb and others express as
2nd Aug. This can be confusing as when we see , we don’t know whether it
is 8th Feb or 2nd Aug. However, it is easy to understand 
or 
as 22nd Sept, because there are only 
months in a year. How many dates in a year can cause this confusion?
Solution
assume a/b has the month first.
January: 1/1 can't cause confusion, 1/2 can. so can 1/3,......1/12. That makes 11.
February: 1/2 can, but 2/2 can't. 2/3...2/12 can, so that's 11 again.
So the first 12 days that aren't in the from x/x will cause confusion, so there are 11 each month.
See also
| 2005 PMWC (Problems) | ||
| Preceded by Problem I7 | Followed by Problem I9 | |
| I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
