2005 PMWC Problems/Problem I8

Problem

Some people in Hong Kong express $2/8$ as 8th Feb and others express $2/8$ as 2nd Aug. This can be confusing as when we see $2/8$, we don’t know whether it is 8th Feb or 2nd Aug. However, it is easy to understand $9/22$ or $22/9$ as 22nd Sept, because there are only $12$ 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.

$11*12=\boxed{132}$



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
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