Best Date for Dating
Andrew calls a date
romantic
if the sum of the numbers assigned to the day and the month in the date equals to the number formed by last two digits of the year. For example, one such example is Valentines' Day 2016 (
) as
.
On Valentine's day, Andrew goes on a romantic date with his girlfriend and impresses her with many surprises. Andrew's girlfriend likes the Valentine's Day date a lot and demands Andrew that they have more dates on romantic dates.
How many romantic dates are still available in the year of 2016, on which it is possible for Andrew to go on a date?
Details And Assumptions:
-
Andrew and his girlfriend go on a date on a romantic date only.
-
No one denies his girlfriend's demands.
This problem is an entry to Valentine's Day Celebration Contest . If you found this submission great, upvote my comment there.
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1 solution
Moderator note:
Great problem! When solving an equation, we have to be mindful of the domain.
Andrew is such a happy and lucky man. Note that we are looking for dates in form D / M / 1 6 where D is the number of day , M is number of month and D + M = 1 6 . Now we write all possible dates:
D + M = 1 6 1 5 + 1 = 1 6 1 4 + 2 = 1 6 1 3 + 3 = 1 6 1 2 + 4 = 1 6 1 1 + 5 = 1 6 1 0 + 6 = 1 6 9 + 7 = 1 6 8 + 8 = 1 6 7 + 9 = 1 6 6 + 1 0 = 1 6 5 + 1 1 = 1 6 4 + 1 2 = 1 6
But note that the first date 1 5 / 0 1 / 2 0 1 6 is already passed and 1 4 / 0 2 / 2 0 1 6 is already used up for dating. So the remaining romantic dates are 1 0 in number.