I just got sick from reading this
If Tuesday was four day before the day after two fortnights ago, what is the least number of days five years after this exact date for which it will be a Wednesday again given that three years ago was a leap year and there will be less than ninety nine days til Christmas Eve starting from the day after tomorrow?
For the sake of simplicity, we assume there are exactly 25% of the years that are leap years.
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1 solution
Moderator note:
Great bookkeeping! Sometimes we just have to slowly tease apart all of these details.
Let's figure this out step by step:
The day 4 days before the day after 2 forthnights ago was a Tuesday.
This is the same as saying:
The day 3 days before 2 forthnights ago was a Tuesday.
But 2 forthnights are just 4 weeks, so the day 2 forthnights ago was the same day of the week as today so:
The day 3 days before today was a Tuesday.
This means today is a Friday.
Now, three years ago was a leap year, so (assuming no multiples of 100 years) there will be another leap year next year, and another one in five years.
The fact that there will be less than ninety nine days til Christmas Eve starting from the day after tomorrow means that the date today is past february, so this exact date next year is 366 days from today. And this exact date in five years is (366 2 + 365 3) days from today, including two february 29ths.
Each leap year is exactly 52 weeks and 2 days, and non leap years are 52 weeks and 1 day, so these five years will be exactly 261 weeks, and this date in five years will be a Friday again. The following Wednesday will be in 5 days.