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"Take any day. Next is the day 2 days before that. And next is the day 2 days before that and so on" Says Grandpa

"That is your sequence? What is that related to?" I ask

"You tell me. Use your imagination. Think out of box. Take a leap of faith. I will give you a hint. Pope." Said Grandpa.

Hmm. I started thinking. Monday-Saturday-Thursday-Tuesday-Sunday-Friday-Wednesday-Monday again and so on. Pope??

What is it that relates to those days in that order?

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Is it:

The day of the week on which the 29th of February falls?

Reason:

Our calendar is the Gregorian Calendar, named for Pope Gregory. Hence, also, leap of faith. Of course, this will fail every 100 years or so, since it's not a leap year when the year is divisible by 100. Of course, the exception to this occurs every 400 years, so 2000 was a leap year because it was the exception to the exception. But your grandfather was likely born after 1900 so maybe he wasn't too worried about that...

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    $\begingroup$ I kinda hope not, because what's being ignored here is actually that pope's contribution, and the sequence without that dates back to 45BC. $\endgroup$ – Gareth McCaughan Jan 4 at 11:52
  • $\begingroup$ @GarethMcCaughan - they way the answer is written, yes. But in the OP, grandpa merely gave 'pope' as a hint. It could be he meant that the pope broke it. $\endgroup$ – deep thought Jan 4 at 19:04

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