8
$\begingroup$

Carl Dane was a man who liked calendars. Luckily, he received a small check for his 18th birthday (he was born in April 1975). And guess on what he decided to spend his money? Yes, calendars.

But Carl Dane was kind of frugal: he figured that he could use and reuse a set of calendars until he died, even if he lived to be as old as the oldest man (verified) who ever walked this planet (we're in 1993, remember). Carl Dane did not care about the irregular holidays like Easter; also, he would never write on a calendar. Carl Dane had a calendar for every year since his birth (birth included), but he didn't want to keep the ones he already had that he didn't need. He would just buy the remaining ones that he would need as time went on.

Given that, can you figure out:

  • how many calendars he got rid of?
  • how many calendars he would need in total?
  • how many years it took him to have all the calendars needed?

You'll assume that he doesn't die before completing his collection.

$\endgroup$
  • $\begingroup$ Excellent puzzle! $\endgroup$ – Rand al'Thor Dec 9 '16 at 0:08
9
$\begingroup$

He needs to cover

14 calendars: 7 calendars for leap years and 7 calendars for regular years, because he wants to have a calendar starting on each weekday, with the leap years treated separately.

For leap years, there are

the first consecutive leap years since he was born (the day of the week belonging to February 29):

  • 1976 Sunday
  • 1980 Friday
  • 1984 Wednesday
  • 1988 Monday
  • 1992 Saturday
  • 1996 Thursday
  • 2000 Tuesday

Then he needs to cover

the normal years, and those will be 1975, 1977, 1978, 1979, 1981, 1982 and 1985, because those are the first years since he was born when there are all possible weekdays for every day in a year.

The answers to your questions:

How many calendars did he get rid of?

7 calendars, if we count 1993. If he doesn't have that one yet then 6: namely 1983, 1986, 1987, 1989, 1990, 1991.

How many calendars would he need in total?

14, as shown above.

How many years did it take him to have all the calendars needed?

Till 2000, so seven years.

$\endgroup$
  • $\begingroup$ Very nice first answer :-). Good job! $\endgroup$ – IAmInPLS Dec 9 '16 at 0:51

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.