Saturday, 24 October 2009

Quick question

...and quick answer required.

Suppose you are a manufacturer of wall calendars showing days and dates for twelve months (as calendars do). You have little imagination and always print them with the same picture.

You want to stock up for one hundred years. How many different kinds of calendar do you have to print?

If it takes you more than ten seconds to find the answer, you are probably on the wrong track.

The answer is HERE


Froog said...

My first thought was to agree with your answer... but, in any given cycle of 100 years, would the 24 or 25 Leap Years necessarily cover all the days of the week? It doesn't matter which date you consider, January 1st or February 29th or whatever: would any given date in the Leap Years encompass all 7 days of the week over that period? I'm not sure that it would, but my grasp of mathematics is too poor to produce a definitive proof either way.

It would be rather satisfying to be able to readily calculate the minimum or maximum (or unvarying) number of years necessary for a series of February 29ths to fall on every day of the week. I sometimes wish I'd paid more attention in maths classes.

Hmm. Actually, it's not that hard to work out, but I'm still frustrated at not being able to formulate a rule to describe it.

If my back-of-an-envelope scribbings are correct, it takes from 9 to 16 Leap Years to work through all the days of the week for the 29th February.

Tony said...

Well, yes, I see what you mean, but my answer still stands. What you are saying is that it is possible that after a hundred years you might be left with one batch of your fourteen unsold. I'm not sure whether this is true or not, but anyway I didn't say that you were stocking up for the NEXT hundred years. At some time in the future there is bound to be a century when all fourteen will be needed.
It's not relevant, but how many people know that a year will be a leap year if it is divisible by 4 but NOT by 100, and that if a year is divisible by 4 AND by 100 it is not a leap year unless it is ALSO divisible by 400? Just thought I'd mention it.

Grumio said...

The chaps and chappesses at Reginald's reckon you can make do with just one and a felt tip to change the days of the week or cross off 29ths of Februaries as and when the occasion calls. It gets messy, but what wonderful doesn't?

Froog said...

'Always buy a Leap Year calendar' is sage advice indeed, Grumio. The extra day gives such added value.