Thread: logical math problem?

Hello everyone,

I don't know much math,but I've been working on a few simple problems and here's one question that has been bothering me for awhile,

Question:

In 1970,I began collecting calendars and I have done so every year since.I will cease collecting when every subsequent year can be served by one,at least,of the calendars I have already collected.What is the last year in which I must collect the calendar ?
(ans: 1996)


I guess I should be looking for some sort of pattern here,but I just don't see one.
Should I be considering leap years here?
Erm...I really really don't know what I should do...

Hope someone can help.
Thank you.

Originally Posted by hana

Hello everyone,

I don't know much math,but I've been working on a few simple problems and here's one question that has been bothering me for awhile,

Question:

In 1970,I began collecting calendars and I have done so every year since.I will cease collecting when every subsequent year can be served by one,at least,of the calendars I have already collected.What is the last year in which I must collect the calendar ?
(ans: 1996)


I guess I should be looking for some sort of pattern here,but I just don't see one.
Should I be considering leap years here?
Erm...I really really don't know what I should do...

Hope someone can help.
Thank you.

For NON Leap year calendars:
January 1 can start on Sunday through Saturday.

For Years that are Leap years:
January 1 can start on Sunday through Saturday.

You will need 14 calendars.
List years from 1970 onward and identify the day of the week January 1 occurs and whether it is a leap year. After you have the 14 calendars you can stop.