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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,608

**The twelve months in the calendar are grouped as given below:**

** {January, October}**

**{February, March, November} **

**{September, December} **

**{April, July}**

**{May}**

**{August}**

**{June}**

**Can you tell on what basis the months are grouped? **

Character is who you are when no one is looking.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Color?

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,560

They certainly are colorful!

As Month Numbers they are {1,10}{2,3,11}{9,12}{4,7}{5}{8}{6}

Maybe something deeper, like what day of the week the 1st of the month is?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

I think you may have got it. Quick check says that you have. The February has to be of the 28-day variety though.

The ordering is a bit strange. Using this year, ganesh has ordered them so that the lists start with Sunday, Wednesday, Friday, Saturday, Monday, Tuesday and Thursday respectively. Were they just arranged randomly, or is this another pattern?

Why did the vector cross the road?

It wanted to be normal.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,608

I think, together, MathsIsFun and mathsyperson have found the solution.

For any year other than a leap year, the months grouped together have the same days for the same dates. For example, since 1982 was not a leap year, Jan 25 and October 25 would have been the same day. Similarly, since 2006 AD is not a leap year, Feb 7, Mar 7 and November 7 would be the same day, that is Tuesday. June, May and August cannot be paired.

However, for leap years this pairing would not be applicable

There is no particular pattern in the arrangement (I didn't think of any).

Character is who you are when no one is looking.

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