## A Conversation for Calculating the Day of the Week

### Negative totals

sidsred2004 Started conversation Apr 5, 2009

The answer to the problem described on the 'grrr!' posting explained why I calculated correctly that December 31st 1999 was a Friday but I kept coming up with January 1st 2000 as a Monday. I forgot that the latter date was the first day of the thirteenth month of the last year of the previous century!

But then I tried March 1st 2000:

Century: -36

Year: 0

Month: 10

Day: 1

Total: -25

Remainder: -4 ... So the day was a Thursday, right?

Well, no. It was a Wednesday.

I then tried several other dates in 2000 and noticed that the total has to be a positive number to give an accurate prediction of the day of the week.

It appears that the remainder, when a negative number has to be subtracted from 7 to give the true answer. Is this correct?

Thanks, Mike

### Negative totals

Icy North Posted Apr 5, 2009

Hi Mike,

Yes, it's conventional in number theory to say that -25 divided by seven is -4 remainder 3. I appreciate this won't be intuitive for everyone, so I'll think up an explanatory footnote.

Thanks for pointing this out!

Icy

### Negative totals

sidsred2004 Posted Apr 22, 2009

Thanks Icy,

I think this will help others like me whose maths education didn't run to Number Theory.

Mike

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