OT - Calendar math puzzle

[QuikSand]

There's a mathematical concept that arises when using standard date notation in this format:

DD / MM / YY

Meaning that today's date would be represented as:

05 / 28 / 04

(Not to worry, our Euro friends - the DD/MM order won't matter here)


The concept is that from time to time, you end up with a date where the number of the day and the month add up to the two-digit number for the year.

The first time this happened in this century was Januay 1, 2002:

01 / 01 / 02 ---> 1 + 1 = 2

So, we will call that a "sum day" when the day and month sum to the year.


The puzzle is in two parts:

(1) What will be the last sum day of this century?

(2) How many sum days, in total, will there be in the entire century?

[Passacaglia]

I'd say the last sum day has to be 09/09/99.

[QuikSand]

I'd say the last sum day has to be 09/09/99.

I think you're missing the concept of sum -- we're not just pushing the digits together, we are adding them.

9 + 9 = 18, so September 9, 2018 would count. Get it?

[digamma]

I'd say the last sum day has to be 09/09/99.
Isn't the sum of that 18?

[QuikSand]

By the way - once someone gets their good answer to (2) above and recognizes that it might be a spoiler for others working on the puzzle... I'd ask that you hold back on posting the spoiler until others have had a fair shot at it.

[Passacaglia]

Oh, I see. I thought the sum of the month plus the sum of the date had to add up to the sum of the digits for the year.

[Maple Leafs]

I think you're missing the concept of sumSome day, I want to have the ability to make simple, straightforward statements that are somehow still dripping with sarcasm. It's a gift, and I want it.

[QuikSand]

Oh, I see. I thought the sum of the month plus the sum of the date had to add up to the sum of the digits for the year.

Might make for a good follow-up puzzle.

I'll rephrase to make the original puzzle clearer.

[gstelmack]

The last sum day would be 12/31/2043 (highest possible month/day numbers). Off to work on #2.

[Passacaglia]

The last sum day would be 12/31/2043 (highest possible month/day numbers). Off to work on #2.

Heh. Reading the answer makes me realize I was wrong again. I should have said I thought the puzzle was the sum of the digits of the date plus the sum of the digits of the month had to equal the sum of the digits of the year. Don't know why I had digits on the mind, even though they were never mentioned.

[QuikSand]

Don't know why I had digits on the mind, even though they were never mentioned.

To your credit, you're not making that all up -- I did mention digits, originally. I have since edited out the potentially misleading text.

[gstelmack]

PM sent with what I think the answer to #2 is.

[Huckleberry]

Won't there be 365 of them in any century?

[ahbrady]

Won't there be 365 of them in any century?

That's my thought as well.

[Huckleberry]

bump

[QuikSand]

365. Yes.

Sorry - I confirmed so many right answers via PM that I forgot to actually do so here.

[Huckleberry]

No worries. SkyDog has frightened me away from the PM system. He's mean.