Here's a puzzle I recently stumbled across. It's quite wonderful.

When I was in Prague in 1975, Bartok told me that he was born on a very hot summer Sunday, and that on his seventh birthday his father took him to the circus, which was visiting the city for the weekend. How old was Bartok when I met Bartok in 1975?

Yes, there's enough info to solve it.

15?

Nope.
By the way, to avoid some ambiguity, I should ask instead, What year was Bartok born?

1944? or 1916?

No and no.

I'll post the answer in a few days ifsomeonedoesn't get the right answer before.

I wasn't sure. There are quite a lot of dates during the summer months that have repeating weekends.

I'm sure I'm forgetting a step along the way, but for the date I used it fit the 7 year gap.

Most likely I'm missing something simple in my process...

Yes, if you actually look at a calendar for the seven years you have in mind, you'll see there's something you didn't take into account...

"Ohhhh..." I say while nodding; pretending like I see that snake in front of my face...

You thought he was 15 in 1975. So look at a calendar for 1960, pick a Sunday birthday, and see what happens on his seventh birthday...

Here's the spoiler (Don't scroll down if you would still like to work on this):







































Suppose the birthday was June 1st for convenience's sake, and it was a Sunday. What you will find is that next year, that date will fall on a Monday, the year after a Tuesday, the year after a Wednesday, and so on. So on the seventh birthday, the date should fall on a Sunday. Except for one little thing...leap years. You see if there's a leap year, then the day skips twice. That is, if June 1 is a Saturday in 2019, it will be a Monday, the next year in 2020, because 2020 is a leap year.

So if someone is born on a Sunday, normally, their seventh birthday will fall on a Monday, not a Sunday because in that seven year interval, there will be at least one leap year.

And yet Bartok seems to be an exception. How?

Because if a year ends in a 00 and is not divisible by 400, it is not a leap year. That is, 1700, 1800, 1900, are not leap years; 1600 and 2000 are. (Don't blame me, I don't make up these rules).

So Bartok's seven year interval must have included 1900 in order to avoid any leap years from happening. We then can calculate that he must have been born in 1896, because if he were born in say 1897, his seventh birthday would have been in 1904, which is a leap year. But the span 1896 - 1903 contains no leap year. Hence Bartok's seventh birthday lands on a Sunday.

One minor problem--what if Bartok was born in 1896 before February 29th? Then indeed, his seventh birthday would have landed on a Monday. But we were told that Bartok was born on a hot summer day, so it must have been after February 29th.

I love this puzzle. I certainly didn't solve it.

I figured it would be something like that. I remember getting excited to learn "A day for any date" in the 13 steps, but my excitement diminished as my eyes glazed over.

The summer day portion made the scope too large for me to confirm a solid date. I did a search for the summer months who's weekends didn't change date and found my original 'guess' as there was unknown wiggle room because we didn't know what part of the year "you" met him.

At first I suspected a play on words as you stated but soon realized a general understanding of a day for any date would also be required.

So you don't know the answer?

Mike, the answer is 1896. It didn't require the date.

What I mean when I said that I didn't solve it, was that I had to find out the answer from someone else. But 1896 is the answer to the problem.

The solution as outlined above doesn't require day for date at all--just the insight that the year had to be the beginning of a seven year period with no leap year.

Great puzzle!

By the way: If Bartok was born on Sunday, 29 February 1920 in Australia (in the Australian summer), his birthday would return for the 7th time on Sunday, 29 February 1948.

Good point.

I especially appreciate considering the issue of northern/southern hemisphere.