Unique Dates

[Michael Wallace]

A gentle puzzle to give you something to think about for five minutes on a Saturday, which I came up with whilst trying to get to sleep the other night.

What's cool about the date 25/04/1983? What about 26/04/1983? Any ideas? Read on when you work it out/give up.






Each of those 8 digits is unique. Cool? Cool. Let's call this a 'unique' date, and go looking for more!

So the question is in two parts:

a) When is the first day in the 20th Century that is a 'unique' date?
ii) How many days in the 20th Century are 'unique' dates?

Post solutions, but it's the working that's interesting, so it'd be cool if people could post their thought process as well (but everything in spoiler colours). Like I said, it's not particularly taxing, but I found it fun, and the answer a bit surprising.

[JimBentley]

Cheers for this, Michael, it's a nice puzzle. I make the first one to be 26th May 1934 (26/05/1934) and the last one 25th June 1987 (25/06/1987).

Wot I done:

You need 8 unique digits from 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

The 1 and 9 are always taken by the century, so the day, month and year must come from 0, 2, 3, 4, 5, 6, 7 and 8.

October (10), November (11) and December (12) are always ruled out by the 1 being used in the century, so the first digit of the month must be 0.

The day can't start 0 or 1, as these are taken, but also 30 and 31 are impossible (0 and 1 again), so must start with a 2.

This gives a date format of 2 _ / 0 _ / 1 9 _ _ with the blanks filled by 3, 4, 5, 6, 7 and 8. The first year possible is therefore 1934 and the earliest date must use the next lowest numbers, so 26/05/1934.

I think there should be 360 such dates in the 20th century, as it's a permutation of 4 from a list of 6. I'm ashamed to say I had to look up how to work this out (well, it is over twenty years since I learnt it), but it's 6!/(6-4)! = 720/2 = 360.

[Michael Wallace]

Yep, Jim's answer(s) agree with mine, glad someone enjoyed it. I was inspired by it because I was thinking about CF's birthday, and noticed that it was nearly a unique date, but not quite (had he been born 2 days earlier it would have been), which then got me thinking about the puzzle in general. I was quite surprised by how few such dates there are.

[JackHurst]

Nice, something to keep me entertained whilst apterous is down.
Im just working out the earliest year, cba to do the real tough bit. Im writing out my thoughts as i am doing this, so this post has all my working.

1 2 3 4 5 6 7 8 9 0
So if we are in the 19th century, we can only use:
2 3 4 5 6 7 8 0
to make the decade and year.
Taking 2 and 0 gives 1902 as the year.
Now we have:
3 4 5 6 7 8
to make the month. Oh shit, you cant make a month out of those.
So lets go back a couple of steps.
Well if I keep a 0 in the year, then I wont be able to make a month at all.
Also, if I keep a 2 in the year then I would have to use a 0 as the first digit of the month. This means the smallest number I could have for the day of the month would be 34, which is not possible, hence the year cannot contain a 2.
So now, having thought a little bit longer about it, it looks like 1934 would be a good starting point.
So if my date looks like xx/xx/1934, i can still chose from:
2 5 6 7 8 0
for the month.
So the smallest number for the month I can make from these is 02, but if I use this I wont be able to use the rest of the numbers to make a valid number of days. So if I try 05 as the month, i can see that the number of days will be 26, and it all falls into place to give:
26/05/1934

[Peter Mabey]

The above shows that the next one is way in the future.
I make it 07/16/2345

[Michael Wallace]

The above shows that the next one is way in the future.
I make it 07/16/2345

Haha, excellent - I happened to be working this out in bed last night.

[Liam Tiernan]

The above shows that the next one is way in the future.
I make it 07/16/2345

Haha, excellent - I happened to be working this out in bed last night.

I think you're about a month out there. 17/06/2345

[Michael Wallace]

The above shows that the next one is way in the future.
I make it 07/16/2345

Haha, excellent - I happened to be working this out in bed last night.

I think you're about a month out there. 17/06/2345

Yeah, good point, I was too distracted by the fact someone had attempted the same thing I'd been thinking about the night before to check whether our answers agreed.

[Howard Somerset]

Nice one. Was away for the weekend, so I've only just seen it. I arrived at the same solutions that have already been given, and my reasoning was almost the same as Jim's, the only exception being:

It's not correct to say that 1 and 9 are always the first two digits of the year in the 20th century. The final year was 2000, but as that year has duplicate zeros, it can be disregarded, so any date meeting the requirements of the puzzle must have 1 and 9 as the first two digits of the year. Thereafter, my reasoning follows Jim's..

[Michael Wallace]

Nice one. Was away for the weekend, so I've only just seen it. I arrived at the same solutions that have already been given, and my reasoning was almost the same as Jim's, the only exception being:

It's not correct to say that 1 and 9 are always the first two digits of the year in the 20th century. The final year was 2000, but as that year has duplicate zeros, it can be disregarded, so any date meeting the requirements of the puzzle must have 1 and 9 as the first two digits of the year. Thereafter, my reasoning follows Jim's..

Heh, yep. When I was writing this up I considered specifying "years from 1900 to 1999", rather than the 20th Century,which as you point out is slightly different, but since it doesn't make a difference to the problem I decided not to bother.

[Howard Somerset]

I enjoyed that puzzle, so considered a similar one over lunch. Can I add it here, or would you like to move it into a different thread?

My digital watch shows time and date in the form hh:mm:ss dd/mm (using 24 hour clock). So that's 10 digits. How many times in a year are those 10 digits all different? And when is the first such occurance in any year. I've come up with a solution. Again, submit your method.

[Michael Wallace]

I enjoyed that puzzle, so considered a similar one over lunch. Can I add it here, or would you like to move it into a different thread?

My digital watch shows time and date in the form hh:mm:ss dd/mm (using 24 hour clock). So that's 10 digits. How many times in a year are those 10 digits all different? And when is the first such occurance in any year. I've come up with a solution. Again, submit your method.

Awesome, and I think in this thread is fine. Shall have a think about this when I inevitably grow tired of 'proper' work this afternoon.

[Gavin Chipper]

I enjoyed that puzzle, so considered a similar one over lunch. Can I add it here, or would you like to move it into a different thread?

My digital watch shows time and date in the form hh:mm:ss dd/mm (using 24 hour clock). So that's 10 digits. How many times in a year are those 10 digits all different? And when is the first such occurance in any year. I've come up with a solution. Again, submit your method.

Just thinking out loud, you want to keep the 0 for the month if possible so the first hour digit is limited to 1, 2 and the first date digit is limited to 1, 2, 3. To have a date in January, the first hour digit would have to be 2 and the first date digit to 3. But the second date digit possibilities are all taken. For February, the first hour digit would have to be 1 and the date 3. But then we're stuck again.

If you had a date in March you would want to use 1 for the first date digit if possible, which would limit the first hour digit to 2, but then the second hour digit could only be 0, 1, 2, 3 which are all taken. So we could have 2 as the first date digit and 1 for the first hour digit. We would need the 4 and 5 for the first minute and second digits. And we can fill in the gaps. But this is just for the first occurrence.

17:48:59 26/03

[Howard Somerset]

I came up with the same answer as you, Gavin, for the first occurrance, but my reasoning followed a completely different course. I worked on establishing how many occurrances there are in the year, and the first was a spin-off from that.

[John Gillies]

26/04/1983 was the 22nd birthday of a girl with whom I was hopelessly infatuated at school 5 years previously. On 25/04/1983 she was 21. We went out a couple of times then she dumped me. I was gutted. She was gorgeous.

On both those dates I was a 21 year old piss-artist uni drop-out. I was also married to my son Scott's mother who was not Scott's mother!

On 26/04 this year Scott begins filiming for Countdown; on 25/04 he won't be.

Is this the correct answer?

[Dinos Sfyris]

I'd been saving this puzzle up for a while now and finally got round to it on a dull Cineworld shift last night. I also entertained myself with the following extension questions for about 5 minutes:

i) How many unique dates are there in the 2nd millenium AD (1000-1999)
ii) How many unique dates are there in the 3rd millenium AD (2000-2999)

[Howard Somerset]

i) How many unique dates are there in the 2nd millenium BC (1000-1999)
ii) How many unique dates are there in the 3rd millenium BC (2000-2999)

Any idea what calendar we were using three to five thousand years ago? Certainly not the present Gregorian one, and also not the previous Julian one.

[Dinos Sfyris]

oops lol edited.

[Ian Volante]

i) How many unique dates are there in the 2nd millenium BC (1000-1999)
ii) How many unique dates are there in the 3rd millenium BC (2000-2999)

Any idea what calendar we were using three to five thousand years ago? Certainly not the present Gregorian one, and also not the previous Julian one.

I doubt any accurate calendar was in use in this land until the Romans arrived. I would reckon that the closest we got would have been the marking of the seasons astronomically and botanically by Druids or equivalent.

[Dmitry Goretsky]

i) How many unique dates are there in the 2nd millenium AD (1000-1999)
ii) How many unique dates are there in the 3rd millenium AD (2000-2999)

iii) How many unique dates are there in the 1st millenium AD (0001-1000)

[Dmitry Goretsky]

I enjoyed that puzzle, so considered a similar one over lunch. Can I add it here, or would you like to move it into a different thread?

My digital watch shows time and date in the form hh:mm:ss dd/mm (using 24 hour clock). So that's 10 digits. How many times in a year are those 10 digits all different? And when is the first such occurance in any year. I've come up with a solution. Again, submit your method.

Just thinking out loud, you want to keep the 0 for the month if possible so the first hour digit is limited to 1, 2 and the first date digit is limited to 1, 2, 3. To have a date in January, the first hour digit would have to be 2 and the first date digit to 3. But the second date digit possibilities are all taken. For February, the first hour digit would have to be 1 and the date 3. But then we're stuck again.

If you had a date in March you would want to use 1 for the first date digit if possible, which would limit the first hour digit to 2, but then the second hour digit could only be 0, 1, 2, 3 which are all taken. So we could have 2 as the first date digit and 1 for the first hour digit. We would need the 4 and 5 for the first minute and second digits. And we can fill in the gaps. But this is just for the first occurrence.

17:48:59 26/03

Here is a solution for the last date.
Impossible possibilities
December (12). Because you should use 0 as the first hour digit and 3 as the first month digit. But 0 and 1 are taken so you can't use it as the second month digit
November (11). LOL
October (10). Just because 01 is impossible, so does 10
Final steps
09
2 as the first hour digit and 3 as the first day digit (or simply 2 and 3). You need to have 1 in both the day and hour. But that's impossible!
1 and 3. Here 31(month) is impossible because 1 is taken by the hour!
0 and 3. LOL
2 and 2. LOLOLOL
We are so close to the solution now!
1 and 2. Of course, possible. So, we only need to place 3, 4, 5, 6, 7 and 8 to make the latest date.
Day. 28. LOL
Hour. 17. LOL
Minute. 56, not 65. LOL.
Second. 43. LOLOLOLOLOL

[Eoin Monaghan]

Err, what's up with all the LOL, this is serious stuff Dmitry.

[Dmitry Goretsky]

Err, what's up with all the LOL, this is serious stuff Dmitry.

I marked obvious with LOL and very obvious with LOLOLOLOLOL

[Howard Somerset]

Err, what's up with all the LOL, this is serious stuff Dmitry.

I marked obvious with LOL and very obvious with LOLOLOLOLOL

Yes, but what did LOLOLOL mean?

[Ian Volante]

Err, what's up with all the LOL, this is serious stuff Dmitry.

I marked obvious with LOL and very obvious with LOLOLOLOLOL

Yes, but what did LOLOLOL mean?

Laugh out loud out loud out loud of course. Or is that Lots of love of love of love? Either way, we're drowning in bodily fluids.

[Dmitry Goretsky]

Err, what's up with all the LOL, this is serious stuff Dmitry.

I marked obvious with LOL and very obvious with LOLOLOLOLOL

Yes, but what did LOLOLOL mean?

That means very obvious, but less obvious than LOLOLOLOLOL. More LOL, more obvious and funny. LOLOL is more obvious than LOL, for example

[Dmitry Goretsky]

LOLOL means lots of laughing out loud. LOLOLOL means lots of lots of laughing out loud

[Andy Wilson]

Or is that Lots of love?

Heard a funny story about a friend's mother, new to text speak sending a consolation text to a friend over the death of a relative and ending the text with lol!

[Charlie Reams]

Or is that Lots of love?

Heard a funny story about a friend's mother, new to text speak sending a consolation text to a friend over the death of a relative and ending the text with lol!

http://www.youtube.com/watch?v=Lv6HHv3xjgg

[Dmitry Goretsky]

Any idea what calendar we were using three to five thousand years ago? Certainly not the present Gregorian one, and also not the previous Julian one.

Maybe Roman?

[Howard Somerset]

Any idea what calendar we were using three to five thousand years ago? Certainly not the present Gregorian one, and also not the previous Julian one.

Maybe Roman?

Unlikely. The Roman Empire dates back to the fist millennium BC. Dinos's question, before he corrected it, referred to the second and third millennia BC

[Ian Volante]

Any idea what calendar we were using three to five thousand years ago? Certainly not the present Gregorian one, and also not the previous Julian one.

Maybe Roman?

Unlikely. The Roman Empire dates back to the fist millennium BC. Dinos's question, before he corrected it, referred to the second and third millennia BC

Who does "we" refer to anyway? In northern Europe, I suspect the neo-agrarian, possibly semi-nomadic tribes followed the seasons and little more, given their probable lack of coherent science systems. I'm not sure what system the Egyptians used at the time, maybe this, and other middle-eastern systems in particular localities were prevalent. WOuld anyone as far back as the Hittites have a decent calendar? Stuffed if I know.