# A primarily 'very special' puzzle

I just found an old riddle that was sent to me years ago. I wasn't able to solve it then and haven't been able to solve it now either. Can you help me out?

This is what he wrote:

"I made this riddle a while back in the 00s (I'll give you this one ;)) when I was in the military, but sending it to you now;

I'm very special. Split me in half and you get the first part - one very special and one not special at all. Split me in three and you get the second part - one very special and two special. Split me in four and none of us are the same yet special.

Exactly when did I make this puzzle? Give me the full answer."

What did he mean by very special, special and not special. How are we suppose to find out exactly when he created it?

Making a new post since I lost access to the original (guest) account and editing my old post seems to be more confusing than just making a new one.

Incorporating all the feedback so far leads me to believe that it was written on

May 23rd, 2007 @ 11:57PM

Reasoning:

Working backwards from the last clue and building off of chandanr777's reasoning on "Very Special" and "Special", how can we split up a number into four where each part is special? Well, the only single digit prime numbers are 2,3,5, and 7. So that checks out. What about the number 2357? It turns out that is also a prime number and would be considered very special since each digit is also prime! Splitting this number in half would yield 23:57. 23 is a very special number, while 57 is a boring composite number. Splitting it in this way also looks like a valid time, specifically 11:57PM. Splitting it into three was a little more tricky until I realized it didn't require it to be split evenly. 2357 can be split into three parts in this way: 23/5/7. 23 is very special while 5 and 7 are just special. Splitting it in this manner looks similar to a date! Thanks to @cap in the comments for pointing out that in the military they use day/month/year format, so that gives us May 23rd, 2007. Putting it all together gives us May 23rd, 2007 @ 11:57PM.

• Looks good now! This is indeed the answer I had in mind. Well done, tick is yours! Commented Aug 29, 2022 at 13:42
• Thank you! This was a fun puzzle! Commented Aug 29, 2022 at 14:19

The riddle was written on

13 July 2003 at 19:31 pm

Explanation

This puzzle is about prime numbers. 2003 is the only prime number year in 00s. Convert 2003 into 12 bit binary code 011111010011. Splitting it into two parts gives us two 6 bit binary codes whose decimal equivalents are 31 and 19. So these two must be the time at which the riddle was created with only 19:31 as the valid time format. Splitting the 12 bit binary code into three parts gives us three parts of four bits each. Translating them into decimal equivalents gives us 7, 13 and 3. 7 is the month, 13 is the date and 3 is the year. Splitting the 12 bit binary code into four parts gives us four parts of three bits each. Translating them into decimal equivalents gives us 3, 7, 2 and 3. All of 3, 7, 2 and 3 are not the same.

Very special, not special and special

Very special numbers are the prime numbers which consist of both prime and non prime digits. 2003, 31 and 13 are very special numbers. Not special numbers are the prime numbers which consist of only non prime digits. 19 is a not special number. Special numbers are the prime numbers which consist of only prime digits. 7, 3 and 2 are special numbers.

Super cool puzzle! I enjoyed solving it.

• When splitting in 4 the clue reads 'none of us are the same' but your answer yields 3,7,2,3 so the 3 appears twice. Commented Aug 24, 2022 at 10:47
• Kicks self for not getting the "primarily" clue in the title. Very cool puzzle!
– JLee
Commented Aug 24, 2022 at 11:04
• Is there a hint that led you to convert and split the numbers the way you did, or was that just a guess? Additionally, I'm not sure how you came to the conclusion that 19 is not special. By your definition, it seems "very special". Commented Aug 24, 2022 at 12:56
• @TheRubberDuck My first intuition was to find a 12 letter word which could be split equally into 2, 3 and 4 parts. Once that didn't work out, I proceeded with trying out with the year. Only way a year could have been represented in 12 characters was through binary. And to answer your other question, 19 is not special because the digits 1 and 9 are both non prime digits. A very special number would have had both prime and non prime digits. Commented Aug 24, 2022 at 13:05
• I can't believe I was treating 9 as prime. BRB, deleting my account. Commented Aug 24, 2022 at 13:07

It was written on

May 7th, 2003 @ 11:57PM

Reasoning:

Working backwards from the last clue and building off of chandanr777's reasoning on "Very Special" and "Special", how can we split up a number into four where each part is special? Well, the only single digit prime numbers are 2,3,5, and 7. So that checks out. What about the number 2357? It turns out that is also a prime number and would be considered very special since each digit is also prime! Splitting this number in half would yield 23:57. 23 is a very special number, while 57 is a boring composite number. Splitting it in this way also looks like a valid time, specifically 11:57PM. Splitting it into three was a little more tricky until I realized it didn't require it to be split evenly. 2357 can be split into three parts in this way: 23/5/7. 23 is very special while 5 and 7 are just special. Splitting it in this manner looks similar to a date! Assuming this is year/month/date format, that gives us May 7th, 2023. However, this date is in the future, so 23 must mean something else. Taking the clue "back in the 00s" we can sandwich the "00" between 2 and 3 to give us 2003, which is also a prime number. Putting it all together gives us May 7th, 2003 @ 11:57PM.

This is my first attempt at a solve on this Stack Exchange! Even if I'm wrong, it was fun!

Edit: Readjusted my logic based on Prim3numbah's feedback.

• I think you got it! Satisfies all the criteria of the riddle. Commented Aug 24, 2022 at 17:28
• I think you missed the clue that it's from the 00's. Commented Aug 24, 2022 at 18:11
• Great job! This is indeed the digits I was looking for, but if it were written on the 00's and not in the future the answer should be..? It's not in conventional format. Commented Aug 25, 2022 at 7:40
• Given that his friend was in the military I think it is much more likely it was rot13(qnl zbagu lrne) which also works without adding digits. Commented Aug 25, 2022 at 19:50
• Yes @cap is right. That was my intention. Just change to what he wrote, and the tick is yours! Commented Aug 26, 2022 at 7:17