# Fill in the two missing places

I've written down some numbers. There are two missing places which need to be filled in. There should not be ambiguity - the missing places have a unique solution.

What are the missing numbers? And what is the meaning behind all the numbers?

5 1
7 2
2 1
3 1
5 0
3 0
6 1
3 2
7 2
4 2
7 ?
? 5


A hint for every day it is unsolved:

Hint 1:

There is a pattern here, but it's not in the numbers provided - it's from where the numbers came from. I also haven't said that each line is the only option - perhaps this is why the question is not "give the next line" where there are multiple options, but rather, "fill the missing places".

Hint 2:

Why not try numbering the lines?

• Yes, it can go infinitely long. However, the continuation will not be unique. (as in, there are many different ways it could continue) Oct 22, 2017 at 7:51
• did these two columns of numbers begin with just 5 1 and then grow from there according to some rule such as a Fib series????? What did it take to seed the sequences of numbers?
– Dr t
Oct 22, 2017 at 19:03
• @ibrahimmahrir I wouldn't usually ask such a question except that in this case it may be nearly impossible to solve the sequence. It isn't binary bit shifting, different base number systems (although there is something kind of 'octal' about it)...just saying that a hint would be nice
– Dr t
Oct 22, 2017 at 19:22
• @Drt I totally agree. Another thing I've noticed is that all the numbers are either sums or absolute diffs of two others (30 = 51 - 21, ...) but that doesn't have a rule neither. My only fear is that this is a US related puzzle as eedrah's other two questions were also related to US, in which case many won't have a clue (me included). Oct 22, 2017 at 19:31
• @ibrahimmahrir I was thinking the same thing and so just eliminated the possibility that it was a list of the number of counties in the different states...that wouldn't produce an "infinitely long" list of numbers...and the "many different ways" implies that there is no RULE!! Or that there is a rule that changes for some reason. It isn't area codes either...no matter how you dissect the lists
– Dr t
Oct 22, 2017 at 19:39

I think (because there is no knowledge tag) it would be:

Modulo:
1 % 5 = 1
2 % 7 = 2
3 % 2 = 1
4 % 3 = 1
5 % 5 = 0
6 % 3 = 0
7 % 6 = 1
8 % 3 = 2
9 % 7 = 2
10 % 4 = 2
11 % 7 = 4
12 % 7 = 5