See if you can find a unique solution to this problem:

2356
1248
1736
5784

The strings of numbers above are all missing two numbers. When the two numbers are put back into the strings, the strings should have these properties:

The numbers 1-8 should each appear in the strings three times.
No string has the same number appearing twice.
Any two strings have exactly four common numbers.

Can you figure out the missing numbers?

This seems ambiguously defined to me.

"...above are missing two numbers" do you mean each string should be of length 6 or do you mean each string should have 6 unique characters/digits?

"The numbers 1-8 should each appear in the strings three times" do you mean for each string or total for all strings combined?

"Any two strings have exactly four common numbers" do you mean a common sub-sequence of length 4 or do you mean only 4 common characters can appear in any chosen pair of two strings?

Finally, can characters like 0 and 9 be used besides the 1-8 already stated? This could allow somebody to get around common subsequences and such.

The latter for the first three. And for the last, why not?

Assuming there is no order requirement:

Since the numbers 1-8 already appear twice inside the sixteen given numbers,
we just need to choose an extra string 1-8, and nothing more. Then, the third
property is a consequence of the last two (and hence, dependent on them), as it
always creates four numbers which are common and four numbers which are not
common between any two strings of (the eventual) six numbers.

After a quick look, it seems there are more than one solutions (I think fifteen),
as depending on the choice of first two strings, we end up with two "searching
possibilities" with either three or two solutions). For example, here's two of them:

2356-14
1248-37
1736-58
5784-26

2356-14
1248-57
1736-28
5784-36

I would suggest imposing a third condition for uniqueness, such as relating
their ascending order.




Pantazis

The first solution that you found was the one that I had intended. The numbers don't mean anything, they're just labels. I wanted to see if there were any puzzles with those rules that had unique solutions, and if larger ones were possible. So is the third rule unnecessary, or can it be changed to make a unique solution? And, yes, needing an extra 1-8 was intended.