Can I find 7 groups of 3 numbers such that every pair of numbers 1 to 7 appears once?

Question

What I am trying to do is find exactly 7 groups of 3 from {1, 2, 3, ..., 7} that have within them all possible pairs of these numbers.
For example, {1, 2, 3} has {1, 2}, {2, 3} and {1, 3} I know there's 21 total pairs from 1 to 7 and 21 pairs generated from the groups of 3 so it should be possible but I just can't find the solution.
(Sorry for the bad formatting and possibly bad tags, I'm a bit new)

Answer 1

Try:

$$ \{1,2,3\}$$ $$ \{1,4,5\}$$ $$ \{1,6,7\}$$ $$ \{2,4,6\}$$ $$ \{2,5,7\}$$ $$ \{3,4,7\}$$ $$ \{3,5,6\}$$