A fake coin problem - to stretch your brains

I read an interesting puzzle once upon a time in one little book. He broke his head all evening and almost all night. And only in the morning I got the idea how to solve such a problem.

There are twelve coins. One of them is fake, but it is not known whether it is heavier or lighter than the others . There are also accurate jewelery scales with two cups, which can either be balanced or not, depending on what coins you put on each side.
You must use three and only three weighings . During these three weighings, you need to determine which of the twelve coins is false, and also heavier or lighter than the others.

If anyone is interested, I decided this:

(1,2,3,4 | 5,6,7,8).
1. (=). 1,...,8 ( ''). . 9,...,12.
(9,10 | 11,).
1.1. (=). , 12. :
(12 | ) .
1.1.1. (>). : 12 [>].
1.1.2. (<). : 12 [<].
1.2. (>). 12, 9,10,11.
(10,11 | ,) .
1.2.1. (>). : 10 [>].
1.2.2. (<). : 11 [<].
1.2.3. (=). : 9 [>].
1.3. (<). 12, 9,10,11.
(10,11 | ,) .
1.3.1. (>). : 11 [>].
1.3.2. (<). : 10 [<].
1.3.3. (=). : 9 [<].
2. (>). 9,...,12; 1,...,8.
(1,2,3,5 | 4,,,) .
2.1. (=). (6 | 7) .
2.1.1. (=). : 8 [<].
2.1.2. (<). : 6 [<].
2.1.3. (>). : 7 [<].
2.2. (>). (1 | 2) .
2.2.1. (=). : 3 [>].
2.2.2. (<). : 1 [>].
2.2.3. (>). : 2 [>].
2.3. (<). 4 5. – . (5 | ) .
2.3.1. (=). : 4 [>].
2.3.2. (<). : 5 [<].
3. (<). 9,...,12; 1,...,8.
(1,2,3,5 | 4,,,) .
3.1. (=). (6 | 7) .
3.1.1. (=). : 8 [>].
3.1.2. (<). : 6 [>].
3.1.3. (>). : 7 [>].
3.2. (>). (1 | 2) .
3.2.1. (=). : 3 [<].
3.2.2. (<). : 1 [<].
3.2.3. (>). : 2 [<].
3.3. (<). 4 5. – . (5 | ) .
3.3.1. (=). : 4 [<].
3.3.2. (>). : 5 [>].

I also found the solution version with the use of the ternary number system interesting: www.computerra.ru/offline/1997/228/969/ (thanks to dna for the reference).