My Attempt To Solve This Riddle

Just in case you have tried completing the riddle on your own. Please watch this video before reading further.

Now my Attempt:

A little background for those who didn’t watch the video.

You’re the realm’s greatest mathematician, but ever since you criticized the Emperor’s tax laws, you’ve been locked in the dungeon. Luckily for you, one of the Emperor’s governors has been convicted of paying his taxes with a counterfeit coin, which has made its way into the treasury. Can you earn your freedom by finding the fake?

Side Note: Just as I was gonna type out my answer on this blog, I decided to visit the site to see if I can get an embed for the riddle but then I saw the discussion and that Pete T. Had answered the riddled with the method I was following so I’m just gonna quote him/her on that since it’s simpler and quicker too.

Possible Alternative (Simpler) Answer

So if you weigh 6 on each pan, the pan that goes up or down is the side that has the counterfit coin.Then split those 6 and compare weights of 3 on each pan. The side that goes up or down has the counterfit. Then take 2 of those 3 and compare the weights. If they are equal, the third is counterfit….if not the pan that goes up or down has the counterfit.
This seems to be a lot simpler method….but maybe I’m missing something!