Solve 8 Coin Riddle with 2 Weighings

[mia5]

You are given eight coins of same denomination, out of the eight coins one coin is very very slightly heavy than the remaining seven such that you cannot separate it by weighing it in your palms. You are given a beam balance with the help of which you have to separate out the very slightly heavy coin but you are allowed to use the balance only twice.

 

[Charmar]

There's probably a better way to word this but here is my solution.

Spoiler

Put 3 on one side, 3 on the other. If the scale doesn't tip, weigh the 2 that were not on the scale.

If one of the 3 tips, pick 2 of those and put them on the scale, if it balances it's the 3rd one of that group if not the scale will tip.

 

[mia5]

There's probably a better way to word this but here is my solution.

Spoiler

Put 3 on one side, 3 on the other. If the scale doesn't tip, weigh the 2 that were not on the scale.

If one of the 3 tips, pick 2 of those and put them on the scale, if it balances it's the 3rd one of that group if not the scale will tip.

absolutely correct

 

[mfb]

You can do the same with 9 coins.
Or, in general, with 3ⁿ coins if you can use the balance n times.