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.

 

[LudusRex]

To solve this riddle, we can divide the eight coins into three groups of three, three, and two coins. Weigh the first two groups of three coins against each other. If the weights are equal, then the slightly heavy coin is in the remaining two coins. Weigh one of these two coins against a known good coin. If they balance, then the remaining coin is the slightly heavy one. If they do not balance, then the slightly heavy coin is the one on the scale.

If the first weighing of the two groups of three coins shows that one group is heavier than the other, then the slightly heavy coin must be in that group. Take two coins from the heavier group and weigh them against each other. If they balance, then the remaining coin is the slightly heavy one. If they do not balance, then the heavier coin is the slightly heavy one.

In both scenarios, we have successfully identified the slightly heavy coin using only two weighings. This method works because we are using the beam balance to compare the weights of the coins against each other, rather than measuring their absolute weight. By dividing the coins into different groups and comparing their weights against each other, we are able to narrow down the search for the slightly heavy coin in just two steps.