Algebra type questions

Question

I have 16 coins and a balance scale. One of them is a lighter counterfeit coin. Explain how you can locate the counterfeit coin with only three weighings.

Answer 1

Cut them into two equal groups, with 8 coins in each. The lighter side has the counterfeit. These 8 are the only ones you will work with from here forward.

Set 2 coins aside, and split the remaining 6 coins into two groups of 3. Weigh these on the balance scale.

If they are EQUAL, then the counterfeit is one of the two set aside.

Weigh these set-aside two and see which one is lighter. That is your counterfeit.

If ONE SIDE IS LIGHTER than the other, the three in the lighter side are the only ones you will work with from here forward. Now you only have one measure left. Put ONE coin aside and measure the other two coins. If they are EQUAL, the the set-aside coin is your counterfeit. If ONE SIDE IS LIGHTER than the other, then the lighter side has your counterfeit coin.