There are nine silver coins marked 1, 2, 3, 4, 5, 6, 7, 8, and 9.
They are supposed to weigh the number of grams that is written on them.
One of the coins is fake and is lighter than it should be.
Find the fake coin using the balance scale twice.
Weighing 1: 1+2+9 vs 3+4+5 with 6,7,8 left off.
Weighing 2: 2+3+7 vs 1+5+6 with 4,8,9 left off.
Each of the nine possible pairs of locations for the light coin occurs one-to-one for each of the nine coins. For example coin 4 is 1st=right, 2nd=off.
Then just by knowing which group the light coin was in each time, the light coin itself can be determined.
Edit: Corrected typo: "1+3+7 vs 2+5+6" to "2+3+7 vs 1+5+6"
Edited on January 19, 2016, 10:03 am
Two preplanned weighings
