Hi Todd,
I can get you part way to the answer.
I need to distinguish among the balls so I am going to imagine that 4 are red, 4 are blue and 4 are green.
Step 1. Put the 4 red on one side of the balance and the 4 blue on the other side. Suppose they balance, then the odd ball is green.
Step 2. Put 1 red and 1 green on the left side of the balance and 2 greens on the right side of the balance.
Suppose they balance, then the odd ball is the one remaining green ball.
Step3. Balance the one remaining green against a red ball to see if the green ball is heavier or lighter than the rest.
Suppose in step 2 that the left side is heavier, then either the green ball on the left is heaver than the rest or one of the green balls on the right is lighter than the rest.
Step 3. Balance the two green balls on the right in step 2 against each other. If they balance then the green ball on the left in step 2 is heavier than all the rest. If they don't balance then the lighter of the two is lighter than all the rest.
Suppose in step 2 that the right side is heavier, then either the green ball on the left is lighter than the rest or one of the green balls on the right is heavier than the rest.
Step 3. Balance the two green balls on the right in step 2 against each other. If they balance then the green ball on the left in step 2 is lighter than all the rest. If they don't balance then the heavier of the two is heavier than all the rest.
How do you proceed if in step 1 the the scale doesn't balance?
Penny
