Much much tougher brain teaser

[ptmusic]

Ok, the way I solved this was to use Scenarios for each possible outcome.

Step 1 always starts the same for each Scenario; Steps 2 and 3 vary depending on the result of Step 1.

I am calling the rocks by number 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

SCENARIO A

Step 1: 1,2,3,4 vs. 5,6,7,8. They are equal.

Step 2: 1,2,3 vs. 9,10,11. They are equal

Step 3: 1 vs. 12. 12 is the odd rock, and it is heavy or light depending on how it weighs against 1.



SCENARIO B:

Step 1: 1,2,3,4 vs. 5,6,7,8. They are equal.

Step 2: 1,2,3 vs. 9,10,11. They are NOT equal. Odd rock is 9, 10, or 11; you know if odd rock is heavy or light now, depending on how this group weighed against 1,2,3.

Step 3a: 9 vs. 10. They are Equal. Odd rock is 11.
Step 3b: 9 vs. 10. They are NOT equal. Odd rock is the heavier rock of the two, if group was heavier in Step 2, or odd rock is the lighter rock if the group was lighter in Step 2.



SCENARIO C:

Step 1: 1,2,3,4 vs. 5,6,7,8. They are NOT equal. Call 1,2,3,4 the side that was lighter. You know the odd rock is one of these 8 rocks. You also know that if it is 1,2,3, or 4 then it is lighter; if it 5,6,7, or 8 then it is heavier. You also know that it is not 9,10,11, or 12.

Step 2: 1,8,9,10,11 vs. 2,3,5,6,12. They are equal. You know that odd is 4 (and light) or 7 (and heavy).

Step 3a: 12 vs. 4. They are equal. 7 is the odd rock and it is heavy.
Step 3b: 12 vs. 4. They are NOT equal. 4 is the odd rock and it is light.



SCENARIO D:

Step 1: 1,2,3,4 vs. 5,6,7,8. They are NOT equal. You know the same information as in Scenario C.

Step 2: 1,8,9,10,11 vs. 2,3,5,6,12. They are NOT equal. If the first group is heavier, 8 is odd rock and it is heavy OR 2 or 3 is odd and light. Go to Step 3a. If 2nd group is heavy, 5 or 6 is odd OR 1 is light; go to Step 3b.

Step 3a: 2 vs. 3. If equal, then 8 is odd rock and heavy. If Not equal, then the lighter of the two is the odd rock.

Step 3b: 5 vs. 6. If equal, then 1 is odd rock and light. If NOT equal, the heavier of the two is the odd rock.


-ptmusic