can do this one in 4 times easy
But that's not the point
Here is my proposed solution - first split the 12 marbles into 3 groups of 4, let's call them A,B, and C. Then weigh A vs. B
There are two possibilities - if A and B are equal, then we know that the odd marble is in Group C. We take any 3 marbles from Group A+B and weigh them against 3 of the 4 in group C. If they are equal, the remaining group C marble is the odd one, and we weigh it against any other marble to determine if it's heavier or lighter. If the 3 from group C do not equal the other three = we know that one of those 3 is the odd one, we know if it is heavier or lighter, and we can weigh two of the three remaining marbles against each other to determine which is the odd one out
Here's the Tricky Part - say group A and B are not equal - for the sake of illustration, let's say A is heavier than B. Given this, we know the following:
- Group C are all the same weight
- If the odd marble is one from Group "A" it must be heavier
- If the odd marble is one from group "B" then it must be lighter.
- We then take 1 marble from Group "B"- let's call it B1 and combine it with any 3 from group C - we then weigh that marble against the 3 remaining marbles in group b, with one of the 4 from A - let's call that 1 A1.
So our Two Groups:
A1, B2, B3,B4
and
B1, C1,C2,C3
We know that C4 is not the odd one
We put A2,A3,A4 on the side - they are still unknown
Here are the possibilities:
- If the side with A1 remains heavier - we know that the marble is either A1 or B1. We weigh one of them against any other marble to find the odd one. If it's A1 then the odd marble is heavier, and if it's B1 then the odd marble is lighter
- If the side with A1 is lighter - we know that the odd marble is one of the three B's on that side, and that it is lighter - we weigh any two against each other to find the odd one out.
- If the two sides are equal, then one of A2,A3,A4 must be the odd ones out, and the odd one is heavier - we weigh any two against each other to find the odd one out.