28 Aug 2022 10:46 am
That's incorrect. Outcome #1 says that if it's Even then you have 3 marbles left, you don't know if it's heavier or lighter, and only have one more chance to weigh them. So you have to rely on luck that it is Odd to get to your solution. Remember, this has to work every time, in the same manner. No changes, and no luck involved.Cannonpointer » 28 Aug 2022, 9:53 am » wrote: ↑ So, your PM delivered ONE viable solution to the problem. If you work my solution, you will find that it works in every scenario. It all comes down to the second weighing, and bringing the suspect list down to no more than three. That is what my solution accomplishes in each of the three possible outcomes.
Second weighing:
Sequester 3 from side a. Move two from side b to side a, and place one control with the remaining 2 on side b. Weigh 3 against 3.
Outcomes:
1. Even: The 3 sequestered are the suspects
2. Odd: side a is now HEAVIER, rather than lighter. The two on side a which came over from side b are the suspects.
3. Odd: side a is STILL lighter. The original side a marble may be lighter, or one of the two original side b marbles is heavier: 3 SUSPECTS.
There are only three outcomes of my second weighing, same as yours - and in all three you are left with three suspect marbles, same as yours. The cuprit can be eliminated through a 1x1 and the lighter vs. heavier question is resolved in every case, same as yours.
So there are at least two solutions that work in 100% of scenarios.