28 Aug 2022 11:13 am
If they are odd, you still have 3 suspects, with only one chance left. Because if it's odd, you still haven't determined if it's heavier or lighter, since you put yellow marbles on both sides.Cannonpointer » 28 Aug 2022, 11:10 am » wrote: ↑ Okay, so we agree that if the scales are ODD, my solution works?
Let us regress, then, to the issue of having only 4 suspects going into weighing #2, instead of 8.
Place 2 suspects on side a and 1 on side b, with 2 controls and 3 controls, respectively.
3 possible outcomes:
1. Even. The sequestered marble is the suspect. Weigh it 1x1 against any of the 11 remaining controls to determine lighter or heavier. Solved.
2. Odd, side a heavier. Weigh the two suspects on side a 1x1 against each other. If they are even, the one on side b is the odd man, and lighter. If odd, the heavier is the culprit. Solved.
3. Odd, side a is lighter. Weigh the two suspects on side 1x1 a against each other. If they are even, the one on side b is the odd man, and heavier. If odd, the lighter is the culprit. Solved.