27 Aug 2022 1:46 am
It's impossible in two tries, unless you get unbelievably lucky.Cannonpointer » 26 Aug 2022, 8:17 pm » wrote: ↑ Exactly.
I have solved it in just two weighings under that condition, but only when replacing 2 marbles from side a and one from side b with control marbles results in an even weighing. I can work it in a single weighing from there. But that is only going to happen 3/8ths of the time. And you will get an even weighing on the original 4x4 only 1/3rd of the time. So it's just over a 70% solution under my scheme.
But if the second weighing is still not even, I cannot work it in a single weighing from there. I need two. So I am either incorrect in my second step, or unable to figure out my last step properly in the event of an odd weighing.
If the second weighing is still odd, that means I have 5 suspect marbles - 3 on one side and two on another. If there's a way to find the suspect in a single move, it sure as hell isn't one I can find. Which makes me think my second step is a half measure in the first place.
But you're on the right track, you start with four, and you need to move those around, and your 2nd weighing is four each as well. And at that point you have all your data to make the final weighing of 1x1. To determine which marble is different, and also if it is heavier or lighter.
You have to remember the way the scales move on each turn.... and remember which marble made the difference... You're doing great!