Liberal Forum

Cannonpointer » 19 Aug 2022, 8:11 pm » wrote: ↑

19 Aug 2022, 8:11 pm

1. 4x4. They are even. All 8 are now control. Remove two marbles from one control and one marble from another. Replace them from the 4 you left out (our suspects).
2a. 4x4. They are even. All 11 are now control. 
3a. The last one which was never weighed is the culprit. Go 1x1 against any control marble and you know whether it is lighter or heavier. 
or...
2b. 4x4. They are odd. Either the side with the two suspect marbles are heavier, or they are lighter.
3b. 1x1. Weigh the 2 against each other. If they are even, the single is the culprit, and whether it was heavier or lighter is known from turn 2b. If they are odd, turn 2b tells you whether the lighter or the heavier is the culprit. 

Unless I am off in my logic, the above steps manage every possibility in the case that the initial 4x4 is evenly weighted. The odds of that happening are one in three - so one in three times, the above steps will always answer both questions put by the riddle. Below, I will deal with the initial 4x4 being odd - which should occur two times out of three.

1. 4x4. They are odd. The remaining 4 are now control. Sequester 1 of the heavier marbles and 2 of the lighter marbles, replacing them from the control group. 
2a. 4x4. They are even. Put the two sequestered lighter marbles against each other. 
3a. 1x1.If they are even, the heavier sequestered marble is the culprit. If they are odd, the lighter of the two is the culprit.
or...
2b. 4x4. They are odd.

****. Now I'm ****. 

I'm going to sleep on this - I don't have 7 hours in yet... I've solved it only bout hlf the time - and that, only if my cackle-eight-shuns are correct. But half of the time, I appear screwt.