your 4/4/4 start is good and you do get a lot of useful information from that weighing. And of course, if you are lucky, the next couple of steps follow quite easily, but …
… if you aren’t so lucky, the next two steps take a bit of careful thinking !!
Of course, it’s quite easy to do in four weighings, but then it wouldn’t be such a tease
There is no rush Eoink, I know you are fully engrossed with diamond transactions at the moment. Perhaps another bottle or two of those delicious red wines you enjoy might assist ???
I’m struggling to generate “symmetrical” pictures of A, B and D. Perhaps it’s just the choice of words. English has so many words with very similar, but nevertheless different, meanings
Do you perhaps mean “reflection” ?
For example, B is a reflection of A about a line drawn Top to Bottom through the letter B so as to bisect picture B. PowerPoint would refer to this as a “Horizontal Flip”.
The drawing below illustrates what I mean by “reflection”. Is this the same as your “symmetry” ?
But there is a better solution, in which three of the pictures can be made to look exactly like each other, and the fourth picture can’t, so is the odd one out.
I think it’s time to close out a few of the open Teasers.
Number the diamonds 1 to 12 and divide them into three groups of 4
1,2,3,4 then 5,6,7,8 and 9,10,11,12
Put the first two groups on the balance IF these two groups balance, the odd diamond is in Group 9,10,11,12
Compare group 1,2,3 (in fact any three diamonds from 1 to 8), with group 9,10,11. IF group 1,2,3 and 9,10,11 balance, then the odd diamond is No 12
Compare 12 with any diamond to discover whether its heavy or light.
Of course, there are a couple of “IFs” in the scenario above. The second “IF” is quite easy to develop ie IF 1,2,3 and 9,10,11 do NOT balance then …