FRaznki
A minor query.
You say you begin by touching two of the corners. You later say, "Either way -- after the first spin -- you will have three glasses facing the same direction".
Now here is the query:
Let us suppose that the four at the beginning are three one way up and one the other. Let us then suppose that you select the diagonal that contains one of each. Your instructions then were that you turn one of these over. Suppose that we call the three the same 'A' and the solitaire 'B'. Now, if you turn over the 'A' , making it a 'B' - and there is a 50/50 chance that you will - you will be left with two 'A's and two 'B's. Surely this is hardly consistent with, "Either way -- after the first spin -- you will have three glasses facing the same direction"?
P.S.
Franki (Sorry about the typo in the previous post)
You also wrote, "If they are different -- leave them be -- and spin again".
But again, surely this is exactly where you and Adrian faulted me - [to misquote Adrian] "You could keep getting that 'different' all day". (It is, after all, another 50/50 chance, just as mine was) I would suggest that this is the same 'lack of guarantee' that I was - rightly - corrected on.
Sorry if this sounds like being picky, but...
.
Mungo
My solution may be incorrect.
I really cannot tell right now -- but your question has me stumped for the moment (I'm working in my head -- and I gotta get out the glasses.
I got a lot of stuff to do. I'll get back to you tomorrow.
That will give me a chance to look at your solution.
I'm now pretty much convinced that my original solution is wrong. I've revised it and will publish it after I study Mungo's.
(And I may steal a couple of ideas from him if I find that after more testing my new solution does not work. :wink: But I think it does!)
Frank
My second query was a nonsense. It would have been a valid comment had you intended to keep trying the same approach until you did get the pair you wanted, but on re-reading, that is not what you were saying at all. First query stands, second query retracted - and I promise to read more carefully in the future.
