Both Albert and Bernard know the ball is at a certain row and at a certain column, respectively. Albert first admits two things:
He doesn’t know where the ball is. Aka, the row containing the ball has more than one ball in it. This isn’t important now, but will be re-used when he asserts it again.
Bernard doesn’t know either. If Bernard knew where the ball was simply from the column, it’d be because that column only had one ball in it. Since he knows that Bernard doesn’t know given just the row, each ball in that row is in a column that contains more than one ball.
This eliminates rows A and B, since B5 and A6 are the only balls in their columns.
For this to work, Bernard now has to understand the above.
Then Bernard admits that now he knows where the ball is. Since we can eliminate or ignore each ball in A and B, it can either be balls D2, C3, and D4 and not any ball in column 1 using logic from #2.
At this point, Albert knows whether the ball is in C or D. If the madman told him the ball was in row C, then he would instantly know the ball is C3 given the elimination of C1 and D1. If he was told it was row D, then he still wouldn’t know.
However, Albert admits the former, which tells us it’s C3.
Thanks for the explanation, but I cannot follow on this line
Since he knows that Bernard doesn’t know given just the row, each ball in that row is in a column that contains more than one ball.
Why is that? Why couldn’t it be A2 or A3? In this case neither Albert nor Bertrand could tell what row/column this was either, because it would be in a row/column with another ball. How can you exclude any row with overlap with any single-ball columns?
Yes and because C3 is a golden ball, you should confidently switch to the second door. Because now it’s just the Monty Hall problem with balls instead of goats.
When the madman chose a door to opened, he deliberately chose a bad (mixed) door, otherwise he would have given away the correct location. The fact, that he opened the third instead of the second gives you new information, that you can take advantage of by switching, increasing your chances. Had the ball been silver, it might have been revealed to come from a bad door.
Edit: damn I just realized he picked the ball from the first door, not the second. Okay in that case we might actually have to calculate probabilities, but I’m too lazy for that.
C3. I used to do these logic puzzles at work.
Both Albert and Bernard know the ball is at a certain row and at a certain column, respectively. Albert first admits two things:
This eliminates rows A and B, since B5 and A6 are the only balls in their columns. For this to work, Bernard now has to understand the above.
Then Bernard admits that now he knows where the ball is. Since we can eliminate or ignore each ball in A and B, it can either be balls D2, C3, and D4 and not any ball in column 1 using logic from #2.
At this point, Albert knows whether the ball is in C or D. If the madman told him the ball was in row C, then he would instantly know the ball is C3 given the elimination of C1 and D1. If he was told it was row D, then he still wouldn’t know.
However, Albert admits the former, which tells us it’s C3.
Thanks for the explanation, but I cannot follow on this line
Why is that? Why couldn’t it be A2 or A3? In this case neither Albert nor Bertrand could tell what row/column this was either, because it would be in a row/column with another ball. How can you exclude any row with overlap with any single-ball columns?
Yes and because C3 is a golden ball, you should confidently switch to the second door. Because now it’s just the Monty Hall problem with balls instead of goats. When the madman chose a door to opened, he deliberately chose a bad (mixed) door, otherwise he would have given away the correct location. The fact, that he opened the third instead of the second gives you new information, that you can take advantage of by switching, increasing your chances. Had the ball been silver, it might have been revealed to come from a bad door.
Edit: damn I just realized he picked the ball from the first door, not the second. Okay in that case we might actually have to calculate probabilities, but I’m too lazy for that.
I have no idea what the ball thing is about. I just assumed that since he was a madman, he was just doing madman things.