Arthur and Bert each writes down a positive integer on a piece of paper and then shows it to Charles. Charles then writes two numbers on a blackboard, visible to Arthur and Bert: one of them is the sum of Arthur's and Bert's numbers, and the other is a random number.
After this Charles asks Arthur if he knows Bert's number. If Arthur says he doesn't know, then he asks Bert if he knows Arthur's number. If Bert says he doesn't know, Charles continues with Arthur, then if necessary with Bert and so on... until he gets a positive answer.
When will Charles get a positive answer?
(In reply to
General formula by Tristan)
Tristan:
I didn't follow your explanation, but I
think that your result and mine are close enough that we might both be
on the same track. Our formula address two slightly different
questions, however, so it is hard to compare.
I calculated
based on the values x and y on the blackboard, and calculated the
maximum number of no responses as ceil((y-1)/(y-x)) if x> y.
You calculated based on A and B and the random number, and proposed the
exact round in which the the no's change to yes.
I think both approaches have merit, and are interesting.
I think there is a problem, however, with your formula.
Consider A = 3, B = 7, y = 6, x = 10. B knows on round 1
what a has. But your formula calculates as min(2*Ceil(3/4),
2*Ceil(7/4)-1) = min (2*1 ,2*2-1) = round 2. I'll bet you just
need to make a small fix to have it come out right. I look
forward to seeing the revised formula.
Edited on October 31, 2005, 8:36 pm
re: General formula
