Question 498405: Megan, Brandon, and Ryan were presented with an unusual challenge. From a group of three red balls and two yellow balls, three balls were chosen at random and each was then concealed in a different box. The challenge was for each person in turn to look inside of two of the boxes to see if they could determine the color of the ball in the other box.
Megan looked inside boxes 1 and 3, but was not able to determine the color of the ball in box 2. Brandon, having watched Megan, then looked inside boxes 2 and 3, but could not then determine the color of the ball in box 1. Having watched both Megan and Brandon, Ryan then stated the color of the ball in one of the boxes without even bothering to look inside the other two.
Which box did Ryan name, and what was the color of the ball inside?
Answer by solver91311(24713)   (Show Source):
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There are only three situations where Box 3 contains a yellow ball:
Case 1: 1:Y 2:R 3:Y,
Case 2: 1:R 2:Y 3:Y, or
Case 3: 1:R 2:R 3:Y
If it were case 1, Mary, knowing there are only two yellow balls and that she has seen both of them, knows immediately that box 2 must contain a red ball.
If it were case 2, Brandon would see two yellow balls in 2 and 3 and would know that Box 1 contained a red ball.
If it were case 3, Brandon, knowing that Mary was unable to tell by looking in 1 and 3 which color was in 2, knows that the ball in 1 could not be yellow. Hence he would know that the ball in box 1 is red.
But none of these cases are true because neither Mary nor Brandon was able to name the color in the unseen box. All other cases have a red ball in box 3, and so Ryan confidently stated.
John
My calculator said it, I believe it, that settles it
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