Holiday Puzzle Solution


Amy and Cindy


To see why, let’s begin with Samuel’s first question (Q1). Now, it is obvious that Amy and Bobby were going to say “No” regardless of the distribution of gifts. On the other hand, if Danny were told that two of the other three received games, then he would know that he received a movie. Similarly, if he heard that the other three all received movies, then he would know that he received a game. Since he said “No” to Q1, we can conclude the following: Exactly one of Amy, Bobby, and Cindy received a game. After Q1, all four kids knew this fact. (Note that Cindy’s answer provides no extra information for anyone to glean.)

But Cindy knew what Amy and Bobby received. So, after the first set of answers (A1), she knew what she received. (If Amy and Bobby both received a movie, then Cindy received a game; otherwise, Cindy received a movie.) So, Cindy answered “Yes” to Q2. Since only one person said “Yes”, Bobby answered “No” to Q2.

But, had Amy been the one kid (among the oldest three) to receive a game, then, after A1, Bobby would have concluded that he received a movie and would have answered “Yes” to Q2. We conclude that Amy did not receive a game. After A2, all the kids knew this (including Amy!).

So, at Q3, Amy and Cindy said “Yes”, while Bobby did not know which of he and Cindy has a game. (Danny, of course, can never get more information than he initially had.)