Brain Teasers
Three Married Couples and a Widow
Four women, Audrey, Brenda, Charlotte, and Dawn, and three men, Edgar, Frank, and George, are tennis players. These seven people consist of three heterosexual married couples, plus one widow. Whenever they play doubles, no man is on the same team as his wife. If a game of doubles is played, there is never more than one couple in this game. One day, four games were played:
1. Audrey and Edgar vs Brenda and Frank
2. Audrey and George vs Dawn and Frank
3. Brenda and Charlotte vs Frank and George
4. Charlotte and Edgar vs Dawn and George
Who is the widow?
1. Audrey and Edgar vs Brenda and Frank
2. Audrey and George vs Dawn and Frank
3. Brenda and Charlotte vs Frank and George
4. Charlotte and Edgar vs Dawn and George
Who is the widow?
Answer
Charlotte is the widow.First, we must figure out who Frank's wife is. From games 1 and 2, we know that Frank's wife cannot be Brenda or Dawn and must be Audrey or Charlotte. Let's make Frank's wife Charlotte and see what happens.
From games 2 and 4, we know that George's wife cannot be Audrey or Dawn, and it obviously cannot be Charlotte either, so it must be Brenda. But game 3 features both Brenda and George, and Charlotte and Frank. So Frank's wife cannot be Charlotte, and must therefore be Audrey.
From game 4, we know that George's wife cannot be Dawn, and it cannot be Audrey either, so it must be either Brenda or Charlotte. If George's wife is Charlotte, then Edgar's wife cannot be Audrey or Charlotte, and must be Brenda or Dawn.
But now Edgar's wife cannot be Brenda because game 1 features both Audrey and Frank, and Brenda and Edgar. It cannot be Dawn either because game 4 features both Charlotte and George, and Dawn and Edgar. Therefore, George's wife cannot be Charlotte and must be Brenda.
If Frank's wife is Audrey and George's wife is Brenda, Edgar's wife must be Charlotte or Dawn. Game 4 tells us that Edgar's wife must be Dawn. Now that Audrey, Brenda, and Dawn have all been assigned husbands, this leaves only Charlotte without a husband.
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