A man has three hats, one red, one white, and one black.
logic/hats.and.coats New
New entry, edited from material collected for the archive and not yet in a released version.
Problem
A man has three hats, one red, one white, and one black. He has three coats, one red, one white, and one black. 1. He never wears his black hat with his white coat. 2. He never wears his white hat with his black coat. 3. He never wears the same hat two days in a row. 4. He never wears the same coat two days in a row. 5. He always wears his white coat on Sunday. 6. He always wears his white hat on Sunday. 7. He always wears his black hat on Monday. 8. His hat and coat match only on Sunday. What color hat and coat will he wear on Saturday?
Show solution
Red hat, black coat. It is necessary to work through the week to get the answer: Day Sun Mon Tue Wed Thu Fri Sat Sun Coat W R B/W R B/W R B W Hat W B R B/W R B/W R W (B/W means black or white, we can't tell which and it doesn't matter) Monday's coat must be red--it cannot be black by virtue of statements 7 and 8, and it cannot be white by virtue of 4 and 5. This means Tuesday's coat must be black or white. It doesn't matter which--either way Tuesday's hat must be red. (If Tuesday's coat is black, Tuesday's hat cannot be black or white by virtue of 2 and 8. If Tuesday's coat is white, Tuesday's hat cannot be black or white by virtue of 1 and 8.) The same reasoning tells us Wednesday's coat is red. We go on the same way until we find that Saturday's hat is red. This means Saturday's coat is black or white, but it cannot be white because the man will wear white the next day, Sunday. So the coat is black. -- Mitch Moetell <mmoetell@counsel.com> [ Editor: a dissenting view: ] The puzzle has the dubious distinction of including redundant information AND not having a unique solution. In addition the two answers that fulfil the 8 conditions are easy to find. Basically, he can wear a red hat and black coat on Saturday, or a black hat and red coat. There's no way of telling which is the intended answer from the conditions supplied! Also given condition 8, one of 5 or 6 (take your pick) is redundant! Condition 7 also seems useless (though in the correctly worded puzzle, I suspect it might be significant). -- Martin Veasey <martin@cheam.demon.co.uk> [ Editor: with condition 7 the answer is unique, as Moetell's table shows. Monday is forced to black hat, red coat; then Tuesday's hat is red, Wednesday's coat red, Thursday's hat red, Friday's coat red and Saturday's hat red. A black hat and red coat on Saturday would need a red coat on two days running (Friday and Saturday), which rule 4 forbids. The second answer appears only if condition 7 is dropped. ]