After the second formal dance the friends had attended, they got ready for this dance, which was based on an article called "Miraculous Melons".

The four friends looked in their closet and decided that they wanted to mix things up. They each picked out one shirt, tie and suspenders from what the four had accumulated. (They had accumulated red, blue, green and white of each.)

When the four friends decided to meet at the dance, they all arrived at slightly different times, and as a result some people got to the dance earlier than others.

After the dance, the old fifth friend (called A) came to visit and asked someone who went (called B) about the dance. Based on the conversation, can you figure out what shirt, tie and suspenders were worn by each person, and in what order they came in?


A: When did everyone arrive at the dance?

B: Well, I know that the only person that came in between the person with the red shirt and the person with the green suspenders (in no particular order) was wearing a white tie.

A: What else did you notice about the time people came in?

B: Well, I know that the person wearing the green shirt came in just before the person wearing the red suspenders, and he came in just before the person wearing the red tie.

A: What did they do do when you were at the dance?

B: We took a picture of all four of us. It showed three of us standing: the person with the blue shirt on the left, the person with the blue tie in the middle, and the person with the white suspenders on the right. The other person was sitting down in the middle because he arrived last of all four of us.

A: I have one more question. I heard that you took off your green tie and gave it to a girl you liked. Did anything happen?

B: I am planning on taking her and I hope to wear the same shirt as I did this year. It was a red or blue shirt, I don't remember which.

A: I have to go now, bye!

What ?? They weren't wearing pants ?!?!

The first to arrive at the dance was the puzzle answerer, "B", wearing a blue shirt, green tie, and green suspenders. He is standing on the left in the photograph. The next person to arrive was wearing a green shirt, white tie, and white suspenders. He is standing on the right in the photo. The third person to arrive was wearing a red shirt, blue tie and red suspenders. He is standing in the middle in the photo. The last person to arrive was wearing a white shirt, red tie and blue suspenders. He is sitting in the photo.

Explanation.

I made the following assumptions, from the wording of the puzzle:

(1) I did not assume that no one wore the same color for any two items of his apparel. In other words, if he wore a blue shirt, he could still have worn a blue tie. Had this been otherwise, it would have been stated explicitly in the puzzle.
(2) From "...the person with the red shirt...the person wearing the green shirt....the person with the blue shirt...", each person wore a different color shirt.
(3) From "...the person with the green suspenders...the person wearing the red suspenders...the person with the white suspenders...", each person wore different color suspenders.
(4) From "...the person wearing the red tie.....the person with the blue tie...the person...was wearing a white tie" ..., each person wore a different color tie.

For each of the four people, use three of the letters R (Red), W (White), B (Blue), and G (Green) to represent the color of his shirt, tie, and suspenders, in that order. (e.g. WRB = "White shirt, Red tie, Blue suspenders"). Let the "less than" symbol, < , indicate an earlier arrival at the dance. ( <> means "not equal to"). Let x's represent the missing letters. The puzzle can now be summarized in five statements:

(a)(Rxx < xWx < xxG) or (xxG < xWx < Rxx)
(b) Gxx < xxR < xRx
(c)(Bxx <> xBx) and (Bxx <> xxW) and (xBx <> xxW)
(d) The last arrival was not Bxx, xBx, or xxW
(e) xGx must be either RGx or BGx

(Therefore the following combinations are disallowed: RWx, RxG, xRR, BBx, xWG, GxR, GRx, BxW, xBW, WGx, and GGx.)

Now isn't this puzzle suddenly a lot easier? What a difference the right use of notation makes !

The only possibility that does not quickly lead to a contradiction of the rules of the puzzle is:

xxG < GWW < RxR < xRB

The only way to fill in the x's without contradiction is:

BGG < GWW < RBR < WRB





























Edited on January 12, 2004, 11:13 am

Posted by Penny on 2004-01-11 21:51:36