5 Girls (named Alice, Betty, Carol, Diane, Emily) visit a mall to shop. They come upon a clothing shop and they decide to buy clothing.

But, for some strange reason, different colored shirts cost different amounts, which now came in increments of 10 dollars. (Every shirt of the same color costs the same amount.) This store doesn't carry very many shirts; the most expensive one is 50 dollars, and they only come in red, green, blue, yellow, and orange.

Each girl goes into the store and finds two different shirts. No two girls got the same pair of shirts, and no girl got a shirt for free. It ended up that each color shirt was bought exactly twice.

Using the following clues, can you figure out the two colors of shirts each girl bought, and how much each color bought, as well as how much each girl spent?

1) When the 5 girls were comparing their purchases, they found that Diane spent the most money, 2 girls tied for second most money spent, and the other 2 girls spent the same amount of money as well.

2) When Carol bought the blue shirt, she was mad that the it was more expensive than the 10-dollar price it was last week, and didn't buy the green shirt because of this.

3) Diane's and Emily's different styles resulted in them not buying any shirts the same color as each other's.

4) Alice and Emily both decided not to buy the orange shirt, but instead, Alice went with Carol to pick out the same color shirt to buy, noting that it didn't cost 20 dollars like last week.

5) As Betty was waiting to buy a red shirt (which she did end up buying), she saw Carol buy a shirt that cost 40 dollars.

(In reply to Hint: by Gamer)

Well, I'm trying to figure out the only cost pair that works and this is what I got. The lowest amount spent possible is 50 because no one got the same two colors and two people tied. I am assuming that no one got two of the same color, thought it is not completely clear in the wording. 60 is also possible for 2 people, as well as 70. 80 and 90 are not, but Diane could possibly have spent that much. This still leaves plenty possibilities.

To try to narrow it down, I take into account number 3. Diane's possible combinations so far are:
50+40
50+30
50+20
40+30
In the last two, the other four people are forced to have the following:
10+40
20+30
10+50
20+40
It looks like this doesn't really narrow down the possibilities, even considering that Carol, someone besides Emily, bought a 40 dollar shirt. If Diane spent 80 or 90, there would be even more possibilities for the other four.

I'm still failing to figure out this problem, but I was sort of doing all this work while I typed, so maybe I just need to think on it more.

Posted by Tristan on 2003-11-06 20:00:09