perplexus.info :: Logic : Girls Just Wanna Have Fun

Girls Just Wanna Have Fun (Posted on 2003-11-06)

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.

Submitted by Gamer

Rating: 3.5714 (14 votes)

Solution: (Hide)

$80 - Diane: green ($50) and orange ($30)
$60 - Emily: blue ($40) and red ($20)
$60 - Alice: green ($50) and yellow ($10)
$50 - Betty: orange ($30) and red ($20)
$50 - Carol: blue ($40) and yellow ($10)
There are five colors of shirts in $10 increments, with the most expensive costing $50, meaning that they cost 10, 20, 30, 40 and 50 dollars in some order. Since each girl bought two different shirts, possible totals are:
$30 = 10 + 20 $40 = 10 + 30 $50 = 10 + 40 $50 = 20 + 30 $60 = 10 + 50 $60 = 20 + 40 $70 = 20 + 50 $70 = 30 + 40 $80 = 30 + 50 $90 = 40 + 50
Since Diane spent the most, and the other two pairs of girls spent the same amounts [1], possible triples of the amounts spent are, at first glance:
50, 60, 70 (10,40;20,30;10,50;20,40;20,50) 50, 60, 70 (10,40;20,30;10,50;20,40;30,40) 50, 60, 80 (10,40;20,30;10,50;20,40;30,50) 50, 60, 90 (10,40;20,30;10,50;20,40;40,50) 50, 70, 80 (10,40;20,30;20,50;30,40;30,50) 50, 70, 90 (10,40;20,30;20,50;30,40;40,50) 60, 70, 80 (10,50;20,40;20,50;30,40;30,50) 60, 70, 90 (10,50;20,40;20,50;30,40;40,50)
However, we are also told that two of each color shirt were bought, eliminating most of the above combinations (the underlined priced appear three times, and the italicized values appear only once in the invalid combinations). The only valid result (in bold), then, is that Diane spent $80, while the other pairs of girls spent $50 and $60 on their clothes, respectively:
80 = 30 + 50 (Diane) 60 = 20 + 40 60 = 10 + 50 50 = 20 + 30 50 = 10 + 40

We know that Diane spent $80 on thirty- and fifty-dollar shirts, and Emily did not buy any shirts of the same colors as she did [3]. Thus, Emily either spent $10 and 40 or $20 and 40, and we know for sure that she did buy a forty-dollar shirt. Also, we are told that Carol bought the other forty dollar shirt [5]:
80 = 30 + 50 (Diane) 60 = 20 + 40 (Emily/Carol) 60 = 10 + 50 (Alice/Betty) 50 = 20 + 30 (Alice/Betty) 50 = 10 + 40 (Emily/Carol)
Carol didn't buy a twenty-dollar shirt with Alice [4]; it must have cost ten dollars [5], and by elimination, we know what price shirts everyone bought:
80 = 30 + 50 (Diane) 60 = 20 + 40 (Emily) 60 = 10 + 50 (Alice) 50 = 20 + 30 (Betty) 50 = 10 + 40 (Carol)
Now, to match prices to colors:
Carol's blue shirt was not ten dollars [2]; it must have been forty dollars. The ten-dollar shirt was not green [2], orange [4], or red [5]; it must have been yellow:
$10: yellow 20 30 40: blue 50
Alice and Betty did not buy any shirts in common [above], so Alice's fifty-dollar shirt was not yellow [$10], blue [$40], orange [4], or red [5]; it was green.
$10: yellow 20 30 40: blue 50: green
By elimination, Betty's twenty- and thirty-dollar shirts were red and orange, in some order. Emily bought a twenty-dollar shirt, but it was not orange [4]; it must have been red. That leaves the orange shirt at $30:
$10: yellow 20: red 30: orange 40: blue 50: green
So, to recap:
$80 - Diane: green ($50) and orange ($30) $60 - Emily: blue ($40) and red ($20) $60 - Alice: green ($50) and yellow ($10) $50 - Betty: orange ($30) and red ($20) $50 - Carol: blue ($40) and yellow ($10)
Taken from DJ's solution here.
Charlie shows how the program is accomplished through a program here.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
solution	K Sengupta	2007-03-02 23:15:18
Solution	Bender	2005-11-05 06:20:51
Solution	Jeff Little	2005-05-27 13:22:24
Incomplete	Catherine	2005-01-03 01:12:52
Complete Walkthrough	DJ	2004-03-13 22:36:21
No Subject	Nick	2004-01-24 12:04:53
The flaw in this puzzle	franny	2004-01-22 15:30:36
My attempt...	Cindy	2004-01-07 23:21:39
correct solution	lesa	2003-11-22 00:44:27
hmmmmmmm	and silvis	2003-11-16 09:50:38
Solution??	magee	2003-11-12 12:49:01
No Subject	gary	2003-11-11 18:46:46
re: Solution:	Charlie	2003-11-08 14:18:00
logic	Tristan	2003-11-08 12:45:36
Solution:	Gamer	2003-11-08 12:03:35
re: Each shirt purchased twice	Charlie	2003-11-08 09:30:42
Ugh...	Charlie	2003-11-07 22:23:31
re: Each shirt purchased twice	Charlie	2003-11-07 21:18:54
Each shirt purchased twice	Gamer	2003-11-07 18:24:02
No Subject	Senthil Kumar	2003-11-07 18:17:55
...	kas	2003-11-07 16:47:06
re: Solution (maybe)	Charlie	2003-11-07 16:33:42
re: Perhaps...	Charlie	2003-11-07 16:25:31
Perhaps...	Maria	2003-11-07 15:56:20
21 solutions?--brute force	Charlie	2003-11-07 15:43:05
re(2): Solution (maybe)	Jun	2003-11-06 22:46:19
re: Possible Impossibility	Victor Zapana	2003-11-06 22:45:45
re: Solution (maybe)	Victor Zapana	2003-11-06 22:42:09
Solution (maybe)	Jun	2003-11-06 22:38:24
Possible Impossibility	Victor Zapana	2003-11-06 21:24:03
re(2): Solution with no proof	Victor Zapana	2003-11-06 20:42:31
re: Solution with no proof	Tristan	2003-11-06 20:24:54
Solution with no proof	morgan	2003-11-06 20:19:28
re: Solution with no proof lol	Victor Zapana	2003-11-06 20:08:10
Solution with no proof lol	Victor Zapana	2003-11-06 20:05:33
re: Hint:	Tristan	2003-11-06 20:00:09
Hint:	Gamer	2003-11-06 19:36:33

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