Three girls went on a vacation, each wearing a red "Love to travel" T-shirt. They each have brought 9 other clean tops, but are fairly active, and as a result each top becomes dirty after wearing it for a day,

They wanted to wear a clean top each day, so fortunately, their cabin came with a washer and drier, however, they could only wash two girls' clothes at a time, so the first and third girls had to wait until the next day to wash their clothes once each.

Their vacation lasted 3 weeks (including the day they left), so each girl washes her clothes twice while on vacation.

Here is a list of when they wore what. (Note they wore only one top per day.)

First girl:

1. Red "Love to travel" T-shirt
2. Floral tank top
3. Green camisole
4. White "I *heart* levik" T-shirt
5. Gray short-sleeve shirt
6. Blue long-sleeve shirt
7. Pink poodle T-shirt
8. Orange tank top
9. Green camisole
10. Yellow "Sled Shiver Sally" T-shirt
11. Floral tank top
12. Gray short-sleeve shirt
13. Black "Night Owl" T-shirt
14. Pink poodle T-shirt
15. Red "Love to travel" T-shirt
16. Yellow "Sled Shiver Sally" T-shirt
17. Blue long-sleeve shirt
18. Orange tank top
19. Floral tank top
20. Green camisole
21. "I *heart* levik" T-shirt

Second girl:

1. Red "Love to travel" T-shirt
2. Floral short-sleeve shirt
3. Orange tank top
4. Green cougar T-shirt
5. Gray long-sleeve shirt
6. White "Mind your Pids and Queues" T-shirt
7. Yellow sunshine shirt
8. Black "Dark as Night" T-shirt
9. Green cougar T-shirt
10. Orange tank top
11. Red "Love to travel" T-shirt
12. Gray long-sleeve shirt
13. Pink tank top
14. Floral short-sleeve shirt
15. White "Mind your Pids and Queues" T-shirt
16. Blue tank top
17. Yellow sunshine shirt
18. Orange tank top
19. Floral short-sleeve shirt
20. White "Mind your Pids and Queues" T-shirt
21. Red "Love to travel" T-shirt

Third girl:

1. Red "Love to travel" T-shirt
2. Floral long-sleeve shirt
3. Gray "Undecision" T-shirt
4. Pink "Pretty in Pink" T-shirt
5. Blue coy toy T-shirt
6. Orange short-sleeve shirt
7. Yellow tank top
8. Floral long-sleeve shirt
9. Blue coy toy T-shirt
10. White "Welcome to Truth Town" T-shirt
11. Yellow tank top
12. Black "Fun at Night" T-shirt
13. Pink "Pretty in Pink" T-shirt
14. Orange short-sleeve shirt
15. Green long-sleeve shirt
16. Gray "Undecision" T-shirt
17. Blue coy toy T-shirt
18. Floral long-sleeve shirt
19. Yellow tank top
20. Black "Fun at Night" T-shirt
21. Red "Love to travel" T-shirt

From this information, what day did each girl wash her clothes?

Notes: Each girl washes her current top when she washes her other dirty clothes, so it is clean for following days. Differences between lights/darks or types of tops do not matter in the washing process.

I agree that there are 6 solutions.

I was disbelieving at first, so tested with a program (in doing so, I also tried without the constraint that two girls washed on one day and the other girl the next - a total of 640 solutions).

Similar problems to this would be interesting, for example if the potential days for the first and second washes overlapped, the leftover first wash could be done at the same time as the earliest second wash. Just a thought.

Posted by snark on 2006-09-12 00:19:38