Deciding to take a lunch break and go over to a local shop at noon, Bill Bonche stumbles upon one of the suspects, walking into the store at the same time as he was! So, he decided to take the opportunity to ask him a few key questions. After the questioning was done, he saw another suspect pull into the parking lot five minutes after the first! So he repeated the procedure. Amazingly, he ended up seeing all of the five suspects come to the store, and all of them five minutes after the previous suspect.

After watching them look around the store (and not buying anything, he noted), they began to leave promptly at 1:30, and again as if on cue, they left in ten-minute intervals. As they were leaving, Bonche asked them to report promptly to the site of the robbery, 17th Ave. S., for he was ready to reveal the culprit!

From the information provided, find out the time each suspect arrived, the color shirt that they were wearing (one was wearing a gray shirt), the amount of money each brought, and the time that each left.

1. The first to arrive was the last to leave and the last to arrive was the first to leave.

2. The suspect with the white shirt came 10 minutes after the suspect who brought $300, who came 5 minutes after the suspect who left last.

3. One suspect stayed at the store for five minutes less than an hour and a half; another stayed for two hours less ten minutes.

4. The suspect with the black shirt arrived earlier than both the men that brought the most money. He did not arrive first, however, and he did not have the smallest amount of money.

5. The suspect that brought $340 came 15 minutes before the suspect that brought $360.

6. The suspect with the red shirt came 5 minutes after the blue-shirted suspect.

7. Each man carried only twenty-dollar bills, in different quantities between 15 and 19.

12:00, blue, $340, 2:10
12:05, red, $300, 1:50
12:10, black, $320, 2:00
12:15, white, $360, 1:40
12:20, gray, $380, 1:30

Ok, so here’s how I got there.

The first clue tells us that 12:00 left at 2:10, and 12:20 left at 1:30.

The second clue tells us that the man with $300 arrived 5 minutes after the man who left last, who we know arrived at 12:00. So the man with $300 arrived at 12:05. Also the white shirt came 10 minutes later, so the white shirt arrived at 12:15.

Looking at the three arrival times and the three departure times, there is only one way for someone to have spent 1 hr 25 min in the store, and that is by arriving at 12:15 and leaving at 1:40. Also there is only way for someone to have spent 1 hr 50 minutes in the store, and that is by arriving at 12:10 and leaving at 2:00. By elimination this means that 12:05 left at 1:50.

The fourth clue tells us the black shirt did not arrive at 12:00, did not have $300 (and so did not arrive at 12:05), but did come before two other people (so did not arrive at 12:15 and 12:20). Therefore the black shirt arrived at 12:10 by elimination. Also, he could only have $320 or $340 on him.

Ok, let’s sum this up for a second. We have:
12:00, 2:10
12:05, $300, 1:50
12:10, black, 2:00
12:15, white, 1:40
12:20, 1:30

Let’s look at the fifth clue. For someone to arrive 15 minutes before someone else, he must arrive either at 12:00 or 12:05. Therefore the man with $340 came at 12:00 or 12:05. But 12:05 already has $300, so $340 came at 12:00. This means that $360 came at 12:15. Remember we said that the 12:10/black shirt could only have $320 or $340. Since $340 has gone to someone else the 12:10/black shirt must have $320. By elimination, $380 came at 12:20.

Looking at the sixth clue, neither the red nor the blue shirt has been placed yet. However, we know they arrive within 5 minutes of each other. The only two times that don’t have shirts already that are 5 minutes apart are 12:00 and 12:05. So red and blue must go there, with blue shirt at 12:00 and the red shirt at 12:05. By elimination that means the gray shirt was at 12:20.

So we have:
12:00, blue, $340, 2:10
12:05, red, $300, 1:50
12:10, black, $320, 2:00
12:15, white, $360, 1:40
12:20, gray, $380, 1:30

Tada!

Posted by nikki on 2004-09-09 14:03:27