Solver's Forum
Messages in this topic - RSS

Home » General Discussion » Trail Mix-Original Logic Problems-August 2012

General Discussion.
11/26/2017 10:14:38 AM

Lynda
Lynda
Posts: 30
The meaning of the word "trip" and "leg" is very confusing. Could anyone shed some light? In the opening storyline the following reads, "The TRIP took place over the course of three days...." and "....each of the nine riders participating in the reenactment began his or her TRIP in a different town...." Clue #1 reads -"The length of either the first or last LEG of the TRIP is equal to the sum of the distances traveled by the fifth rider and either the first or the last rider." I'm tempted to ask for a small hint but I'll hold off and keep trying once I know for sure just what a TRIP and LEG mean. Thanks a bunch.

11/26/2017 10:54:35 AM

Semipro
Semipro
Posts: 292
Hi, here I am again. A trip is a complete journey, from point of origin to destination. A leg is a segment of that journey. On a flight from Seattle to New York, if you change planes in Chicago, the first leg is Seattle to Chicago and the second leg is Chicago to New York. In your Pony Express puzzle, a leg is the travel between two consecutive towns on a rider's route.

I'm not sure whether a trip can have more than two legs.

11/26/2017 3:47:11 PM

Lynda
Lynda
Posts: 30
Hi Again, You are so good to take the time to help me and I hate to keep doubting your explanations but if a LEG is a segment of a journey and I agree that it is then since there are 9 riders (3 each day for 3 days) they must mean there are 9 LEGS? See, I assumed there are 3 LEGS (one each day) and maybe that's why I'm having such a hard time coming up with a total that will equal 93, 96 or 111 miles. I was using the 5th rider's amount plus the first (or the last) and never having enough miles because the 5th trip always comes up to be 21 miles and no one rode over 60 so that only gives you 81. I'm going to try it again using your reasoning and see what I come up with. Wish me luck. Semipro wrote:
Hi, here I am again. A trip is a complete journey, from point of origin to destination. A leg is a segment of that journey. On a flight from Seattle to New York, if you change planes in Chicago, the first leg is Seattle to Chicago and the second leg is Chicago to New York. In your Pony Express puzzle, a leg is the travel between two consecutive towns on a rider's route.

I'm not sure whether a trip can have more than two legs.

11/26/2017 9:59:41 PM

Semipro
Semipro
Posts: 292
I can't say how many legs there are because I don't know the puzzle. It would specify how many towns each rider visited in a day, for example. All I've done is explain what a leg is.

11/27/2017 9:48:57 AM

Lynda
Lynda
Posts: 30
Yes, but I think the word LEG has two possible meanings in this particular problem. Maybe this opening quote will help: "The TRIP took place over the course of thee days, with each day's journey divided among three riders. Each of the nine riders participating began his or her trip in a different town (10 towns) and covered a different number of miles (300 total - one is 111 and one is 96) before handing off his or her message to the next carrier in a different town."

What I'm asking is this: could the word LEG refer to one of the three days or does it refer only to one of the nine TRIPS? I just can't understand why they would use the word LEG unless it meant something else besides a single TRIP because it's the only time they use that word in the entire problem. If LEG meant TRIP then why didn't they just say TRIP? Would you like me to copy this problem and send it to you? I'd love it if someone else could go crazy with me!

Semipro wrote:
I can't say how many legs there are because I don't know the puzzle. It would specify how many towns each rider visited in a day, for example. All I've done is explain what a leg is.

11/27/2017 8:42:23 PM

Semipro
Semipro
Posts: 292
Lynda wrote:
"Each of the nine riders participating . . . covered a different number of miles (300 total - one is 111 and one is 96)"


BUT earlier you said "no one rode over 60." So there's another source of confusion. I can't make sense of this problem with the numbers given. 300 miles total, 9 riders, therefore the average rider's trip was 33.3... miles, therefore (with 111 and 96 in the mix) some trips were very short.

I don't want to attack the problem myself. It seems to me that the use of "leg" is ambiguous and it'd be nice if an editor would step in.

11/27/2017 10:32:03 PM

Frances
Frances
Posts: 698
Hi Lynda,

This discussion has begun to pique my interest----now I'd like to have a go at it. smile Could you possibly type up the intro/clues, or post a link to a picture of the puzzle?

Frances.

11/28/2017 8:29:57 AM

Lynda
Lynda
Posts: 30
Yes, yes, yes. I'd love to have someone else doing the same puzzle. First, I'll try to post a link (please excuse the markings) and if that doesn't work then I'll type it all out. Here goes and thanks so much for your interest. Good luck.

Frances wrote:
Hi Lynda,

This discussion has begun to pique my interest----now I'd like to have a go at it. smile Could you possibly type up the intro/clues, or post a link to a picture of the puzzle?

Frances.

11/28/2017 10:56:26 AM

Lynda
Lynda
Posts: 30
TRAIL MIX

When he heard that Pentland County would be reenacting its first pony express ride in over 100 years, Sherman Palomino jumped at the chance to participate and follow in his great-great-grandfather's footsteps. The trip took place over the course of three days, with each day's journey divided amoung three riders. Following the trails used by real pony express riders over a century ago, each of the nine riders participating in the reenactment began his or her trip in a different town and covered a different number of miles before handing off his or her message to the next carrier in a differrent town. From the information provided, determine the order in which each rider carried his or her message, his or her point of origin and destination, and the number of miles each covered.

1. The total distance covered is exactly 300 miles. No single rider traveled more than 60 miles or fewer than 15 miles. The number of miles traveled by each person is a multiple of 3, and no one rode exactly 39 miles. The length of either the first or last leg of the trip is equal to the sum of the distances traveled by the fifth rider and either the first or the last rider.

2. Kensington and the town that is exactly 21 miles from Lakeview (which isn't Danville) were visited immediately before and after Lakeview, in some order. Morris covered exactly 45 miles.

3. The person who traveled from Rainier to Gravesend, who rode the shortest distance, was neither the first nor the last rider that day. There were at least five towns between Bethel and Newton, in some order. Seagate and Rainier were not consecutive stops.

4. Union Falls and Seagate are exactly 111 miles apart, and Seagate and Kensington are exactly 96 miles apart; both of these distances were full-day runs, and one of them included the longest distance traveled by a single rider. Neither Elias nor Nadia traveled on either of these two days.

5. Three consecutive riders, either from the first to last or from last to first, are Sherman, Claire, and Oscar (who didn't make the shortest trip).

6. Vivian and Herbert visited the same town, which isn't Bethel. Elias's trip is either the one that began in Woodbury or the one that ended in Woodbury. Joan was the first rider on one of the three days. The longest trip either began or ended in Danville.

7. Vivian traveled exactley 3 fewer miles than Sherman (who rode at least 10 fewer miles than another person) but exactly twice as many miles as another rider (who isn't Herbert).

8. Elias didn't ride immediately after the person whose point of origin was Bethel. Two consecutive riders traveled a total of exactly 75 miles between them.

11/28/2017 2:43:35 PM

Frances
Frances
Posts: 698
So far, I've been trying to figure the "map". Initial letters represent towns, riders going left to right.

Clue 2: A town is 21 miles from Lakeview, and since no distance is less than 15, there are no towns between the two. So: K L (21) ? or ? (21) L K
Clue 4: U??S??K or K??S??U, 2 days distance.
Clue 3: 5 towns between B and N. From R to G, neither first or last rider, must be middle leg of a day. Plus R can't be next to S.

With the above, I got these possibilities:

1. ?B?URGSNLK
2. ?N?URGSBLK
3. ?BLKRGSN?U
4. ?NLKRGSB?U

Clue 4: U and S, 111 miles apart; S and K, 96 miles apart. Each one day. Therefore, the first day must be 93 miles to add to 300 total.

Longest day within 111 or 96 distance, and begin or end in Danville. Will only fit in #3 or #4 above. Woodbury is the only other missing, so must be starting point.

So I got 2 possible maps:
1. WBLKRGSNDU
2. WNLKRGSBDU

Elias not in 111 or 96, so in 93, first day, and has to start in Woodbury (clue 6). Miles before Lakeview is 21. But Rainier to Gravesend shortest, so is 15 or 18.
And that's all I've got so far.

11/28/2017 5:51:22 PM

Lynda
Lynda
Posts: 30
Frances, I'm impressed. It took me days to get as far as you. The biggest problem I keep coming up against is Danville. Just don't know where to stick it (but I have an idea). I'll work on it tomorrow morning. Gotta chill a little right now. You're a doll for getting together with me on this crazy puzzle. Later
edited by lynkosy on 11/28/2017

11/28/2017 7:17:05 PM

Semipro
Semipro
Posts: 292
Would dividing all numbers by 3 make the whole thing easier to think about? In clue 7, round 10 up to 12, yielding 4.

11/29/2017 10:02:16 AM

Lynda
Lynda
Posts: 30
Semipro, I'm not sure if that would help as the nine numbers that are needed to
solve the puzzle have to come from the following list: 15, 18, 21, 24, 27, 30, 33, 36, 42, 45, 48, 51, 54, 57 and 60. Remember that 21 and 45 are given and there is no 39 Glad to have you on board. Frances has come up with the same map as I so now we have to place names and numbers. I'm having trouble getting two consecutive trips to equal 75 though so I'm still working on it.

Semipro wrote:
Would dividing all numbers by 3 make the whole thing easier to think about? In clue 7, round 10 up to 12, yielding 4.

11/29/2017 11:12:21 AM

Semipro
Semipro
Posts: 292
Lynda, all I had in mind with that suggestion is that 5, 6, 7, . . . are handier to work with than 15, 18, 21, . . . Then the total miles would be 100.

11/29/2017 11:48:39 AM

Lynda
Lynda
Posts: 30
Okay. I'm sorry.

Semipro wrote:
Lynda, all I had in mind with that suggestion is that 5, 6, 7, . . . are handier to work with than 15, 18, 21, . . . Then the total miles would be 100.

11/29/2017 1:33:30 PM

Frances
Frances
Posts: 698
Working with Clue 7, and rounding up 10 to 12 is good:

Vivian rode twice as far as unknown. Sherman rode 3 miles more than Vivian. Sherman rode 12+ miles fewer than unknown. Range is 15 to 60. Possible:

15-18-21 = Unknown
30-36-42 = Vivian
33-39-45 = Sherman
45-51-57 = least amount more than Sherman

No 39, and Morris is 45, not Sherman.

So: Shortest distance, Rainier to Gravesend, is 15. Vivian is 30, Sherman is 33. From either Newton or Bethel to Lakeview is 21. Morris is 45.

That's all additional I've gotten.

11/29/2017 1:49:05 PM

Semipro
Semipro
Posts: 292
Then Sherman-Claire-Oscar, from clue 5?

11/29/2017 2:35:57 PM

Lynda
Lynda
Posts: 30
Me too. Looks like we're getting there. Except I also have Elias as #1 (27), Nadia #2 (21) and Morris #3 (45) and Sherman (#4 or 6), Claire (#5) and Oscar (#4 or 6) but I'm ready to change it because I can't get 2 consecutive riders to equal 75 when I leave it like that.


Frances wrote:
Working with Clue 7, and rounding up 10 to 12 is good:

Vivian rode twice as far as unknown. Sherman rode 3 miles more than Vivian. Sherman rode 12+ miles fewer than unknown. Range is 15 to 60. Possible:

15-18-21 = Unknown
30-36-42 = Vivian
33-39-45 = Sherman
45-51-57 = least amount more than Sherman

No 39, and Morris is 45, not Sherman.

So: Shortest distance, Rainier to Gravesend, is 15. Vivian is 30, Sherman is 33. From either Newton or Bethel to Lakeview is 21. Morris is 45.

That's all additional I've gotten.

11/29/2017 2:38:39 PM

Lynda
Lynda
Posts: 30
Yeah, I know. That's a tough one. I put those three in the middle but it's not working out so maybe I'll switch them with Joan, Vivian and Herbert. Are you having fun yet? Dummy me, I just realized I can't switch them because Claire has to be the shortest. Right? And what do they mean "either from first to last or from last to first"? They usually say "in some order" so maybe they don't all go on the same day. Maybe Joan could be #4 and the other 3 could follow and that would still leave room for Vivian and Herbert to visit the same town. What do you think?

Semipro wrote:
Then Sherman-Claire-Oscar, from clue 5?

edited by lynkosy on 11/29/2017

11/30/2017 11:03:22 AM

Semipro
Semipro
Posts: 292
Lynda, I think they said "either from first to last . . ." because they're naming three riders and they want you to know which one is in the middle. "In some order" works with two riders but not with three who are lined up.

As for the other details, I don't know. I'm not taking on this puzzle. It looks like something that could eat my time for days.

Home » General Discussion » Trail Mix-Original Logic Problems-August 2012





7.2.12.0