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11 Jul 2024, 18:37
Kudos
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Options for Run
124
135
234
9 for Center (All have center as final option)
7: 9-2 = 7 as Route 1 does not have have Lane option.
124
135
234
9 for Center (All have center as final option)
7: 9-2 = 7 as Route 1 does not have have Lane option.
said.tojiboev
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11 Jul 2024, 18:42
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Bunuel
Possible combinations:
- 3 miles + 3 miles + 4 miles = 10 miles
- 4 miles + 4 miles + 2 miles = 10 miles is impossible as there's no 2-mile route.
Possible Pattern over 3 days:
Day 1:
- Route 1 (3 miles)
- Route 2 (3 miles)
- Route 4 (4 miles)
Day 2:
- Route 1 (3 miles)
- Route 3 (3 miles)
- Route 5 (4 miles)
Day 3:
- Route 2 (3 miles)
- Route 3 (3 miles)
- Route 4 (4 miles)
Analysis of City Centre Visits:
- Every route returns to the City Centre.
- In each day, the runner starts and ends at the City Centre three times.
- Over 3 days, she visits the City Centre: 3×3=9 times.
Analysis of Laurel Lane Visits:
- Routes involving Laurel Lane: Route 2, Route 3, Route 4, and Route 5.
- In Day 1, Route 2, and Route 4 involve Laurel Lane: 2 times.
- In Day 2, Route 3 and Route 5 involve Laurel Lane: 2 times.
- In Day 3, Route 2, Route 3, and Route 4 involve Laurel Lane: 3 times.
- Summing these, over 3 days, she runs towards Laurel Lane 2+2+3=7 times.
11 Jul 2024, 19:22
Kudos
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The only way to reach exactly 10 miles with the given routes is to a 3-mile route twice and a 4-mile route once. The question also states that the runner "does not run any of the routes more than two days in a row and never avoids a route two days in a row". In order to meet these conditions, the runner must run a 3-3-4 variation one day and then a different 3-3-4 variation the next and since she cannot avoid a route two days in a row, must go back to the first 3-3-4 variation.
Therefore the runner could do something like
DAY 1. Route 1, Route 4, Route 3.
For Day 2 she would not be able to repeate any of the routes she ran on Day 1 and therefore would have to run from the remaining routes, which are Routes 2 and 5. Since Route 5 is 4 miles long, she would have to run Route 2 twice that day, since the question did not say anything about running the same route twice in one day.
DAY 2. Route 2, Route 5, Route 2
Then for Day 3 it would be back to the Day 1 run so
DAY 3. Route 1, Route 4, Route 3
Here is where it gets interesting. The question asks how many times the runner runs towards the City Centre over the span of any 3-day period and how many time she runs towards Laurel Lane over the span of any 3-day period. Since every route starts and ends with the City Center it is quite easy to calculate that she runs a total of 3 times towards the city center in one day and therefore 9 times in a 3-day period.
The answer is not as evident in the case of Laurel Lane. This is because one of the routes, Route 1, does not have it as a stop. If you calculate this as the amount of times she arrives at Laurel Lane then you will get either 7 or 8 depending on which day you start. HOWEVER, the question does not ask how many times she arrives at Laurel Lane or runs through Laurel Lane but towards, meaning the direction of. Since she always starts at the same place and finishes at the same place, then essentially she is making a lap. When you make a lap or a circle then you must, by definition, cover a 360° field view, meaning that you will at some point head in every single direction. We can also see with Route 5 that she runs City Centre – Songbird Park – Market Square – Laurel Lane – City Centre. During Route 1 she runs City Centre – Market Square – Songbird Park – City Centre, which is a very similar route but starting the opposite direction and without the Laurel Lane stop. If we were to add a Laurel Lane stop to Route 1, then it would most likely be between City Centre and Market Square, which would mirror Route 5. So we can assume that somewhere during her Route 1 run between City Centre and Market Square, she will be running towards Laurel Lane.
Therefore the total number of times the runner will run towards the city centre over the span of any 3-day period is 9 times and the total number of times the runner will run towards Laurel Lane over the span of any 3-day period is 9 times.
Therefore the runner could do something like
DAY 1. Route 1, Route 4, Route 3.
For Day 2 she would not be able to repeate any of the routes she ran on Day 1 and therefore would have to run from the remaining routes, which are Routes 2 and 5. Since Route 5 is 4 miles long, she would have to run Route 2 twice that day, since the question did not say anything about running the same route twice in one day.
DAY 2. Route 2, Route 5, Route 2
Then for Day 3 it would be back to the Day 1 run so
DAY 3. Route 1, Route 4, Route 3
Here is where it gets interesting. The question asks how many times the runner runs towards the City Centre over the span of any 3-day period and how many time she runs towards Laurel Lane over the span of any 3-day period. Since every route starts and ends with the City Center it is quite easy to calculate that she runs a total of 3 times towards the city center in one day and therefore 9 times in a 3-day period.
The answer is not as evident in the case of Laurel Lane. This is because one of the routes, Route 1, does not have it as a stop. If you calculate this as the amount of times she arrives at Laurel Lane then you will get either 7 or 8 depending on which day you start. HOWEVER, the question does not ask how many times she arrives at Laurel Lane or runs through Laurel Lane but towards, meaning the direction of. Since she always starts at the same place and finishes at the same place, then essentially she is making a lap. When you make a lap or a circle then you must, by definition, cover a 360° field view, meaning that you will at some point head in every single direction. We can also see with Route 5 that she runs City Centre – Songbird Park – Market Square – Laurel Lane – City Centre. During Route 1 she runs City Centre – Market Square – Songbird Park – City Centre, which is a very similar route but starting the opposite direction and without the Laurel Lane stop. If we were to add a Laurel Lane stop to Route 1, then it would most likely be between City Centre and Market Square, which would mirror Route 5. So we can assume that somewhere during her Route 1 run between City Centre and Market Square, she will be running towards Laurel Lane.
Therefore the total number of times the runner will run towards the city centre over the span of any 3-day period is 9 times and the total number of times the runner will run towards Laurel Lane over the span of any 3-day period is 9 times.
Bunuel
