08-29-2019, 01:53 AM
(This post was last modified: 08-29-2019, 01:54 AM by Tir - the teacher.)
The last assignment took many a student longer than anticipated; the answer is as simple as most, if not all, suspect - but it’s the reasoning behind the intuitive logic that Tir is trying to extract from each of them. Maths is not always about calculation - it’s logic and abstract thinking, that solves a problem more often than not.
However, many fail to find the correct answer and less find the reason why it should be. Time for a lesson, he thinks. He recalls what was given:
The class is transported to an outside setting: in front of you is a creek, one bucket each, and a trail that’s sure to test you. At first glance it looks simple - the trail runs from the creek into a plains, though the way is obscured by rocks and crevices so deep Pangea looks like child’s play. Looking closely, it more resembles a labyrinth - and for those looking even closer, you’ll find that there is no water source on the trails. There is a pool on the other side, but you’d have to reach it first to refill.
Three trails are marked: with 1, 5, and an infinity symbol.
Tir appears with his instructions.
“Only one of the marked paths will bring you to the other side. This path will wind around the trail for 5 hours and bring you to the other side, but the buckets you’ve each received can only hold enough water to last 4 hours. If you’re out of water, apart from getting terribly thirsty, you’ll have failed your test.
This task is not impossible - you are not alone, and the water source (here, being a creek,) will not run out. How many horses (each carrying one bucket) should you take with you to still make it to the other side? That’s the path you seek.
I’ll see you there in five hours - or when I have to magically transport you out of the maze, which means you’ve failed. Good luck.”
When some make it out and some don’t, Tir decides to wait no longer with his wrap-up and pulls out those who have taken the incorrect path of have run out of water. He presents them with the solution:
“Remember what I said. The trail will take 5 hours but one horse can only carry 4 hours worth of water. All other calculations are irrelevant - the problem would have been the same if it took 5 days, 5 months or 5 years.
This poses the problem: on your own, you will never make it because you can only walk 4/5th of the trail before you run out of water. However, should you take one other horse with you, you would make it.
But only if you’re both clever enough to walk 1/5th of the trail double, and work together to refill your buckets.”
The solution is presented before them, an illusion playing out like a little movie in which the trail would be seen from above.
A white and black horse each start the 5-hour distance. After 1/5th of the trail, the white horse fills up the black horse’s bucket back to the brim, and returns to refill. Thus, the black horse makes it to the other side, and the white horse now has again, 4/5th of water to walk the trail.
The black horse refills their bucket on the other side and walks back 1/5th of the trail, which is the place that the white horse will reach at the same time because both have by then doubled back, though each on the other side. The white horse and black horse share their remaining water for the last 1/5th of the trail, and both make it to the other side with water to spare.
“Refilling at 2/5th leaves the horse walking the same 2 hours back without water, so that’s not an option.”
He flicks through their answers, seeing how they made it and where they made a wrong decision if they did.
Lepis tried to cheat the magical path and buckets by running, but finds that running doesn’t affect the time it takes to cross. She eventually made it by sacrificing her new friend Blackie. Though not the answer Tir seeks, because Blackie didn’t make it, she presented some clever reasoning.
Nolin indeed shared his water with Cyprin, and ran back to refill. However, they make a miscalculation and Nolin gets stuck 1/5th before the end.
Cyprin calculated that with one refill they will have 3 buckets, thus 12 hours worth of water, of which 8 remains after the refill - but if she looks closely at both their buckets, she will find that Nolin had to use some of his water to make the trip back and forth to the beginning, as well as that Nolin filled her bucket with just one more hour because the bucked doesn’t hold more water than 4 hours total.
So it turns out that Nolin effectively walked 1/5th of the trail 3 times and thus had to cross a 7-hour trail. Cyprin carried a total of 5 hours worth of water and made it across, but Nolin had 1 hour of water to walk forth, 1 hour of water walking back, and then 4 hours of water to cross the trail (bucket holds no more), which makes a total of 6 hours worth of water.
This leaves Nolin with 1 water-hour less than he actually needs.
Aeolus tries to cheat by running twice as fast like Lepis, and will find that running makes one sweat more, and that some of the drops perhaps have run over the bucket’s side or he’s taken double swigs without noticing. After all, the magic 5-hour trail and 4-hour buckets will not be cheated on. Although he shares with Benny, without the two refills, they still don’t make it.
Olver almost didn’t make it, if he hadn’t found someone waiting for him somewhere near the end of the way. Nevertheless, he refills the bucket once to rescue them, which was half of the solution.
Cassian’s reasoning saves his grade and both Elaina and Lilliana, by coming up with the right solution. Tir already knew he was intelligent, and thinks it’s a shame he didn’t show this to class earlier. He might have earned much higher grades.
Interestingly enough, Bethlehem’s solution is nearly the same as the answer one needs, but somehow he ends up with a group of five to make it, while with the same reasoning, he might have made it with just one other horse extra.
@[Ruinam] fails to take the trail at all, nor does he come up with a solution. Tir frowns on such irresponsible behavior, and defects him for a minimum of 12 months. Ruinam will only be able to talk when he incorporates a number in his sentences for this coming year (defect starts to take effect with the next new thread he is in, old threads may be safe if you want).
This places Lilliana first, Aeolus comes in second, and third is Elaina.
@[lilliana] has earned an elemental Healing trait, for she has shown she values friendship, working together, and Tir has the feeling she seeks to be useful. This may be genetic or non-genetic. Please post in updates which element you want your healing to be.
@[Aeolus] would like to bring his friends to the ocean. He gets the trait Zoolingualism to make new friends in the water, instead of having to bring non-waterbreathers down with him. This may be genetic or non-genetic, please post an update.
@[Elaina], you seek beauty but forget you already are. To help you understand the dangers of beauty, I give you the trait Siren Song. This may be genetic or non-genetic, please post an update.
Tir looks at the rest of them, and smiles. ”Each of you may pick a marking, black or white pending your coat colour, of a geometrical shape. A cube, star, trapezium, circle, you name it.”
For @[Olver]’s hard work in placing fourth, the defect “mute” may be altered to either “mute during the day” or “may only speak in rhyme”; please post in updates which one you prefer.
However, many fail to find the correct answer and less find the reason why it should be. Time for a lesson, he thinks. He recalls what was given:
The class is transported to an outside setting: in front of you is a creek, one bucket each, and a trail that’s sure to test you. At first glance it looks simple - the trail runs from the creek into a plains, though the way is obscured by rocks and crevices so deep Pangea looks like child’s play. Looking closely, it more resembles a labyrinth - and for those looking even closer, you’ll find that there is no water source on the trails. There is a pool on the other side, but you’d have to reach it first to refill.
Three trails are marked: with 1, 5, and an infinity symbol.
Tir appears with his instructions.
“Only one of the marked paths will bring you to the other side. This path will wind around the trail for 5 hours and bring you to the other side, but the buckets you’ve each received can only hold enough water to last 4 hours. If you’re out of water, apart from getting terribly thirsty, you’ll have failed your test.
This task is not impossible - you are not alone, and the water source (here, being a creek,) will not run out. How many horses (each carrying one bucket) should you take with you to still make it to the other side? That’s the path you seek.
I’ll see you there in five hours - or when I have to magically transport you out of the maze, which means you’ve failed. Good luck.”
When some make it out and some don’t, Tir decides to wait no longer with his wrap-up and pulls out those who have taken the incorrect path of have run out of water. He presents them with the solution:
“Remember what I said. The trail will take 5 hours but one horse can only carry 4 hours worth of water. All other calculations are irrelevant - the problem would have been the same if it took 5 days, 5 months or 5 years.
This poses the problem: on your own, you will never make it because you can only walk 4/5th of the trail before you run out of water. However, should you take one other horse with you, you would make it.
But only if you’re both clever enough to walk 1/5th of the trail double, and work together to refill your buckets.”
The solution is presented before them, an illusion playing out like a little movie in which the trail would be seen from above.
A white and black horse each start the 5-hour distance. After 1/5th of the trail, the white horse fills up the black horse’s bucket back to the brim, and returns to refill. Thus, the black horse makes it to the other side, and the white horse now has again, 4/5th of water to walk the trail.
The black horse refills their bucket on the other side and walks back 1/5th of the trail, which is the place that the white horse will reach at the same time because both have by then doubled back, though each on the other side. The white horse and black horse share their remaining water for the last 1/5th of the trail, and both make it to the other side with water to spare.
“Refilling at 2/5th leaves the horse walking the same 2 hours back without water, so that’s not an option.”
He flicks through their answers, seeing how they made it and where they made a wrong decision if they did.
Lepis tried to cheat the magical path and buckets by running, but finds that running doesn’t affect the time it takes to cross. She eventually made it by sacrificing her new friend Blackie. Though not the answer Tir seeks, because Blackie didn’t make it, she presented some clever reasoning.
Nolin indeed shared his water with Cyprin, and ran back to refill. However, they make a miscalculation and Nolin gets stuck 1/5th before the end.
Cyprin calculated that with one refill they will have 3 buckets, thus 12 hours worth of water, of which 8 remains after the refill - but if she looks closely at both their buckets, she will find that Nolin had to use some of his water to make the trip back and forth to the beginning, as well as that Nolin filled her bucket with just one more hour because the bucked doesn’t hold more water than 4 hours total.
So it turns out that Nolin effectively walked 1/5th of the trail 3 times and thus had to cross a 7-hour trail. Cyprin carried a total of 5 hours worth of water and made it across, but Nolin had 1 hour of water to walk forth, 1 hour of water walking back, and then 4 hours of water to cross the trail (bucket holds no more), which makes a total of 6 hours worth of water.
This leaves Nolin with 1 water-hour less than he actually needs.
Aeolus tries to cheat by running twice as fast like Lepis, and will find that running makes one sweat more, and that some of the drops perhaps have run over the bucket’s side or he’s taken double swigs without noticing. After all, the magic 5-hour trail and 4-hour buckets will not be cheated on. Although he shares with Benny, without the two refills, they still don’t make it.
Olver almost didn’t make it, if he hadn’t found someone waiting for him somewhere near the end of the way. Nevertheless, he refills the bucket once to rescue them, which was half of the solution.
Cassian’s reasoning saves his grade and both Elaina and Lilliana, by coming up with the right solution. Tir already knew he was intelligent, and thinks it’s a shame he didn’t show this to class earlier. He might have earned much higher grades.
Interestingly enough, Bethlehem’s solution is nearly the same as the answer one needs, but somehow he ends up with a group of five to make it, while with the same reasoning, he might have made it with just one other horse extra.
@[Ruinam] fails to take the trail at all, nor does he come up with a solution. Tir frowns on such irresponsible behavior, and defects him for a minimum of 12 months. Ruinam will only be able to talk when he incorporates a number in his sentences for this coming year (defect starts to take effect with the next new thread he is in, old threads may be safe if you want).
| Horse | Timing | Path | Teamwork (or NPC) | Reasoning | Refills | Obstacle | Total | Assign1 | Assign2 | Total |
|---|---|---|---|---|---|---|---|---|---|---|
| Olver | 90 | 100 | 70 | 80 | 50 | 100 | 80.0 | 85.6 | 95.8 | 87.1 |
| Lepis | 100 | 100 | 50 | 100 | 0 | 100 | 70 | 86.3 | 88.3 | 81.5 |
| Cassian | 90 | 100 | 100 | 95 | 100 | 95 | 98.0 | 78.1 | 73.3 | 83.1 |
| Cyprin | 100 | 100 | 50 | 80 | 50 | 90 | 76.0 | 91.3 | 93.3 | 86.9 |
| Nolin | 100 | 100 | 90 | 80 | 50 | 100 | 84.0 | 85.6 | 75.0 | 81.5 |
| Lilliana | 100 | 100 | 100 | 75 | 100 | 90 | 93.0 | 91.9 | 92.5 | 92.5 |
| Aeolus | 100 | 100 | 100 | 90 | 50 | 100 | 88.0 | 86.9 | 95.0 | 90.0 |
| Bethlehem | 80 | 50 | 100 | 85 | 100 | 50 | 77.0 | 90.6 | 86.7 | 84.8 |
| Elaina | 100 | 100 | 100 | 75 | 100 | 100 | 95.0 | 78.8 | 93.3 | 89.0 |
This places Lilliana first, Aeolus comes in second, and third is Elaina.
@[lilliana] has earned an elemental Healing trait, for she has shown she values friendship, working together, and Tir has the feeling she seeks to be useful. This may be genetic or non-genetic. Please post in updates which element you want your healing to be.
@[Aeolus] would like to bring his friends to the ocean. He gets the trait Zoolingualism to make new friends in the water, instead of having to bring non-waterbreathers down with him. This may be genetic or non-genetic, please post an update.
@[Elaina], you seek beauty but forget you already are. To help you understand the dangers of beauty, I give you the trait Siren Song. This may be genetic or non-genetic, please post an update.
Tir looks at the rest of them, and smiles. ”Each of you may pick a marking, black or white pending your coat colour, of a geometrical shape. A cube, star, trapezium, circle, you name it.”
For @[Olver]’s hard work in placing fourth, the defect “mute” may be altered to either “mute during the day” or “may only speak in rhyme”; please post in updates which one you prefer.