Escape from the Vampire's Castle
Three travelers, in a horse drawn wagon, were heading to the nearest village to purchase medicine for a family member, who was gravely ill. Because the distance to the village was a three day ride, they decided to travel day and night, taking turns at the horse reins.
During the second night of travel, they were attacked by a vampire. He captured them, tied them up, and using their wagon, took them back to his castle. His captives were taken up a circular staircase and placed in the small room at the top. He freed their bonds, and locked the door as he left.
The plain circular room has one window. Looking for an escape, Rendal looks out the window and sees something which may assist them. This tower of the castle must have been recently added, because the masons left a 2 bucket, rope, and pulley system attached to the top of the tower. The buckets had been used to raise stone and lower debris during construction. A sign on one bucket indicated that the bucket weight differential should be 10 lbs. This weight differential would allow the heavier bucket to slowly descend to the ground while raising the other to the window. Stacked against the wall, Rendal noticed 13 roughly hewn stones, each weighing very close to 10 lbs. They had obviously been used by the masons as counterweights for the bucket system. The buckets seemed large enough to carry a person.
Rendal weighed 180 lbs. His wife, a small lady, was 100 lbs, and their young son tipped the scales at 80lbs.
As the sun rose the next morning, the vampire slept. Rendal and his family used the bucket system to escape the tower. They found their wagon and hurried away from the castle to purchase the needed medicine.
(amendment: the 13 roughly hewn stones were stacked against the wall in the room in which the people were held captive)
Explain how they accomplished the escape.
During the second night of travel, they were attacked by a vampire. He captured them, tied them up, and using their wagon, took them back to his castle. His captives were taken up a circular staircase and placed in the small room at the top. He freed their bonds, and locked the door as he left.
The plain circular room has one window. Looking for an escape, Rendal looks out the window and sees something which may assist them. This tower of the castle must have been recently added, because the masons left a 2 bucket, rope, and pulley system attached to the top of the tower. The buckets had been used to raise stone and lower debris during construction. A sign on one bucket indicated that the bucket weight differential should be 10 lbs. This weight differential would allow the heavier bucket to slowly descend to the ground while raising the other to the window. Stacked against the wall, Rendal noticed 13 roughly hewn stones, each weighing very close to 10 lbs. They had obviously been used by the masons as counterweights for the bucket system. The buckets seemed large enough to carry a person.
Rendal weighed 180 lbs. His wife, a small lady, was 100 lbs, and their young son tipped the scales at 80lbs.
As the sun rose the next morning, the vampire slept. Rendal and his family used the bucket system to escape the tower. They found their wagon and hurried away from the castle to purchase the needed medicine.
(amendment: the 13 roughly hewn stones were stacked against the wall in the room in which the people were held captive)
Explain how they accomplished the escape.
posted by Zaux at
9:02 AM
13 Comments:
well, if the stones were stacked up "against the wall", i don't see how the 3 people would be able to move them into the buckets in the first place, unless there were stones already in the bucket(s)...
Assuming that against the wall is referring to inside the room at the top of the tower, the following pattern will work
bucket 1: 1 stone 10lbs
Bucket 2: 2 stones 20lbs
Bucket 1: 3 stones 30 lbs
Bucket 2: 4 stones 40 lbs
Bucket 1: 5 stones 50 lbs
Bucket 2: 6 stones 60 lbs
Bucket 1: 7 stones 70 lbs
Note that at this point you are using all 13 stones
Bucket 2: Son 80 lbs
Bucket 1: 9 stones 90 lbs
Bucket 2: Mom 100lbs
This will slowly lower the mom to the ground:
Throw 7 stones down to the mom on the ground.
Now bucket 2 is on the ground with 170 lbs Mom and 7 stones
Bucket 1: Dad 180 lbs
Throw down 9 stones.
Dad is now on the ground.
Bucket 1: 9 stones 90 lbs
Bucket 2: Mom 100 lbs
Mom is now on the ground
Throw down 7 stones
Bucket 2:7 Stones
Bucket 1: son 80 lbs
Now all three are on the ground.
I hope the wagon is some where on the ground for them to find!
They put all the weights, about 130 pounds in one bucket on the floor,where they were locked in.
The mother and son also added weight to the bucket while the father slid down the rope to the ground, then the mother slid down, and last the son.
I think the idea is that the buckets must differ in weight by 10 lbs to move from up to down and vice versa, but can have any weight differnce when stationary. If you had more than a 10 pound difference, the system would, presumably, break. So if bucket 1 is at the top, you must put 2 stones in in to make it go down. Then when the other one comes up, you could put 2 stones in it to make it go down, etc.
Start bucket A at top, B at bottom - both are empty.
Add 1 stone to A: A+1 goes down, B comes up.
Add 2 stones to B, B+2 goes down, A+1 comes up.
Add 2 stones to A, A+3 goes down, B+2 comes up.
Add 2 stones to B, B+4 goes down, A+3 comes up.
Add 2 stones to A, A+5 goes down, B+4 comes up.
Add 2 stones to B, B+6 goes down, A+5 comes up.
Add 2 stones to A, A+7 goes down, B+6 comes up.
Remove the 6 stones from B, boy gets in =>
B+boy goes down. A+7 comes up.
Add 2 stones to A, A+9 goes down, B+boy comes up.
Swap mum with boy. B+mum goes down, A+9 comes up.
Remove 9 stones from A, mum gets out (on the ground).
Now throw or ferry, 7 stones down to mum.
Assume end with A on ground (else swap the bucket names).
mum+7 get into A. Dad gets into B. mum+7 gets out (at top)
dad get out at the ground.
Add 1 stone to A: A+1 goes down, B comes up.
Add 2 stones to B, B+2 goes down, A+1 comes up.
Add 2 stones to A, A+3 goes down, B+2 comes up.
Add 2 stones to B, B+4 goes down, A+3 comes up.
Add 2 stones to A, A+5 goes down, B+4 comes up.
Add 2 stones to B, B+6 goes down, A+5 comes up.
Add 2 stones to A, A+7 goes down, B+6 comes up.
Remove the 6 stones from B, add boy=>
B+boy goes down, A+7 comes up.
Add 2 stones to A, A+9 goes down, B+boy comes up.
Replace boy with mum.
B+mum goes down, A+9 comes up.
Remove the stones from A, mum gets out on the ground.
Repeat the very first instructions, but the boy gets
at the ground and the bucket system is demolished.
I've just re-read David and Kimmy's post. They'd done better than I thought (I'm very tired and should have gone to bed hours ago). I see their method is quicker (and so better) than mine.
a clarifying amendment has been added to the problem statement
Bit late with that Zaux. You've got two solutions that assumed it. I can't imagine what Anonymous first post was thinking.
better late than ...
I really like Ragknot's solution!
So do I.
they all climbed down from a nerby tree =)
Rendal went down 1st, with mom & 7 stones in 2nd bucket.
Mom went down next with son in 2nd bucket.
Finally son went down last with 7 stones in 2nd bucket.
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