Answer to puzzle question #13: Circular Field, Hungry Dog
I really like this one, at first I thought it wasn't possible, we'll go through one of the ways that doesn't work...
Consider the diagram below:
R - is the radius of the circle
X1 - is the radius of the inner dotted circle
X2 - is the radius of the outer dotted circle
R/v > πR/(4v)So clearly we need to be closer to the edge than just in the middle, let us work out how far away from the centre we have to be in order that we have the advantage over the dog. Let our distance from the centre be xR where x is a number less than one eg. if R were 10m and we were 1.5m from the centre then x=0.15 Assuming that we can get the dog on the opposite side of the circle to us (I'll come back to that,) then the distance we must run is (1 - x)R where as the dog must always run πR we can equate the time associated with these distances, remembering the dog runs at 4v.
(1 - x)R/v = πR/(4v)
x = 0.2146
The strategy is to run in a circle of 0.2146R < radius < 0.25R until the dog is on the opposite side then make for the fence like the clappers.
Other PossibilitesIt seems possible that there are other solutions. Such as a spiral giving an angular component to your velocity. This would not work if your direction of travel was always away from the dog, (as in Θdog + π,) which was my first thought because at some point all your velocity would be angular. We could assume the dog would always move so as it would always run to try to match Θhuman. This seems solvable. You would need to consider that your radial velocity would be less than V because there is a tangental component. You could model with different angular velocities.
Alternate versionsI've seen this written with a duck on a round lake, surrounded by a forest. At the edge of the lake is some kind of monster that can't swim. I suppose that makes sense as to why the monster can't get on the lake. But can't ducks fly?
I like this one.
Neither AI covered themselves in glory on this one.
If you're curious what Bard made of this puzzle...
The dog can run four times as fast as you, so if you run in a straight line, the dog will catch you. The only way to escape is to run in a zigzag pattern. The dog will have to turn corners, which will slow it down. If you run fast enough, you can stay ahead of the dog and eventually escape the field.
Here are the steps on how to escape the field:
- Stand in the center of the field.
- Run in a zigzag pattern, making sure to turn corners as sharply as possible.
- Run as fast as you can.
- Keep running until you reach the edge of the field.
Here are some additional tips to help you escape the field:
- Look for obstacles in the field that you can use to your advantage, such as trees, bushes, or rocks. You can use these obstacles to slow down the dog or to hide from it.
- If you have any objects with you, such as a stick or a rock, you can use them to defend yourself from the dog.
- If you are able to climb a tree, you will be out of reach of the dog.
- If you are able to find a hole in the fence, you can escape through it.
If you're curious what ChatGPT made of this puzzle...
If you want to escape the circular field while avoiding the hungry dog, you should run towards the edge of the field, but not in a straight line. Instead, you should run in a zigzag pattern, changing direction frequently. This strategy is known as "jinking."
By running in a zigzag pattern, you can increase the distance that the dog needs to run to catch up with you. Since the dog is faster than you, it will be able to run in a straight line and eventually catch up with you if you run in a straight line. However, by changing direction frequently, you force the dog to also change direction frequently, and it will need to run a longer distance to catch up with you.
To maximize the distance between you and the dog, you should try to move in a direction that is perpendicular to the direction that the dog is currently running. This will make it harder for the dog to change direction quickly and catch up with you.
Additionally, you should try to run towards a part of the fence that is farthest from the dog. This will give you more time to climb over the fence and escape.
Overall, the key to escaping the circular field while avoiding the dog is to use jinking to increase the distance between you and the dog, and to run towards the part of the fence that is farthest from the dog to give yourself the best chance of climbing over it and escaping.
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