95 votes

Chasing pirates

Stay put for about 45 days, after which the pirates would have circumnavigated the globe and returned to your current position.
  • 1,044
60 votes
Accepted

The lion and the zebras

Here is the strategy:   It works because:
  • 7,688
56 votes
Accepted

Chasing pirates

If we assume the ocean is flat and extends indefinitely in all directions, there is a strategy that guarantees we can catch the pirates in at most 800,000 years. Put our current location as the ...
  • 13.9k
45 votes
Accepted

Can the Policeman catch the Thief?

Yes, the policeman can catch the thief, although it may take a very long time. In particular, the following strategy works: The policeman starts in the center. First, he makes a counterclockwise loop ...
  • 7,741
41 votes
Accepted

Game of Drones - Zap it!

The attack drone should fly to a virtual target that is always at 29/30 of the way from the center of the room to the target drone. That point moves 3.3% slower than the target drone. Since the ...
  • 22.5k
32 votes

The lake monster

It is possible to escape a monster that is a little more than $4.6$ times faster. Given a monster running at speed $X$ times rowing speed and a lake with radius $R$, you must first row to the circle ...
  • 2,029
24 votes
Accepted

The lake monster

First of all, row out to a radius $R/4$ (where the lake has radius $R$) keeping you, the centre of the lake and the monster in a straight line - with you on the far side to the monster. This is always ...
22 votes

Chasing pirates

Drive 20 hours in a direction we will denote with as having $\theta=0$. Drive in a spiral pattern such that you are $20t+20$ nautical miles away from you starting position. $t$ is time in hours from ...
  • 9,012
21 votes

Variant of lion and 100 zebras

I have no idea who can win, but I do want to clear up one point that some other people seem to be overlooking. Namely, the lions can always surround some plurality of zebras so any strategy to keep ...
  • 1,555
20 votes

Can the cop catch the thief?

It's undefined although a slight tightening up of the question would make it defined. What the question lacks is a specification of what happens when a player reaches the limit of the universe. To be ...
16 votes
Accepted

Hunter chasing a fox on a graph

Number the nodes as follows: A valid solution is to check: To see that this works, first note that the fox can only go from a hole in an even-numbered level of the tree to a hole in an odd-numbered ...
  • 21.4k
16 votes
Accepted

Angels & Demons (Open question)

  • 15.3k
15 votes
Accepted

Can the cop catch the thief?

Fundamentally, the issue is that For every fixed cop strategy, there exists a thief strategy that beats it. For every fixed thief strategy, there exists a cop strategy that beats it. For an easier ...
  • 495
14 votes
Accepted

Escaping a hungry lion you can't outrun

First, run 1/3 of a unit toward the center of the arena. The radius of the arena is 1 unit and the lion runs at the same speed as you, so the lion will not catch you. Now, we run along a series of ...
  • 13.9k
14 votes
Accepted

Spiders and Ant on a Cube

A more simplified/intuitive way to think about it is if you have the following: No matter where the ant and spider start, the spiders go into this formation: Where the red dots are the spiders, and ...
  • 5,868
14 votes
Accepted

Star-Lord and the Space Police

Here's my answer: Once this is settled, we can easily say the problem can be solved The strategy being: Bonus: Second Bonus FTW:
  • 461
13 votes

The lion and the zebras

This is not an answer, but rather a counter to Micael Rize's answer. I don't intend for this to be picking on him, but it is too difficult to explain in a comment, and there are many arguments about ...
  • 8,851
13 votes

Angels & Demons (Open question)

I just came back home and was about to draw a diagram illustrating this, but I can't do any better than @noedne already did.
12 votes

Lions and Zebras on a Chess Board

I will place the Zebras as follows : Then whenever the knight attacks any piece, I will move it to its adjacent diagonal so that it is contained within these boxes : Now, the knight cannot fork two ...
12 votes

Spiders on a cube

Not a definite answer but I narrowed it down to 2 possibilities. It's either In this case or the second possible answer is Because
  • 11.1k
11 votes
Accepted

The lion and the zebras II: The lion with millimeter-long claws

Zebras can always win if the lion claw length $r=0$, but the lion wins with claws $r>0$. When the lion has claws, the safety-buffer distance $b$ would have to grow with the number of chasing turns ...
11 votes

Can the cop catch the thief?

is right, basically because The problem with one of the two suggested approaches is that The space in which they're moving is sort of like a 1-dimensional hyperbolic space: they can get ...
11 votes

Can the cop catch the thief?

Cleaned up answer: To make things concrete, let's say that the cop's strategy is represented as a function c(t), which is dependent on the thief's trajectory w(t), and vice-versa. The cop's strategy ...
  • 3,066
10 votes

Chasing pirates

Assuming there is no wind, your boat was completely still on the water before it was boarded by pirates, the pirates stepped off your boat at its center of gravity, and the pirates used motorized ...
9 votes

Lions and Zebras on a Chess Board

Note: The following full answer expands on the previous partial answer, which has been retained below. Full answer To analyze all the possible states, the algorithm Ken Thompson described in his ...
  • 778
9 votes

How long can you survive at the devil's playground?

You're screwed in constant time, no matter your speed, since the devil has a good strategy. I cannot claim to having found the devil's optimal strategy, but I do claim that there is an upper bound to ...
8 votes

Pursuit Problem: Mutineer trapped on an island

For the square island, you need Not sure if I can provide an escape strategy for one less ship patrolling. Should be something like "approach one corner, lure the ships towards it, and then ...
  • 987
8 votes

The lake monster

The monster wants to eat me, but he is also particuarly fond of my boat since "he will always run towards the closest bit of shore to your boat." So I row the boat in one direction and then jump off ...
  • 251
8 votes

The lion and the zebras II: The lion with millimeter-long claws

Zebras win with an up (or down) and across strategy. Start with Lopsy's idea of vertical strips, with each strip 400m wide. We call a strip empty if it contains no zebras (it may contain the lion). ...
  • 7,794
8 votes

Pursuit Problem II: Surrounded in Marauders' Circular Cove

Surprisingly, Suppose you have a very very high number of smugglers. The strategy to escape is approaching the coast as much as possible (the more the smugglers, the closest you have to be), then ...
  • 12.5k

Only top scored, non community-wiki answers of a minimum length are eligible