Questions tagged [pursuit-evasion]

Any puzzle where a team of pursuers must capture a team of targets, with movement limited to some given space. The goal is to find a winning strategy either for the pursuers or for the evaders.

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20
votes
3answers
5k views

The lake monster

You are on a rowboat in the middle of a large, perfectly circular lake. On the perimeter of the lake is a monster who wants to eat you, but fortunately, he can't swim. He can run (along the perimeter)...
46
votes
4answers
5k views

The lion and the zebras

The lion plays a deadly game against a group of 100 zebras that takes place in the steppe (= an infinite plane). The lion starts in the origin with coordinates $(0,0)$, while the 100 zebras may ...
67
votes
5answers
6k views

Can the Policeman catch the Thief?

The town of Squareshire has six streets: four sides of a square and the lines joining the midpoints of opposite sides. $\hskip2in$ A policeman is chasing a thief along these streets. If they are ...
12
votes
2answers
1k views

Escaping a hungry lion you can't outrun

You are at the edge of an enormous circular arena. A hungry lion is eying you from the centre of this area. You are both capable of running at the same maximum speed, but constraint within the arena. ...
9
votes
5answers
663 views

Wolves and a Hare on a tiny planet

On a tiny spherical planet there exist $N$ wolves and 1 hare. The planet is so small any of these creatures can circle it in exactly 1 day. No creature needs to sleep or eat. The wolves communicate ...
11
votes
1answer
1k views

Star-Lord and the Space Police

Star-Lord is on a deserted planet along with two space policemen. If he runs into either of them, he will get immediately arrested. Fortunately for Star-Lord, somewhere on two opposite ends of the ...
17
votes
2answers
2k views

Game of Drones - Zap it!

Your programmable drone is pitted against another drone in a rectangular 3D arena measuring 40 meters long, 40 meters wide and 20 meters high. You have equipped your drone with a laser gun that will ...
12
votes
4answers
808 views

Pursuit Problem II: Surrounded in Marauders' Circular Cove

(This is the sequel to this puzzle. It has a similar setup, but believe me, the solution is very different. Be careful! The answer is counterintuitive. It shocked me at first.) You are a pirate. ...
25
votes
3answers
1k views

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

This is a variant of this excellent question. The rules of the lion-zebra hunger games are exactly the same: The lion plays a deadly game against a group of 100 zebras that takes place in the ...
18
votes
6answers
2k views

Pursuit Problem: Mutineer trapped on an island

You are a pirate. One of your crew ran off in the night, swam to your secret island, and dug up your life's treasure. You need to capture her. You may deploy $n$ pirate ships to patrol the boundary ...
11
votes
2answers
831 views

Spiders and Ant on a Cube

There are three spiders and an ant, crawling on the edges of a wire frame cube. The spiders can crawl exactly one third as fast as the ants. Show that the spiders can catch the ant. Think of bugs as ...
3
votes
2answers
903 views

Game against the Devil

While browsing through S.E you notice a spider crawl right out from under your keyboard! Startled, you twitch your hand and left clicked your mouse. You look up in shock as you notice that you just ...