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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Why does this solution guarantee that the prince knocks on the right door to find the princess?
I found this puzzle online:
On the top floor of a castle lives a princess. The floor has 17 bedrooms arranged in a row. Each bedroom has doors connecting to the adjoining bedrooms as well as to the ...
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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)...
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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 ...
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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. ...
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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 ...
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Catching a Cat on an infinite Line
Upon entering a (very) large room, you are faced with an infinite line of cardboard boxes that are labeled, in order, by the nonnegative integers. In one of these boxes, a cat is hiding, but you do ...
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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 ...
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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 ...
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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 ...
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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 ...
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Variant of lion and 100 zebras
Note: This problem remains unsolved, as of 19 April 2020, so do try it out. 400 rep bounty guaranteed for a correct answer
This a variation of this question by @Gamow
Suppose there are $100$ lions ...
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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 ...
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Catch the invisible and omniscient thief
The thief has stolen two powerful artifacts: the Cloak of Invisibility and the Glasses of the Oracle. Now they're equipped with both. The cop at the bottom, not knowing where the thief is, is trying ...
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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 ...
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How long can you survive at the devil's playground?
The devil has trapped you in his playground.
The devil knows that you can't cross over the burning boundary of his circle, so he allows you to choose a position within the circle before he starts to ...
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