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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Quirky chasing problem along train network [closed]
Echidna and Numbat are friends, so they decide to go on vacation together to visit Central American caves and volcanos. But these two friends have very different traveling philosophies. Numbat prefers ...
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More Catching of Cats
After my first puzzle on this theme was solved relatively quickly, here is a (trickier) follow up question in the same vein!
The setup is similar - you are in a room with an infinite line of boxes, ...
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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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How long will it take for the horse to be captured?
Source: https://open.kattis.com/problems/ambush
Problem: When Farmer Oskar doesn’t watch his cows closely enough, they tend to wander off into the forest to hunt for horse spies. To catch an enemy ...
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Flee the Bandits
You're heading out to pick up your partner in crime's little sister from the train station. You're nearly there: between you and the train station is a small square of blocks, with 5 North-South ...
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Caught in the storage maze, part 2
One of your sister's former friends has gotten herself lost in a storage room in some abandoned building, and you've decided to go capture her and turn her in.
However, when you enter you realize ...
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Caught in the storage maze
Two of your sister's former friends have gotten themselves lost in a storage room in some abandoned building. While your girlfriend managed to get one of them out, the other one apparently got turned ...
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How will the wolf catch the sheep in minimum time?
A wolf is trying to catch two sheep. At time $0$ the wolf's at $(0,0)$ and the sheep are at $(1,0)$. All animals move continuously in real time and react instantaneously according to each other's ...
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Can you stop copy Alice?
At time 0, Alice and you both move freely at speed 1 on the plane.
As each hour passes, all copies of Alice will subdivide into 2, each moving at half the speed of the parent. So if left alone, at ...
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Can you Avoid the Spear-Wielding Gladiator?
You are trapped in a circular coliseum, and a gladiator with a spear is chasing you. You can't defend yourself, but you can run faster than the gladiator.
You run at 11 feet per second, and 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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Can you escape from two lions?
You're at the center of a circular arena. A pair of lions are at the border, planning to catch you. One of them moves as fast as you, but the other moves slower than you. The three of you are confined ...
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Can the lion protect the sheep from the wolves?
In a closed arena, three wolves are on the vertices of an equilateral triangle at the border. The sheep and his lion friend are at the center.
The wolf eats the sheep if their distance is $0$, and ...
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Police and Thieves
I played this game when I was young, but cannot find it online. It is played on a checkers board (e.g. the black squares of a chess board) between two players P and T. The game goes as follows:
P ...
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Can the cop catch the thief?
The cop and the thief, both mathematical points, live in an open interval $(0,1)\subset \mathbb{R}$. That is, their universe is a line segment of length 1 without the 2 endpoints. We know that both ...
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Catching the Vegetable-Goose [closed]
After an altercation involving giant bees, you have been sentence to some hard labour, specifically harvesting barnacle-lambs: a gourd-like fruit that grows geese in its shell
While working, you get ...
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Spiders on a cube
Two spiders are trying to catch an ant. All are constrained to move along the edges of a transparent cube. The speed of the ant is $1$. The speeds of the spiders are $v_1$ and $v_2$ respectively. What'...
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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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1 lion, with a zebra and a fixed enclosure
Background
See the puzzle Variant of lion and 100 zebras from @ghosts-in-the-code which remains unsolved years after it was posted.
Several times in the last couple of years I've started to write up ...
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Angels & Demons (Open question)
This puzzle was given to me by a friend of mine, who in turn heard it from someone else who neglected to provide the answer. The text of the puzzle as it was given to my friend is below:
Angels ...
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Hiding Cat Puzzle on a Grid
The Youtube channel MindYourDecisions posted a video about the "Hiding Cat Puzzle". In the puzzle, you have a line of five boxes, one of which contains a cat. You don't know where the cat is, and your ...
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Hunter chasing a fox on a graph
This is a variant of the sleeping princess puzzle.
There are fifteen foxholes, connected by underground tunnels as shown below. A fox is sleeping in one of them.
Every day, a hunter checks one of ...
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Can the policeman actually catch the thief, instead of shooting?
The ACLU won a lawsuit against the Squareshire Police Department, alleging that his policy of shooting suspected thieves on sight was unconstitutionally excessive force.
The argument that carried the ...
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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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Sly Cooper and the Space Police
Last Space Police question...
Sly Cooper has landed on a deserted planet with 2 policemen. He is moving around the planet, painting a line along his path, claiming any land which is surrounded by ...
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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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Riddick and the Space Police [duplicate]
The next problem may be way too easy, but will post it anyway.
Riddick, trying to escape from the space police, lands on a deserted
planet. How many cops should the space police send to the ...
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Lions and Zebras on a Chess Board
The black knight is our lion chasing 8 white bishop zebras which can't capture. Can the zebras evade the lion forever, if team zebra positions all the pieces and has the first turn?
Rules:
The game ...
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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 ...
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Spiders and Invisible Ant on a Tetrahedron
There are three spiders and an ant on the edges of a wireframe regular tetrahedron. The spiders all move at the same speed, which is faster than that of the ant. Though the ant can always see the ...
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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. ...
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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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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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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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Precision Tag - can the lion win?
This is a spin-off motivated by Lopsy's interesting variant of Gamow's lion and zebras puzzle. It arose from a line of enquiry that tried to extend the vertical run past 5000km (or characterise the ...
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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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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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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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Chasing pirates
You are asleep on your boat on open sea. When you wake up you discover you have been robbed. A quick inspection of security cam footage reveals that the pirates who robbed you left your ship exactly ...
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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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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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