All Questions
Tagged with pursuit-evasion geometry
15
questions
4
votes
1
answer
181
views
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 ...
- 41
1
vote
1
answer
323
views
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 ...
- 6,536
16
votes
2
answers
891
views
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 ...
- 6,536
0
votes
1
answer
150
views
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 ...
- 1,487
19
votes
4
answers
1k
views
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 ...
- 6,536
2
votes
1
answer
417
views
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 ...
- 3,885
10
votes
2
answers
822
views
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 ...
- 6,964
11
votes
1
answer
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 ...
- 6,964
4
votes
1
answer
192
views
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 ...
- 6,964
14
votes
4
answers
1k
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. ...
- 7,984
21
votes
6
answers
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 ...
- 7,984
9
votes
5
answers
726
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 ...
- 9,122
10
votes
3
answers
2k
views
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 ...
- 7,939
38
votes
11
answers
4k
views
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 ...
- 7,016
16
votes
2
answers
2k
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. ...
- 4,400