All Questions
Tagged with pursuit-evasion mathematics
28
questions
2
votes
2
answers
179
views
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 ...
- 21
7
votes
1
answer
836
views
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, ...
- 2,477
19
votes
4
answers
2k
views
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 ...
- 2,477
7
votes
4
answers
403
views
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 ...
- 6,536
17
votes
6
answers
1k
views
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 ...
- 6,536
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
25
votes
12
answers
4k
views
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 ...
- 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
13
votes
3
answers
1k
views
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 ...
74
votes
5
answers
8k
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 ...
- 19.7k
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