All Questions
Tagged with pursuit-evasion strategy
26
questions
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
21
votes
9
answers
3k
views
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 ...
- 6,536
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
4
votes
0
answers
203
views
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 ...
- 1,236
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
14
votes
7
answers
3k
views
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'...
- 6,536
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
1
answer
1k
views
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 ...
- 14.5k
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
26
votes
4
answers
2k
views
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 ...
- 4,273