Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with recreational-mathematics
Search options not deleted
user 75935
Applications of mathematics for the design and analysis of games and puzzles
2
votes
The motorcyclist's challenge
Well, this is not really an answer. It is motivated by fedja's comment. In the original problem we do allow motorcyclist (M) to drive walkers backward. If not, I think I can say something more:
If dr …
- 2,591
8
votes
2
answers
1k
views
The motorcyclist's challenge
n walkers ${A}_{i}$ start out from X to Y simultaneously with speeds ${a}_{i}$, $i=1,2,...,n$. ${a}_{i}\neq {a}_{j}$ if $i\neq j$. At the same time, a motorcyclist M with speed $m=1$ starts out from Y …
- 2,591
0
votes
1
answer
389
views
Zermelo's stone game in 3 dimensional space
Well, first let me make this clear: I'm actually not sure about the background of the game, whether it was really posed (and solved) by Zermelo. But I'll state the game anyway (perhaps someone can inf …
- 2,591
9
votes
2
answers
3k
views
The duel problem
The following duel problem is due to Ben Polak (maybe there's earlier origin, which I'll be glad to be informed about). The rule is as follows:
Two players 1 and 2 start a duel $N$ steps away from ea …
- 2,591
2
votes
0
answers
117
views
Can you escape from two lions in a closed arena?
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 …
- 2,591
3
votes
2
answers
750
views
Truel extended to n persons
n players numbered 1~n play a shooting game. Their accuracy rates p1~pn are strictly between 0 and 1, and strictly increases from p1 to pn. This is common knowledge.
Before the game starts, the refer …
- 2,591
9
votes
3
answers
598
views
The devil's playground
On the $\mathbb{R}^2$ plane, the devil has trapped the angel in an equilateral triangle of firewalls.
The devil
starts at the apex of the triangle.
can move at speed $1$ to leave a trajectory of fir …
- 2,591
0
votes
Brinksmanship: how to achieve the best outcome by a single statement
If only one contender is allowed to make a statement, we have the following Theorems:
Theorem 1: If $N\gt 3$, then survival probability for that contender must be strictly less than $\frac{N-1}N$.
P …
1
vote
1
answer
232
views
Brinksmanship: how to achieve the best outcome by a single statement [closed]
This game is taken from Schelling's Game Theory: How to Make Decisions by R.V. Dodge, in which contenders practice brinksmanship to their own advantages. It goes as follows:
Anderson, Barnes, and Coo …
- 2,591
9
votes
2
answers
752
views
Can the thief escape (from a smooth, simple closed curve)?
Let $C\subset \mathbb{R}^2$ be a smooth, simple closed curve. The thief is inside $C$. Before he starts to move, the police bureau of the $\mathbb{R}^2$ world can freely place countably infinite offic …
- 2,591
1
vote
1
answer
259
views
Is there an equilibrium for this non-zero-sum game?
The game $G(N,M)$ is played:
$N$ ($N\geq 2$) is the number of players, labeled $1$~$N$. In the beginning they have a pot with some chips in it. Players move alternatively in the order from $1$ to $N$ …
- 2,591
20
votes
3
answers
640
views
Escaping from infinitely many pursuers
The fugitive is at the origin. They move at a speed of $1$. There's a guard at $(i,j)$ for all $i,j\in \mathbb{Z}$ except the origin. A guard's speed is $\frac{1}{100}$. The fugitive and the guards mo …
- 2,591
9
votes
The lion and the zebras
Zebras win for all $N$.
I didn't realize Lawrence's answer in the source is actually sound (or so I think, when I really took some time to read it through this morning). Below I basically adopt Lawre …
- 2,591
27
votes
1
answer
935
views
The lion and the zebras
The lion plays a deadly game against a group of $N$ zebras that takes place in the steppe (= an infinite plane). The lion starts in the origin with coordinates $(0,0)$, while the $N$ zebras may arbitr …
- 2,591