2
votes
2answers
83 views

Winning a restricted game of Nim?

Given the following piles, find the Grundy number of the initial position and make the first move in a winning strategy given that no more than two sticks may be removed from a pile at any time. Pile ...
2
votes
1answer
64 views

Maximal number of kings on a chessboard, but this time two can be adjacent.

How many kings can be placed on an $8 \times 8$ chessboard such that every king can capture (is adjacent to) at most one other king? I can do 26, but can not prove that this is optimal.
1
vote
1answer
135 views

How many unique patterns exist for a 5x5 grid with paths of spaces intersecting at 1 space and leading to each edge of the grid?

I'm try to design a game in which the board is made up of a 3x3 grid of square tiles. Each tile is a 5x5 grid of spaces. Each tile has 4 exit spaces each located on 1 of the middle 3 spaces along ...
5
votes
2answers
177 views

A puzzle on game theory

Bob and Alice are playing a game. They will start with an integer $n$. Alice goes first, in each turn, a player can choose an integer between 1 and 13 and that number is to be subtracted from $n$. ...
2
votes
3answers
116 views

Multilingual hedge fund - Puzzle

I'm having difficulty finding the solution for the following problem: A hedge fund has 70 employees. For any two employees $X$ and $Y$ there is a language that $X$ speaks but $Y$ does not, and there ...
0
votes
2answers
90 views

A Nim variant: Number of stones

Alice and Bob play the following game. There is one pile of $N$ stones. They take turns to pick stones from the pile, Alice will play first. In each turn, a player can only pick $k$ $(a \le k \le b)$ ...
3
votes
3answers
246 views

A puzzle about graph coloring.

Let $G$ be a graph with three disjoint triangles(i.e. the graph is not connectd and has three connected components each of which is a triangle). If each vertex of G is assigned a red or a green color, ...
1
vote
1answer
137 views

Winning single-pile, variable limits Nim [duplicate]

Possible Duplicate: Winning strategy for a matchstick game The rules of this variant of Nim are as follows: Starting at zero, each player counts up between 1-N numbers. The person that ...
0
votes
1answer
327 views

Nim Variant (Restricted removal)

Alice and Bob play the following game : There are $N$ piles of stones with $S_i$ stones in the $i$th pile. Piles are numbered from 1 to $N$. Alice and Bob play alternately, with Alice starting. In a ...
2
votes
1answer
299 views

Nim Variant (reducing by divisors)

Alice and Bob play the following game. They choose a number $N$ to play with. The rules are as follows: Alice plays first, and the two players alternate. In his/her turn, a player can subtract from ...
23
votes
3answers
1k views

Guaranteed Checkmate with Rooks in High-Dimensional Chess

Given an infinite (in all directions), $n$-dimensional chess board $\mathbb{Z^n}$, and a black king. What is the minimum number of white rooks necessary that can guarantee a checkmate in a finite ...
3
votes
1answer
215 views

Divisor/multiple game

Two players $A$ and $B$ play the following game: Start with the set $S$ of the first 25 natural numbers: $S=\{1,2,\ldots,25\}$. Player $A$ first picks an even number $x_0$ and removes it from $S$: ...
8
votes
0answers
369 views

Irreversible chess [closed]

Suppose we play a chess-variant, where any finite number of pieces are allowed, and the board is as large as we wish, but only two kings in total. And there is no 50 move-rule, no castling and no ...
6
votes
1answer
551 views

Stone picking puzzle

Two players are playing a stone picking game. The players pick a stone from two pile of stone in turn. One can choose to pick any number of stones from either pile, or pick the same number of stone ...