1
vote
1answer
48 views

Subtraction Game

I recently read about the Nim Subtraction Game. I have a variant, Suppose you have N stones and two players Alice and Bob, who can choose to pick either 1 stones or K stones. If Alice plays first when ...
2
votes
0answers
271 views

What is the highest possible score in 2048 hard?

There is a variant of the popular game 2048, called 2048 hard or 2048 impossible, which automatically places each new tile in the hardest possible location. Is this variation possible to solve, and if ...
2
votes
2answers
125 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
72 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
198 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
198 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
131 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
103 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
260 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
145 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
350 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
324 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 ...
24
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
224 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
470 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
656 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 ...