# Tagged Questions

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 ...
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 ...
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 ...
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.
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 ...
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 $n$. ...
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 ...
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 $k$ $(a \le k \le b)$ ...
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, ...
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 ...
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 ...
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 ...
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 ...
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 $S$: ...