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Questions tagged [nim]

A strategy game in which players take turns to reduce the number of objects in some sets, the aim being either to remove the last object or _not_ to do so.

8
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3answers
608 views

Double or Take game

Double or Take is a two-player number game. Alice starts by selecting any positive integer. Bob's options are to: subtract a positive perfect square subtract a positive perfect cube, or double the ...
0
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1answer
86 views

A short nim game [duplicate]

There are 50 lucifers on the table. The rules are: -You must take 1, 2, 3, 4, or 5 lucifers each turn. -After player 1 has taken some amount of lucifers, it is player 2's turn, and vice versa. -...
3
votes
1answer
160 views

Another variation of the game of Nim

Two players set several piles of chips. The piles are arranged in a row from left to right. By turns each player takes one chip from one of the piles and adds at will as many chips as he/she wishes (...
0
votes
1answer
137 views

Who wins the game?

Two people play a game. The first one (A) picks one number from 1 to 10 and then the second one (B) also picks a number from 1 to 10 and adds it to the first number; the next round continues in the ...
7
votes
1answer
237 views

Paper, pencil and a bunch of bars

An entry for the Fortnightly Topic Challenge #40. Alice and Bob are two rational players who are playing a simple pencil-and-paper game. In the beginning, there are fifteen small vertical bars on ...
7
votes
6answers
862 views

Single-pile Nim with Three Players

Three perfectly rational logicians (Alice, Bob and a Quetzalcoatlus) are playing a game. (Charlie couldn't make it, so he asked the Quetzalcoatlus to fill in for him.) The rules are very simple: ...
2
votes
2answers
572 views

Can you help me understanding the Stones game?

I am trying to understand the Stones game stated here. The stones game is a simple game, it is also a very old game which is unknown to almost everyone. The game starts with N stones and M ...
5
votes
3answers
382 views

Removing green marbles from the table

Alice and Bob play the following game that starts with $N\ge3$ green marbles on the table. Alice and Bob move alternatingly. Alice makes the first move. In this first move, Alice removes $x$ green ...
10
votes
2answers
606 views

Ninety-nine non-negative numbers

Alice and Bob play the following game with $99$ numbers $M_1,\ldots,M_{99}$. In the beginning, the $99$ numbers take the values $1,2,4,8,16,\ldots,2^{97},2^{98}$. Then Alice and Bob alternatingly ...
4
votes
1answer
491 views

Generalisation of Nim

I'm asking for a general formula/algorithm that can be used in such a game. There are $n$ piles, with varying number of pebbles. The number of pebbles in each pile is given by an array from $pile[...
13
votes
3answers
1k views

eXtreme Nim: A Game With *Lots* of Pebbles

Two children are playing a game with several piles of rocks. Each turn they do the following: They choose some pile of rocks. They count how many rocks are in this - let this be $n$. We remove this ...
11
votes
1answer
392 views

Dim - A Game with Pebbles

Alice and Bob play a game with a pile of $n$ pebbles. They take turns, with Alice going first. On their turn, a player can remove any number of stones from the pile which is a proper divisor of the ...
6
votes
2answers
521 views

Unsportsmanlike Aliens

It was the first meeting of the humans and the aliens, and things were going well: The humans and aliens had learned to understand each other's language and found that both were hoping for a peaceful ...
1
vote
1answer
658 views

Eat sweets and start your own business!

The manager of the local sweetshop, one Minty Ball, has announced a grand closing down sale. They sell $n$ varieties of sweets: toffees, sherbets, fudge, and so on. Let's just call the varieties $V_1,\...