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299 views

### Marbles on a Mancala Board

I would like to introduce an ancient African board game I've just invented. Until someone comes up with a better name, it's called Marble Mancala. The rules are pretty simple: There are two ...
126 views

### A pile of chips involving powers of 2

Ann and Bob play alternately on a pile of chips. On each play, any number of chips, which is a power of 2 (including 1=$2^0$), can be removed from the pile. Obviously the number of chips to be removed ...
175 views

### A pile of chips involving primes

Ann and Bob play alternately on a pile of chips. On each play, either 1, 2 or 3 chips can be removed except if the number of chips is a prime number. In that case either 1, 2, 3, 4 or 5 chips can be ...
254 views

### Game Night at the Binomial Elks Club

The Binomial Elks Club, being predominantly composed of ambitious and competitive personalities, often held game nights in which members enjoyed battling each other for high stakes and bragging rights....
652 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 ...
93 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. -...
287 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 (...
1k 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: ...
539 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 ...
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 ...