All Questions
15
questions
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
2answers
654 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 ...
11
votes
1answer
418 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 ...
8
votes
3answers
647 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 ...
7
votes
6answers
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:
...
7
votes
2answers
273 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 ...
7
votes
1answer
251 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....
6
votes
1answer
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 ...
6
votes
2answers
532 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 ...
5
votes
3answers
410 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 ...
5
votes
2answers
123 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 ...
4
votes
1answer
529 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[...
3
votes
1answer
272 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 (...
1
vote
1answer
666 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,\...
0
votes
1answer
92 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.
-...
