23
23 Coins start in a pile. Players take turns removing 1,2, or 3 coins from the pile. The player to pick up the last coin wins. The game could be modified to start with different number of coins in pile or you pick up a different number of coins on your turn. Does it matter who goes first? Does it matter how many coins we start with in the pile? When did you realize that you won the game?
3 Piles
3 piles with any number (>1) in each pile, with a total of 24 coins. Players take turns removing 1 or more coins from a single pile. The player who removes the last coins wins. The game could be modified to start with different number of coins in pile.
Cut the Cake
Set up the game with coins arranged with an equal amount in rows (Ex. 5x6 grid). Grid size could be varied. Players take turns removing either a single row or column. This move make split the cake in multiple pieces. The next player may only remove a row or column from one piece. The player that picks up the last coin wins.
Coins in a Circle
12 coins arranged in a circle. Players take turns removing 1 or 2 coins next to each other. from any point in the circle. They cannot remove coins on either side of a gap. The player that picks up the last coin wins.
2 Piles
2 piles of 10 coins, take 1 or more coin from one pile or exactly 1 coin from both piles. The player that picks up the last coin wins. Modify game by changing the number of coins in each pile. Does it matter who goes first? Does it matter how many you start with in each pile?
Turning Turtles
13 coins laid randomly H vs. T. A player can turn over a single coin and if desired, one coin to the left of it. The player that turns the last coin tails, wins.
Nimble
10 square aligned in a row with a coin in each box. The first box is labelled finish. You can move a coin any number of moves to the left and multiple coins can occupy any box. The player that moves the last coin to the finish wins.
2D Nim
Lay out a 3x3 grid. Place 4 coins randomly in the squares. Players take turns moving a coin any number of moves down or to the left. The player to move the last coin to the finish wins.
Picking from a Tree
Coins are set up with 1 in the first row, 3 in the second, then 5, then 7. Players take turns pick any number or coins from one of the rows. The player who picks up the last coin wins.
The 100 Game
A similar version is the "100 game": Two players start from 0 and alternately add a number from 1 to 10 to the sum. The player who reaches 100 wins.
Grundy's Game
In Grundy's game, another variation of Nim, a number of objects are placed in an initial heap and two players alternately divide a heap into two nonempty heaps of different sizes. Thus, six objects may be divided into piles of 5+1 or 4+2, but not 3+3. Grundy's game can be played as either misère or normal play.