2 players play a game where an infinity 1-dimentional board is divided into cells numbered 0 1 2...

4 coins are placed on some cells in this board, the second coin from the left is gold:

(the position of the coins in this picture is just for show)

The players take turns, each player chooses one of the four coins and moves it 1 or more cells to the LEFT, you cannot surpass a coin or land on the same cell.

If you move a coin beyond the leftmost cell it is taken out of the game, whichever played takes out the gold coin wins...

So in the above example the player who's turn it is could either move the leftmost coin 1 cell or take it out by moving it 2 cells, or move the gold coin 1 or 2 cells, or move the third coin 1 cell, or move the fourth coin 1 2 or 3 cells...

Develop a strategy for winning the game given the initial positions of the coins...

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2 players play a game where an infinity 1-dimentional board is divided into cells numbered 0 1 2...

4 coins are placed on some cells in this board, the second coin from the left is gold:

(the position of the coins in this picture is just for show)

The players take turns, each player chooses one of the four coins and moves it 1 or more cells to the LEFT, you cannot surpass a coin or land on the same cell.

If you move a coin beyond the leftmost cell it is taken out of the game, whichever played takes out the gold coin wins...

So in the above example the player who's turn it is could either move the leftmost coin 1 cell or take it out by moving it 2 cells, or move the gold coin 1 or 2 cells, or move the third coin 1 cell, or move the fourth coin 1 2 or 3 cells...

Develop a strategy for winning the game given the initial positions of the coins...

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