Amazons is a two-player partisan game in which each turn moves a piece and then permanently blocks a cell by shooting an arrow. The usual
board has 
square cells and four
pieces, called amazons, for each player (Müller and Tegos 2002, pp. 243-244;
Numberphile 2019).
Number columns from left to right and rows from bottom to top, using 1 through 10, and view the first player's side as the bottom. Its initial cells are 
, 
,
, and 
. The other player's initial cells are 
, 
,
, and 
.
Players alternate turns and move only their own amazons. An amazon moves a positive number of cells along a row, column, or diagonal, through empty cells to an empty destination. From its new cell, that same amazon shoots an arrow along a row, column, or diagonal, again through one or more empty cells. Only the arrow's landing cell becomes permanently blocked. Neither amazons nor arrows may cross or land on blocked cells or cells occupied by another amazon. There are no captures. The first player with no legal move loses.
Relocating an amazon vacates one cell and occupies another, so it does not change the number of empty cells. The arrow then blocks exactly one empty cell. Every completed
turn therefore reduces the number of empty cells by one. On an 
board with 
amazons and 
blocked cells, at most 
further turns are possible. Thus play is finite. All
pieces and blocked cells are public, and the rules contain no chance moves, making
Amazons a combinatorial game.
