DAMA + MATH = DAMATH
DaMath is a math board game coined from the word dama, a Filipino
checker game, and mathematics. It was invented by Jesus Huenda, a high school
teacher from Sorsogon, Philippines. It became very popular in the 1980s and
until now played in many schools in the Philippines.
DaMath can be used to practice
the four fundamental operations and also the order of operations. It has
numerous variations, but in the tutorial below, we will
discuss the Integers DaMath. Note that explaining this game is quite
complicated, so I have divided the tutorial into three posts
The
DaMath Board
The
board is composed of 64 squares in alternating black and white
just like the chessboard. The four basic mathematical operations are written on
white squares as shown in Figure 1 and 2. Each square
is identified by a (column, row) notation. The top-left square, for example, is
in column 0 and row 7, so it is denoted by (0,7).
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| Figure 1. DaMath board used in playing Integer, Rational and Radical DaMath. |
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| Figure 2. DaMath board used in playing Polynomial DaMath. |
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DaMath
is played by two opposing players. In this article, we will refer to them as
the Blue Player and Red Player. The players take turns in moving the pieces
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| Figure 3. The initial position of the pieces |
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The pieces are moved by sliding
forward diagonally to a vacant adjoining square. This means that you can only
move the pieces to white squares. All movements have to be diagonally forward;
backward movements can only be made when capturing pieces or can be made by
using a dama. A dama (like a Queen in chess) can also move backward
and capture pieces backward. We will discuss the movements of damas
in another post.
Suppose the Red Player moves
first, he can move any of the four pieces in the front row one square forward
diagonally. For instance, in Figure 3, the Red Player moved 6 to (2, 3) and then, the Blue Player moved -9 to (7,4).
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| Figure 4 – Position of the board after two moves |
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We summarize the movements of the two players. Take
note that the notation below is written on the scorecard during tournaments and
school competitions.
First Move: Red 6 → (2,3); Blue -6 → (7,4).
Capturing
the Pieces and Scoring
A piece captures an opposing
piece by jumping over it diagonally and landing on the adjoining vacant square.
Capturing is mandatory. In Figure 4, the Red Player moved -1 to (5, 3). The
Blue Player is obliged to capture -1 using -9. He can do this by jumping -9
over -1 landing to (5,2) and removing -1 from the board. Here, -9 captured -1
and landed on a square with a + sign. Therefore, the score will
be (-9)
+ (-1)
= -10.
Blue Player’s Score: (-9) + (-1) = -10
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Figure
5 shows the position of the pieces after the Blue Player captured -1. It is now the Red Player’s turn to
capture -9. As we can see, he
can choose to use a 7 or a 10 to capture -9. However, using a 7
will yield a higher score. Using a 7 will result
to 7 –
(-9) = 16, while using a 10 will result to 10 + (-9)
= 1
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| Figure 6. Capturing a piece |
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Red Player’s Score: 7 – (-9) = 16
We can see that the Red Player
is ahead of points. The players can continue playing and add the obtained
scores each time a piece is captured. The player with the higher points at the
end of the game wins the game.
A piece can also capture
backward. In the board position below, if it is the Blue Player’s turn to move,
he can oblige the Red Player to capture 2 by moving 2 to the square on (4,5).
The Red Player will have to capture 2 and -11 x 2 = -22 will be added to
his score (i.e. Blue Player’s advantage).
A piece can also capture
backward. In the board position below, if it is the Blue Player’s turn to move,
he can oblige the Red Player to capture 2 by moving 2 to (4,5). The Red Player
will have to capture 2 and -11 x 2 = -22 will be added to his score (i.e.
Blue Player’s advantage)
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| Figure 6. Capturing backward. |
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For more information on how to play DAMATH, please feel freee to watch the videos below.
