Algebraic Thinking in Traditional Māori Games

Challenge 1 · Mu Tōrere Strategy

Mu tōrere is a 2-player board game played on an 8-pointed star (pūtahi/centre and kāwai/points) with 4 pieces per player. The goal is to block the opponent.

1. When the board is set up, how many legal opening moves exist for the first player? Explain your count:

2. If each player had $n$ pieces (instead of 4), what would be the total number of playing pieces on the board? Express this algebraically:

Total pieces $P=$

3. Predict the minimum number of total moves required to block an opponent from the opening position (assuming perfect play):

Minimum moves $=$

Challenge 2 · Poi Rākau Rhythm Sequences

Poi rākau involves passing wooden sticks rhythmically in a circle. Each sequence follows a predictable algebraic pattern ($t$ represents the beat number, $n$ represents the step in the sequence: $n=1,2,3...$).

1. Fill in the missing algebraic rules and values in the sequence table below:

2. Create your own rhythmic passing sequence (describe it):

3. Represent your created sequence algebraically as a rule for beat $t$ in terms of step $n$:

$t=$

Challenge 3 · Whai (String Patterns)

Whai involves creating complex geometric patterns using a loop of string. Each step of looping increases the number of loops or crossings on your fingers.

Suppose an opening figure has 2 crossings, and every subsequent loop step adds 2 more crossings. Express the total number of crossings ($C$) after $s$ steps:

$C=$