THE OWARI SERIES: AN ILLUSTRATIVE EXPLORATION OF SUMMATION AND PARTIAL FRACTIONS IN A 2-OR-3 SCORING VARIANT.

This paper presents a recreational mathematical exploration derived from the traditional African board game Owari (Mancala). The study examines a specific variant where a score is achieved only if a player casts marbles totaling exactly two or three into the opponent’s home, with no scoring occurring in one’s own home. Both players sow anticlockwise relative to their own perspective; because they sit opposite one another, their physical trajectories on the board are opposite. It is conjectured that this opposing dynamic may produce alternating signs in a telescoping series, though this remains an open question (see Section 5.6). The game’s scoring sequence is illustrated using arithmetic progressions (AP), geometric progressions (GP), and telescoping series as analogies. The paper analyzes two distinct illustrative games: the first is a concrete 10-round example whose residual happens to be 1/12; the second is an illustrative game with final scores of 23 and 25, where the cumulative scores sum to 48. By representing score distributions through partial fractions, thestudy illustrates possible analogies with telescoping series. Additional variants including 1-or-4 scoring and symmetric sowing are introduced as worked examples. The paper does not claim to derive the sequences from the rules; rather, it illustrates possible mathematicalanalogies.