Gomoku is sometimes (correctly) known as Go-Moku.  I've also seen it played on a 13x13 board (as opposed to a 15x15 as sensei states).

It's also worth noting that six stones in a row does NOT count as a win!  It must be exactly five.  I don't know whether this was an omission on sensei's part or just a variation of the game.

Also, in the variation I've played, if the board is filled up with stones, the game is NOT a draw!  White wins.  This is a compensation for the advantage Black has by going first--it is thought that if Black is unable to procure a win, he deserves to lose.
 

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