The chess problem was a type of command authorization code using moves of chess pieces on a chessboard (be it 2- or 3-dimensional) as signs and countersigns in covert or insecure communications.

Captain Kirk and his senior officers used a chess-based code as transporter clearance in 2268, during their visit to the Elba II asylum. Chief Engineer Scott declined to beam Garth, disguised as Kirk, to the Enterprise, because Garth did not know the code response "queen to king's level 1" when Scott queried with the code phrase "queen to queen's level 3." (TOS: "Whom Gods Destroy")

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