A table game management system according to the present invention includes a camera that images a game token placed on a game table, and a management control device that grasps a type of the game token placed on the game table based on a color of a side face of the game token imaged by the camera.

Systems and methods for solving and generating a mathematical puzzle are presented. A puzzle may comprise areas comprising mystery number regions, pair clue regions interposing pairs of mystery value numbers, and a central clue region located centrally to the mystery number region. Solving a puzzle may comprise deterministic search methods coupled with heuristic approaches. Puzzle generation may comprise adding conforming clues until a puzzle has only one possible solution, the clues chosen based on heuristics for adding clues while minimizing incremental change in puzzle difficulty; or reducing the number of solutions/partial solutions to the puzzle.

A detection system according to the present invention includes a control device that detects fraud conducted on a game table by using the image analysis result obtained by an image analysis device. In addition, each game token used in this detection system has a multilayer structure having plastic layers with a plurality of different colors stacked on each other, with a colored layer being provided at least intermediately, and white layers or light-colored layers (not illustrated, but may be any layers lighter in color than the colored layer) being stacked on two sides of the intermediate colored layer. As described above, this game token has a multi-layer structure including the colored layer, with the white layers or light-colored layers (not illustrated, but may be any layers lighter in color than the colored layer) being stacked on the two sides of the intermediate colored layer.