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The bridge and torch problem (also known as The Midnight Train [1] and Dangerous crossing [2]) is a logic puzzle that deals with four people, a bridge and a torch. It is in the category of river crossing puzzles , where a number of objects must move across a river, with some constraints.
restarea: (interchangeable with bridge=) the name of the rest area, with full wiki markup if needed. tunnel: (interchangeable with bridge=) the name of the tunnel crossing, with full wiki markup if needed. bspan: spans the bridge, place, restarea or tunnel by the number of rows entered. Any parameter which is empty can be omitted.
Well-known river-crossing puzzles include: The fox, goose, and bag of beans puzzle, in which a farmer must transport a fox, goose and bag of beans from one side of a river to another using a boat which can only hold one item in addition to the farmer, subject to the constraints that the fox cannot be left alone with the goose, and the goose cannot be left alone with the beans.
The two solutions with the vertical axis denoting time, and brown, grey, green and beige paths denoting the wolf, goat, cabbage and boat, respectively The first step that must be taken is to let the goat go across the river, as any other actions will result in the goat or the cabbage being eaten.
By way of specifying the logical task unambiguously, solutions involving either reaching an island or mainland bank other than via one of the bridges, or; accessing any bridge without crossing to its other end; are explicitly unacceptable. Euler proved that the problem has no solution.
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As it is usually presented (on a flat two-dimensional plane), the solution to the utility puzzle is "no": there is no way to make all nine connections without any of the lines crossing each other. In other words, the graph K 3 , 3 {\displaystyle K_{3,3}} is not planar.
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