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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.
However, all four of the land masses in the original problem are touched by an odd number of bridges (one is touched by 5 bridges, and each of the other three is touched by 3). Since, at most, two land masses can serve as the endpoints of a walk, the proposition of a walk traversing each bridge once leads to a contradiction.
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.
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However, Dudeney states that the problem is "as old as the hills...much older than electric lighting, or even gas". [3] Dudeney also published the same puzzle previously, in The Strand Magazine in 1913. [4] A competing claim of priority goes to Sam Loyd, who was quoted by his son in a posthumous biography as having published the problem in 1900 ...
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.
Crossing Coordinates Built Heritage status Locality Notes Refs Image Source of the River Wye - Plynlimon: Included for completeness Y Drum Bridge grid reference: 1965 Pont Rhydgaled The first bridge over the Wye, 3.2 kilometres (2.0 mi) below its source.
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