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# The Four Elopements - Solution

Puzzles -> Sam Loyd Puzzles

 The Puzzle: The story of four elopements says that four men eloped with their sweethearts, but in carrying out their plan were compelled to cross a stream in a boat which would hold but two persons at a time. It appears that the young men were so extremely jealous that not one of them would permit his prospective bride to remain at any time in the company of any other man or men unless he was also present.Nor was any man to get into a boat alone, when there happened to be a girl alone on the island or shore, other than the one to whom he was engaged. This feature of the condition looks as if the girls were also jealous and feared that their fellows would run off with the wrong girl if they got a chance. Well, be that as it may, the problem is to guess the quickest way to get the whole party across the river according to the conditions imposed. Let us suppose the island to be in the middle of the stream. Now, tell how many minimum number of trips would the boat make to get the four couples safely across in accordance with the stipulations?

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## The Solution . . .

Answer: 17 trips - complying with the conditions that no young lady was to be in the company of any gentleman unless her fiance was present, and no man was to be alone in a boat, if any young lady was left alone, except the one to whom he was engaged.

Describing the young men as A, B, C, D, and their respective brides by a, b, c, d; the 17 trips of the boat can completed as follows . . .

 1 2 Shore Island Over ABCDabcd -- -- ABCDcd -- ab ABCDd -- a ABCDcd b a CDcd b ABa BCDcd b Aa BCD bcd Aa BCDd bc Aa Dd bc ABCa Dd abc ABC Dd b ABCac BDd b ACac d b ABCDac d bc ABCDa d -- ABCDabc cd -- ABCDab -- -- ABCDabcd

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