# Solution

(related to Problem: Five Jealous Husbands)

It is obvious that there must be an odd number of crossings, and that if the five husbands had not been jealous of one another the party might have all got over in nine crossings. But no wife was to be in the company of a man or men unless her husband was present. This entails two more crossings, eleven in all.

The following shows how it might have been done. The capital letters stand for the husbands and the small letters for their respective wives. The position of affairs is shown at the start, and after each crossing between the left bank and the right, and the boat is represented by the asterisk. So you can see at a glance that $a, b,$ and $c$ went over at the first crossing, that $b$ and $c$ returned at the second crossing, and so on.

| ABCDE abcde * | .. | :------------- |:------------- |:------------- |:------------- 1.| ABCDE de | ..| $\ast$ abc 2.| ABCDE bcde | ..| a 3.| ABCDE e | ..| $\ast$ abcd 4.| ABCDE de | ..| abc 5.| DE de | ..| $\ast$ ABC abc 6.| CDE cde | ..| AB ab 7.| cde | ..| $\ast$ ABCDE ab 8.| bcde | ..| ABCDE a 9.| e | ..| $\ast$ ABCDE abcd 10.| bc e *| ..| ABCDE a d 11.| | ..| $\ast$ ABCDE abcde

There is a little subtlety concealed in the words "show the quickest way."

Everybody correctly assumes that, as we are told nothing of the rowing capabilities of the party, we must take it that they all row equally well. But it is obvious that two such persons should row more quickly than one.

Therefore in the second and third crossings, two of the ladies should take back the boat to fetch d, not one of them only. This does not affect the number of landings, so no time is lost on that account. A similar opportunity occurs at crossings $10$ and $11,$ where the party again had the option of sending over two ladies or one only.

To those who think they have solved the puzzle in nine crossings I would say that in every case they will find that they are wrong. No such jealous husband would, in the circumstances, send his wife over to the other bank to a man or men, even if she assured him that she was coming back next time in the boat. If readers will have this fact in mind, they will at once discover their errors.

Thank you to the contributors under CC BY-SA 4.0!

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### References

#### Project Gutenberg

1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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