River crossing (1)

There are many river crossing problems, and in this post I’d like to take a look at one of them. The basic of river crossing puzzles go back to the book Propositiones ad Acuendos Juvenes, probably published around 900AD.

In this first post on river crossing problems I’d like to take a look at a simple river crossing problem:
1) Man, wife and 2 kids*
A man and a woman of equal weight, together with their two children, each of half their weight, wish to cross a river using a boat which can only carry the weight of one adult.
How many trips do they need?

For the solution see Solution 4

Because this type of puzzle is so old, it has spread wide. Here is a Russian variant:
2) Three soldiers*
Three soldiers must cross a river. Two boys have a boat and are willing to help. Their small ferry can hold either the two boys or one soldier. How many moves are necessary to get all across?

For the solution see Solution 43

It is easy to see that the two boys can ferry an arbitrary number of soldiers across, the puzzle becomes in a way easier when the boys have to ferry 10 or 15 soldiers across, as the reader is forced to design a scheme to do it.
In fact, that is exactly what the famous British puzzle author Henry Dudeney (10 April 1857–23 April 1930) did when he formulated the puzzle as:
3) The British batallion*
During the Turkish stampede in Thrace, a small detachment found itself confronted by a wide and deep river. They discovered a boat with two rowing children. It was so small that it could hold only the two children, or one grown up person.
How did the officer get himself + his 537 soldiers across the river and leave the two children in possession of their boat? And how many times need the boat to pass from shore to shore?
Henry Dudeney published this puzzle ands Martin Gardner republished it in “536 puzzles & Curious problems”. I still wonder if there is any relation between the 536 and the 537.

For the solution see Solution 53

Dudeney also published this small variation:
4) The Softleigh family*
During a country ramble Mr. and Mrs. Softleigh found themselves in a pretty little dilemma. They had to cross a stream in a small boat which was capable of carrying only 150 lbs. weight. But Mr. Softleigh and his wife each weighed exactly 150 lbs., and each of their sons weighed 75 lbs. And then there was the dog, who could not be induced on any terms to swim. On the principle of “ladies first,” they at once sent Mrs. Softleigh over; but this was a stupid oversight, because she had to come back again with the boat, so nothing was gained by that operation. How did they all succeed in getting across? The reader will find it much easier than the Softleigh family did, for their greatest enemy could not have truthfully called them a brilliant quartette—while the dog was a perfect fool.

For the solution see Solution 63

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