self Maths Puzzle

Many years ago, when Barnum's Circus was of a truth "the greatest show on earth" the famous showman got me [Sam Loyd] to prepare for him a series of prize puzzles ... Barnum was particularly pleased with the problem of the cat and dog race ...

"A trained cat and dog run a race, 100 feet straightaway and return. The dog leaps three feet at each bound and the cat but two, but then she makes three leaps to his two. Now, under those circumstances, what are the probabilities or possibilities in favor of the one that gets back first?"

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self Other Question

An old man goes to a bank with a check of $200 and asks the cahier "Give me some one-dollar bills, ten times as many twos and the balance in fives!".

What will the cashier do? 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?