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Amusements in Mathematics

the ten miles have taken him if there had been a perfect calm? Of course, the hydroplane's
engine worked uniformly throughout.
During a visit to the seaside Tommy and Evangeline insisted on having a donkey race
over the mile course on the sands. Mr. Dobson and some of his friends whom he had met
on the beach acted as judges, but, as the donkeys were familiar acquaintances and
declined to part company the whole way, a dead heat was unavoidable. However, the
judges, being stationed at different points on the course, which was marked off in quarter-
miles, noted the following results:—The first three-quarters were run in six and three-
quarter minutes, the first half-mile took the same time as the second half, and the third
quarter was run in exactly the same time as the last quarter. From these results Mr.
Dobson amused himself in discovering just how long it took those two donkeys to run the
whole mile. Can you give the answer?
A man had a basket containing fifty potatoes. He proposed to his son, as a little
recreation, that he should place these potatoes on the ground in a straight line. The
distance between the first and second potatoes was to be one yard, between the second
and third three yards, between the third and fourth five yards, between the fourth and fifth
seven yards, and so on—an increase of two yards for every successive potato laid down.
Then the boy was to pick them up and put them in the basket one at a time, the basket
being placed beside the first potato. How far would the boy have to travel to accomplish
the feat of picking them all up? We will not consider the journey involved in placing the
potatoes, so that he starts from the basket with them all laid out.
At first sight you would hardly think there was matter for dispute in the question involved
in the following little incident, yet it took the two persons concerned some little time to
come to an agreement. Mr. Smithers hired a motor-car to take him from Addleford to
Clinkerville and back again for £3. At Bakenham, just midway, he picked up an
acquaintance, Mr. Tompkins, and agreed to take him on to Clinkerville and bring him
back to Bakenham on the return journey. How much should he have charged the
passenger? That is the question. What was a reasonable fare for Mr. Tompkins?