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all the ladies immodestly kissed the curate, although they were not
(except the sisters) kissed by him in return ? No ; because, in that
case, it would be found that there must have been twelve girls, not
one of whom was a sister, which is contrary to the conditions. If,
again, it should be held that the sisters might not, according to the
wording, have kissed their brother, although he kissed them, I reply
that in that case there must have been twelve girls, all of whom
must have been his sisters. And the reference to the ladies who
might have worked exclusively of the sisters shuts out the possibility
of this.
106.—The Adventurous Snail.
At the end of seventeen days the snail will have climbed 17 ft.,
and at the end of its eighteenth day-time task it will be at the top.
It instantly begins slipping while sleeping, and will be 2 ft. down the
other side at the end of the eighteenth day of twenty-four hours. How
long will it take over the remaining 18 ft. ? If it slips 2 ft. at night
it clearly overcomes the tendency to slip 2 ft. during the daytime, in
climbing up. In rowing up a river we have the stream against us, but
in coming down it is with us and helps us. If the snail can climb 3 ft.
and overcome the tendency to slip 2 ft. in twelve hours' ascent, it could
with the same exertion crawl 5 ft. a day on the level. Therefore,
in going down, the same exertion carries it 7 ft. in twelve hours ;
that is, 5 ft. by personal exertion and 2 ft. by slip. This, with the
night slip, gives it a descending progress of 9 ft. in the twenty-four
hours. It can, therefore, do the remaining 18 ft. in exactly two
days, and the whole journey, up and down, will take it exactly
twenty days.
107.—The Four Princes.
When Montucla, in his edition of Ozanam's " Recreations in
Mathematics," declared that " No more than three right-angled
triangles, equal to each other, can be found in whole numbers, but
we may find as many as we choose in fractions," he curiously over-
looked the obvious fact that if you give all your sides a common

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