Three
distinct 3-digit positive decimal (base 10) integers
P,
Q and
R, having no leading zeroes and with
P >
Q >
R, are such that:
(i)
P,
Q and
R (in this order) are in geometric sequence, and:
(ii)
P,
Q and
R are obtained from one another by
cyclic permutation of digits.
Find all possible triplet(s)
(P, Q, R) that satisfy the given conditions.
Note: While the solution may be trivial with the aid of a computer program, show how to derive it without one.
Suppose you had five sticks of length 1, 2, 3, 4, and 5 inches. If you chose three at random, what is the likelihood tht the three sticks could be put together, tip to tip, so as to form a triangle?
Now suppose you had twenty sticks, of lengths 1 through 20 inches. If you picked three at random, what is the likelihood that the three could be put together, tip to tip, to form a right triangle?
(Assume that a triangle has to have some area)
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