Volume 48
, Issue 2

2012

Welcome to this issue of Parabola incorporating Function. The issue starts with David Angell's article on solving a class of second order recurrences.
First consider a sequence, by which we mean a list of numbers which goes on forever.  An example is the well-known Fibonacci sequence
$$0, 1, 1, 2, 3, 5, 8, 13, 21, 34,...$$
in which every number (except for the first two) is the sum of the previous two.
A popular classical problem can be stated as follows:

There are five monks, one monkey and pile of coconuts on a desert island.

My title for this column is that of an influential book, first published in 1935 by the American psychologist L. L. Thurstone.

Q1391 Jack looked at the clock next to his front door as he left home one afternoon to visit Jill and watch a TV programme.  Arriving exactly as the programme started, he set out for home again when it finished one hour later.
Q1381 It is commonly believed that the minute hand and the hour hand on a clock are in exactly symmetrical positions when the time is 10:08 and 42 seconds.

(a) Without detailed calculations, prove that this is wrong.