A page of trivia
- The game of Moo (pdf), otherwise known as
Mastermind, is a simple game that could be used as an example for a
computer course. It is sufficiently complex that a complete analysis
can take many hours of cpu time to evaluate, even today,
but small enough to be easily programmed when suitable value functions
are thought up. This paper examines a few value functions. An odt version is also available.
- The disjoint interval problem (pdf).
Consider a sequence of points all in a given interval, such that the
first two are in different halves of the interval; the first three are
in different thirds, the first four in different quarters, etc. How
long can the sequence be? There is an odt format document, too.
- The Unique Pairs problem (pdf). Define a set, S, of n
non-negative integers such that all possible pairwise sums, i+j: (i,j)
in S, i ≠ j, are distinct. What is the smallest possible largest
element of S? What is the smallest possible sum of all elements in S?
These were found for small values of n by an exhaustive
computer-aided search. There is also an odt format document.
- Giving change (pdf) is
further work done on the question of whether the average number of
coins needed to make monetary values up to one GB pound can be reduced
by changing the denominations of coins used. There is an odt format version, too.
- The Reve's Problem (pdf). In the
traditional Towers of Hanoi, there are three pegs on one of which are
heaped a number of discs of different diameters with no disc resting on
a smaller one. These are to be transferred to another one moving only
one disc at a time from one peg to another, and such that at no time
during the moving process does a disc rest on a smaller one. H. E
Dudeney, a well-known early 20th century English puzzlist, suggested
the generalisation to any number of discs. There is an odt format document, too.
- Pythagorean quadrilaterals (pdf)
are convex quadrilaterals whose diagonals intersect at right angles and
whose sides and diagonals all have integral lengths. This paper is an
edited copy of a paper first published in the Journal of Recreational
Mathematics, and describes a search for small such quadrilaterals (also
known as kites) especially where all the four right triangles are
primitive Pythagorean ones. There is an odt format document, too.
- Notes on the “four digits problem” (pdf)
in W.W. Rouse Ball's Mathematical Recreations and Essays. This is a
note confirming the limits that he found and a table of the methods up
to 312. There is also an odt format document. These results are based on my notes of 50 years ago.
© Copyright Andy Pepperdine, 2009, 2010
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