Dear colleagues,
"It's a kind of magic" is the title of an article by Ian Stewart (Prof at
Warwick Univ, and well known author of popular articles on mathematical
topics) in the 4th January 2003 issue of the New Scientist. I have just
placed a colour photocopy of it (two pages only) on the unofficial (open)
mathematics board opposite my office in E block. I hope you will make time
to glance at it.
For me the timing of Stewart's article is perfect, since the topic of his
article (an extraordinary card trick, devised by William Finch Cheney, Jr,
(Cheney was awarded the first Mathematics PhD at the renowned MIT)) forms a
(small) part of my new 3rd year BA course - Challenging Mathematical Puzzles
and Problems - that I have just begun.
The trick is this: choose any 5 cards from a 52 pack of cards, and pass them
to my assistant, who - having looked at them - passes a certain 4 of them to
me. I can then tell you the card that my assistant still holds. There are no
mirrors, touching ears, etc. The problem-to-be-solved is of course: how is
it done?
Incidentally the mathematics of it ensures that the same trick may be done
with any pack of cards (still choosing 5) up to a maximum of 124 cards. If
one were to allow a choice of 6 cards, then the maximum may be increased to
725, ... , and if one were to drop back - as it were - then a choice of 3
allows for a maximum of 8, and at the absolute lowest a choice of 2 allows
for a maximum of 3 (so let the 'cards' be '1', '2', and '3'; choose any 2 of
those, pass them to my assistant, who then passes just 1 of those to me. I
may then 'reveal' the 'other' card. HOW? Yes, yes, of course that's simple,
but how about the 52 cards pack...).
Pleasant thoughts (nay dreams),
John