Card Colms

Card Colm is a column on mathematical card principles and effects sponsored by the Mathematical Association of America which has appeared at MAA.org bimonthly since Oct 2004. It's very much inspired by the extensive writings of Martin Gardner (1914-2010) on the subject, going back to his seminal Mathematics, Magic and Mystery (1956).

There are more notes below related to card stuff, but first here's a guide to topics we've explored in Card Colms old and new at MAA.org over the past ten years. "Level U/P" refers to two things, firstly (U) how much mathematics is Used and secondly (P) how hard the tricks are to Perform. Sometimes the underlying mathematics can be at quite a different level from the chops needed to do the trick for an audience! Also, some of the ideas (e.g., the First Gilbreath Principle) have much simpler, less mathematically rococo, applications than those indulged in here.

Stop press: due to extensive reorganization of MAA.org in Jul 2013, some of the links below may need to be updated.

Title Date Contents Level U/P
Foregone OutsetApr 2014 The coin problem Some/Moderate
Postage Stamp IssueFeb 2014 The postage stamp problem Some/Moderate
X-Ray VisionDec 2013 Probability-defying cycle principle Some/Moderate
The Sequence I Desire. Magic: When Divided, No RemainderOct 2013 Polydivisible numbers Some/Easy
Rosette Shuffling Multiple PilesAug 2013 Riffle shuffling more than two piles Some/Moderate
Subtler Bracelets and
Dissociative Disorders
Jun 2013 Sum-rich bracelets and sets Some/Moderate
Never Forget a Face
(Double-Dealing with a Difference)
Apr 2013 Low-down double dealing Some/Easy
Flushed with EmbarrassmentFeb 2013 The Triskadequadra principle Some/Moderate
Predictability Outranks LuckDec 2012 Kruskal principle Some/Easy
All or Nothing Trickle TreatOct 2012A non-assosiative binary operation Some/Easy
Gilbreeath ShuufflingAug 2012 Gilbreath shuffling variation Some/Moderate
Something Old, Something True, Something Borrowed, Something NewJun 2012 Poker hand control via Bill Simom principle, position parity, and monge shuffles Some/Moderate
Splitting the Pot Apr 2012 Hall's marriage theorem Some/Moderate
Amazon Arrays (Large Action) Feb 2012 Graeco Latin squares Some/Easy
Magical Mathematics: Recurring Cycles of Ideas of Cycles Dec 2011 Universal cycles Some/Easy
A Third Selection of Mathemagical Amusements
with Cards in Martin Gardner's Own Words
Oct 2011 Various Some/Easy
A Call For A New Shuffle Principle (Need Rot Sextet?)Aug 2011 New Gilbreath principle? Some/Easy
Out Of This Whirled (Twisted Mess) Jun 2011 Parity principle Some/Easy
Twisting the Knight Way (No Big Deal) Apr 2011 Twisting principle Some/Easy
Low-Down Double Dealing With the Big BoysFeb 2011 Double deal palindrome principle Some/Easy
It's Red or Black and Blue All OverDec 2010 Small linear ternary code
(two person magic)
Some/Hard
The Three Piles (This Isn't That Trick)Nov 2010 Small linear binary codes
(two person magic)
Some/Hard
Celebration of MindOct 2010 Martin Gardner events) ---/---
Also In His Own Words: More Mathemagical Games (and Tricks) With Cards From Martin GardnerAug 2010 Highly varied Some/Moderate
In His Own Words: Mathemagical Card Tricks From Martin Gardner (1914-2010)Jun 2010 Highly varied Some/Moderate
Mathematical Idol 2010Apr 2010 2 items predict the 3rd
(two person magic)
Some/Hard
Tighter Ascertainments: Matching Interest RatesFeb 2010 Summand deduction using balanced ternary representations
Some/Moderate
The Boldgach ConjectureDec 2009 Matches from shuffled palindromic stacks
Little/Moderate
Poker-Faced Over the PhoneOct 2009 Small linear binary codes
(two person magic)
Some/Hard
The Bligreath PrincipleAug 2009 Gilbreath twistSome/Easy
Two Summer Difference CertaintiesJun 2009 Sum-rich (Sidon) sets Some/Moderate
The Yummie Deal and VariationsApr 2009 Special deals Some/Easy
Esteem SynergismFeb 2009 Spelling miracles Little/Easy
What's Black and Red and Red All Over?Dec 2008 Binary de Bruijn sequencesSome/Moderate
Monge Shuffle CliquesOct 2008 Monge shuffle invarianceSome/Moderate
(A) Pi Evolved Set--Harmonic Split DrillAug 2008 Palindromic stack invariance Some/Moderate
Sum-Rich CirculantsJun 2008 Summand deduction from cycling sums Some/Moderate
Projective GeometryApr 2008 The Fano planeSome/Easy
Additional CertaintiesFeb 2008 Summand deduction via Fibonacci Numbers and Zeckendorf representationsSome/Moderate
Plurality Events, Standard Deviations and Skewed PerspectivesDec 2007 Mean, Standard Deviation & Skewness Some/Moderate
A Magic Timepiece Influenced By Martin Gardner (Celebrating His 93rd BirthdayOct 2007 Cycling quadruple sum forces Some/Easy
Sixy Alpha OmegasAug 2007 Alternating triple sum forces Some/Easy
Gibonacci Bracelets Jun 2007 Fibonacci sequences mod m Little/Easy
Magic Circles of Eight
Apr 2007 Magic circlesLittle/Easy
Quasi-Masked Forcing
Kind of Magic Squares
Feb 2007 Magic squaresLittle/Easy
Quantitative Reasoning in
Small Groups
Dec 2006 Z2, Z3, Klein-4 groupSome/Easy
Martin Gardner's Magic SpellsOct 2006Interview & 10-card pyramid spellerNone/Easy
The Second Norman InvasionAug 2006The Second Gilbreath principleLittle/Moderate
Better Poker Hands GuaranteedJun 2006Birthday card matches applicationsLittle/Easy
Bill Simon's Sixty-Four PrincipleApr 2006Two ways to force 4 of 8 cardsSome/Moderate
Many Fold SynergiesFeb 2006Parity principlesLittle/Easy
Luckation Is EverythingDec 2005Completing to 13 and advantages of knowing the 26th cardLittle/Easy
Subtraction Is AddictiveOct 2005Subtraction principlesLittle/Moderate
The First Norman InvasionAug 2005The First Gilbreath principleSome/Easy
A Little Erdös/Szekeres MagicJun 2005Any 5 has 3 in order
(two person magic)
Some/Moderate
The Down Under Deal
(aka the Australian Shuffle)
Apr 2005Down under deals and powers of 2Little/Easy
Fitch Four GloryFeb 20053 cards predict the 4th
(two person magic)
Some/Hard
Sheer LuckDec 2004Elimination dealsSome/Moderate
Low-Down Triple DealingOct 2004Triple deal principle/
quad run false shuffle
Little/Easy

Pre-Card Colm, several mathematical card tricks---including a new two-person effect based on (the first non-trivial case of) a combinatorial result by Erdös & Szekeres---were featured on the AMS's What's New in Mathematics site in Oct 2000.

The Order In the Ranks puzzle in the New York Times (10 May 2010) was a cardless reworking -- wrapped up in a convoluted plot line involved the President and Vice President of the USA as guests on the Daily Show -- of the Erdös/Szekeres trick mentioned above. (That five-card trick had also featured in the Jun 2005 Card Colm.) Some quick-witted NYT readers, over time, figured out the solution (7 Jun 2010) .

Upon reflection, it seems that the above ranking trick was the second substantive Card Colm creation, which is a curious coincidence. Six months before the NYT ran the politicized version mentioned above, the first Card Colm trick (invented in early 1999) was presented in the NYT, on 7 Dec 2009, in the form of a puzzle in Magic Phone Calls.

(It's the second effect pulled off by the Wizard there, and unlike the first, it involves no hokey pokey whatsoever; the communication is entirely mathematical. It's the Fitch Four Glory (Feb 2005) four card twist on the classic Fitch Cheney Five-Card Trick, which was first published in 1950 as a telephone effect. We urge interested readers to try to solve it before clicking on the link below.)

A spirited discussion of the Magic Phone Calls effects ensued on the associated NYT blog, and eventually one clever reader figured out precisely how it could all be done. The beans were finally spilled a few weeks later, in the delightfully illustrated Wizard's Clock (24 Dec 2009).

A big thanks to Pradeep Mutalik for featuring these puzzles in the NYT!

A curious spelling/numerical duality is explored with cards in "One of Six and Another of Half a Dozen" in the May 2007 issue of Word Ways (The Journal of Recreational Linguistics),

An article called "An ESPeriment with Cards," combining the Erdös/Szekeres and Gilbreath principles, was published in MAA Horizons in Feb 2007.

An article on the ever popular "Fitch Cheney Five-Card Trick and Generalizations" was published in MAA Horizons in Feb 2003. It also appears in the book The Edge of the Universe--Celebrating Ten Years of Math Horizons book (MAA, Aug 2006), edited by Deanna Haunnsperger & Stephen Kennedy.