Card Colms
Card Colm is a column on mathematical card principles and effects sponsored by the Mathematical Association of America which appeared at MAA.org bimonthly from 2004 to 2014. It's very much inspired by the extensive writings of Martin Gardner (1914-2010) on the subject, going back to his seminal book Mathematics, Magic and Mystery (1956).
Much of the best Card Colm material resurfaced in Mathematical Card Magic: Fifty-Two New Effects (AK Peters/CRC, 380 pages, 128 illus, Aug 2013).
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 those 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 |
| Certain Glory Marks Martin Gardner's Centennial | Oct 2014 | Ternary logic | Some/Moderate |
| Trim Hex Anagrams | Aug 2014 | Magic hexagram | Some/Moderate |
| Dicey Cards | Jun 2014 | Non-transitivity | Some/Moderate |
| Foregone Outset | Apr 2014 | The coin problem | Some/Moderate |
| Postage Stamp Issue | Feb 2014 | The postage stamp problem | Some/Moderate |
| X-Ray Vision | Dec 2013 | Probability-defying cycle principle | Some/Moderate |
| The Sequence I Desire. Magic: When Divided, No Remainder | Oct 2013 | Polydivisible numbers | Some/Easy |
| Rosette Shuffling Multiple Piles | Aug 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 Embarrassment | Feb 2013 | The Triskadequadra principle | Some/Moderate |
| Predictability Outranks Luck | Dec 2012 | Kruskal principle | Some/Easy |
| All or Nothing Trickle Treat | Oct 2012 | A non-assosiative binary operation | Some/Easy |
| Gilbreeath Shuuffling | Aug 2012 | Gilbreath shuffling variation | Some/Moderate |
| Something Old, Something True, Something Borrowed, Something New | Jun 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 Boys | Feb 2011 | Double deal palindrome principle | Some/Easy |
| It's Red or Black and Blue All Over | Dec 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 Mind | Oct 2010 | Martin Gardner events) | ---/--- |
| Also In His Own Words: More Mathemagical Games (and Tricks) With Cards From Martin Gardner | Aug 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 2010 | Apr 2010 | 2 items predict the 3rd (two person magic) | Some/Hard |
| Tighter Ascertainments: Matching Interest Rates | Feb 2010 | Summand deduction using balanced ternary representations | Some/Moderate |
| The Boldgach Conjecture | Dec 2009 | Matches from shuffled palindromic stacks | Little/Moderate |
| Poker-Faced Over the Phone | Oct 2009 | Small linear binary codes (two person magic) | Some/Hard |
| The Bligreath Principle | Aug 2009 | Gilbreath twist | Some/Easy |
| Two Summer Difference Certainties | Jun 2009 | Sum-rich (Sidon) sets | Some/Moderate |
| The Yummie Deal and Variations | Apr 2009 | Special deals | Some/Easy |
| Esteem Synergism | Feb 2009 | Spelling miracles | Little/Easy |
| What's Black and Red and Red All Over? | Dec 2008 | Binary de Bruijn sequences | Some/Moderate |
| Monge Shuffle Cliques | Oct 2008 | Monge shuffle invariance | Some/Moderate |
| (A) Pi Evolved Set--Harmonic Split Drill | Aug 2008 | Palindromic stack invariance | Some/Moderate |
| Sum-Rich Circulants | Jun 2008 | Summand deduction from cycling sums | Some/Moderate |
| Projective Geometry | Apr 2008 | The Fano plane | Some/Easy |
| Additional Certainties | Feb 2008 | Summand deduction via Fibonacci Numbers and Zeckendorf representations | Some/Moderate |
| Plurality Events, Standard Deviations and Skewed Perspectives | Dec 2007 | Mean, Standard Deviation & Skewness | Some/Moderate |
| A Magic Timepiece Influenced By Martin Gardner (Celebrating His 93rd Birthday | Oct 2007 | Cycling quadruple sum forces | Some/Easy |
| Sixy Alpha Omegas | Aug 2007 | Alternating triple sum forces | Some/Easy |
| Gibonacci Bracelets | Jun 2007 | Fibonacci sequences mod m | Little/Easy |
| Magic Circles of Eight | Apr 2007 | Magic circles | Little/Easy |
| Quasi-Masked Forcing Kind of Magic Squares | Feb 2007 | Magic squares | Little/Easy |
| Quantitative Reasoning in Small Groups | Dec 2006 | Z2, Z3, Klein-4 group | Some/Easy |
| Martin Gardner's Magic Spells | Oct 2006 | Interview & 10-card pyramid speller | None/Easy |
| The Second Norman Invasion | Aug 2006 | The Second Gilbreath principle | Little/Moderate |
| Better Poker Hands Guaranteed | Jun 2006 | Birthday card matches applications | Little/Easy |
| Bill Simon's Sixty-Four Principle | Apr 2006 | Two ways to force 4 of 8 cards | Some/Moderate |
| Many Fold Synergies | Feb 2006 | Parity principles | Little/Easy |
| Luckation Is Everything | Dec 2005 | Completing to 13 and advantages of knowing the 26th card | Little/Easy |
| Subtraction Is Addictive | Oct 2005 | Subtraction principles | Little/Moderate |
| The First Norman Invasion | Aug 2005 | The First Gilbreath principle | Some/Easy |
| A Little Erdös/Szekeres Magic | Jun 2005 | Any 5 has 3 in order (two person magic) | Some/Moderate |
| The Down Under Deal (aka the Australian Shuffle) | Apr 2005 | Down under deals and powers of 2 | Little/Easy |
| Fitch Four Glory | Feb 2005 | 3 cards predict the 4th (two person magic) | Some/Hard |
| Sheer Luck | Dec 2004 | Elimination deals | Some/Moderate |
| Low-Down Triple Dealing | Oct 2004 | Triple 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.