Maths Numbers

Stewart Lamle

14th Century Decks of one-sided Tarot playing cards first appeared in Europe. They were soon banned by the Church. Cards, like other forms of entertainment and gambling, competed with Holy services. Card-playing spread like wildfire. 16th Century The four suits were created to represent the ideal French national, unified feudal society as promoted by Joan of Arc Nobility, Aristocracy, Peasants, the Church Spades, Diamonds, Clubs, Hearts . 18th Century Symmetric backs and fronts were designed to...

Robert E Neale

Flexagons are paper structures that can be manipulated to bring different surfaces into view. The four-sided ones discussed here are flexed by folding them in half along an axis, and then opening them up a different way to reveal a new face. Sometimes the opening is in a different direction (mountain or valley fold), sometimes along the other axis, and sometimes both. Although usually constructed from a strip of paper with attachment of the ends, flexagons seem more elegant when no glue or...

Pollys Flagstones

I wish to report on some recent correspondence with my good friends the Gahns in Calcutta. You may remember meeting Paul in The Puzzling World of Polyhedral Dissections. His wife Polly is an avid gardener. She presented me with the following problem. Polly places precisely fitted flagstones around various plantings in her garden in order to suppress weeds. She and Paul have a bent for geometrical recreations, so they are always on the lookout for creative and original solutions to their various...

Bill Gosper

Atlanta International Museum of Art and Design Martin Gardner, by singlehandedly popularizing Conway's game of Life during the 1970s, sabotaged the Free World's computer industry beyond the wildest dreams of the KGB. Back when only the large corporations could afford computers because they cost hundreds of dollars an hour, clandestine Life programs spread like a virus, with human programmers as the vector. The toll in human productivity probably exceeded the loss in computer time. With the...

Card Tricks Even

Here's an example that sounds a bit different, yet meets the two criteria for a black hole. It's a classic card trick. Remove 21 cards from an ordinary deck. Arrange them in seven horizontal rows and three vertical columns. Ask somebody to think of one of the cards without telling you which card he (or she) is thinking of. Now ask him (or her) which of the three columns contains the card. Regroup the cards by picking up the cards by whole columns intact, but be sure to sandwich the column that...

OBeirnes Hexiamond

Tom O'Beirne is not as celebrated a puzzler as he deserves to be, particularly on this side of the Atlantic. When I began to write this article, I was sure that I would find references to the Hexiamond in Martin Gardner's column, but I haven't found one yet. Nor is it mentioned in O'Beirne's own book 4 . But it does appear in his column in the New Scientist. Maybe the only other places where it has appeared in print are Berlekamp et al. 1 and the not very accessible reference Guy 2 . It must...

Solutions to Medium Problems

M1. (a) 32 moves (37, 0, 0), (31, 0, 6), (31, 6, 0), (25, 6, 6), (25, 11, 1), (36, 0, 1), (36, 0, 0), (30, 0, 6), (30, 6, 0), (24, 6, 6), (24, 11, 1), (35,0, 1), (35, 0, 0), (29, 0, 6), (29, 6, 0), (23, 6, 6), (23, 11,1), (23, 11,0), (23, 5, 6), (29, 5, 0), (29, 0, 5), (18, 11, 5), (18, 10, 6), (24, 10, 0), (24, 4, 6), (30, 4, 0), (30, 0, 4), (19, 11, 4), (19, 9, 6), (25, 9, 0), (25, 3, 6), (31, 3, 0) (b) 40 moves (37, 0, 0), (26, 11, 0), (26, 1, 10), (26, 0, 10), (36, 0, 0), (25, 11, 0), (25,...