In 1974, the brilliant Hungarian professor of architecture, Ernö Rubik, invented the puzzle that has made his name familiar all over the world. When it was mass-produced, from 1980 onwards, the cube became an international craze; vast numbers were made and they brought both great fun and great frustration to millions of children of all … Continue reading Rubik’s Cube Solvable in 20 Moves
Tag: Games
Poincare’s Square and Unbounded Gomoku
Henri Poincar'e was masterful in presenting scientific concepts and ideas in an accessible way. To explain that the Universe might be bounded and yet infinite, he imagined that the temperature of space decreased from the centre to the periphery in such a way that everything contracted with the distance from the centre. As travellers moved … Continue reading Poincare’s Square and Unbounded Gomoku
Hanoi Graphs and Sierpinski’s Triangle
The Tower of Hanoi is a famous mathematical puzzle. A set of disks of different sizes are stacked like a cone on one of three rods, and the challenge is to move them onto another rod while respecting strict constraints: Only one disk can be moved at a time. No disk can be placed upon … Continue reading Hanoi Graphs and Sierpinski’s Triangle
John Horton Conway: a Charismatic Genius
John Horton Conway was a charismatic character, something of a performer, always entertaining his fellow-mathematicians with clever magic tricks, memory feats and brilliant mathematics. A Liverpudlian, interested from early childhood in mathematics, he studied at Gonville & Caius College in Cambridge, earning a BA in 1959. He obtained his PhD five years later, after which … Continue reading John Horton Conway: a Charismatic Genius
The Mathematics of Fair Play in Video Games
Video games generate worldwide annual sales of about $150 billion. With millions of people confined at home with time to spare, the current pandemic may benefit the industry. At the core of a video game is a computer program capable of simulating a range of phenomena in the real world or in a fantasy universe, … Continue reading The Mathematics of Fair Play in Video Games
ToplDice is Markovian
Many problems in probability are solved by assuming independence of separate experiments. When we toss a coin, it is assumed that the outcome does not depend on the results of previous tosses. Similarly, each cast of a die is assumed to be independent of previous casts. However, this assumption is frequently invalid. Draw a card … Continue reading ToplDice is Markovian
The Beer Mat Game
Alice and Bob, are enjoying a drink together. Sitting in a bar-room, they take turns placing beer mats on the table. The only rules of the game are that the mats must not overlap or overhang the edge of the table. The winner is the player who puts down the final mat. Is there a … Continue reading The Beer Mat Game
Franc-carreau or Fair-square
Franc-carreau is a simple game of chance, like the roll-a-penny game often seen at fairs and fêtes. A coin is tossed or rolled down a wooden chute onto a large board ruled into square segments. If the player's coin lands completely within a square, he or she wins a coin of equal value. If the … Continue reading Franc-carreau or Fair-square
Factorial 52: A Stirling Problem
How many ways can a deck of cards be arranged? It is very easy to calculate the answer, but very difficult to grasp its significance. There are 52 cards. Thus, the first one may be chosen in 52 ways. The next one can be any of the remaining 51 cards. For the third, there are … Continue reading Factorial 52: A Stirling Problem
Fun and Games on a Honeycombed Rhomboard.
Hex is an amusing game for two players, using a board or sheet of paper divided into hexagonal cells like a honeycomb. The playing board is rhomboidal in shape with an equal number of hexagons along each edge. Players take turns placing a counter or stone on a single cell of the board. One uses … Continue reading Fun and Games on a Honeycombed Rhomboard.
Game Theory & Nash Equilibrium
Game theory deals with mathematical models of situations involving conflict, cooperation and competition. Such situations are central in the social and behavioural sciences. Game Theory is a framework for making rational decisions in many fields: economics, political science, psychology, computer science and biology. It is also used in industry, for decisions on manufacturing, distribution, consumption, … Continue reading Game Theory & Nash Equilibrium
The Tragic Demise of a Beautiful Mind
John Nash, who was the subject of the book and film A Beautiful Mind, won the Abel Prize recently. But his journey home from the award ceremony in Norway ended in tragedy [see this week’s That’s Maths column (TM069): search for “thatsmaths” at irishtimes.com]. We learn at school how to solve polynomial equations of first … Continue reading The Tragic Demise of a Beautiful Mind
Biscuits, Books, Coins and Cards: Massive Hangovers
Have you ever tried to build a high stack of coins? In theory it's fine: as long as the centre of mass of the coins above each level remains over the next coin, the stack should stand. But as the height grows, it becomes increasingly trickier to avoid collapse. In theory it is possible to … Continue reading Biscuits, Books, Coins and Cards: Massive Hangovers
Chess Harmony
Long ago in the Gupta Empire, a great-but-greedy mathematician, Grababundel, presented to the Maharaja a new game that he had devised, called Chaturanga. Thirty-two of the Maharaja's subjects, sixteen dressed in white and sixteen in black, were assembled on a field divided into 64 squares. There were rajas and ranis, mahouts and magi, fortiers and … Continue reading Chess Harmony
The Beautiful Game
What is the most beautiful rectangular shape? What is the ratio of width to height that is most aesthetically pleasing? This question has been considered by art-lovers for centuries and one value appears consistently, called the golden ratio or Divine proportion. I must admit that the notion of an ideal ratio makes me uncomfortable. How … Continue reading The Beautiful Game
No Maths Involved!
Whether or not you enjoy solving them, those 9x9 grids with numbers and blank cells cannot have escaped your notice. Sudoku puzzles have swept the world since exploding on the scene in 2005. They are found in newspapers everywhere, providing daily amusement to all who like a minor mathematical challenge. The objective of Sudoku is … Continue reading No Maths Involved!
Sproutology
Sprouts is a simple and delightfully subtle pencil-and-paper game for two players. The game is set up by marking a number of spots on a page. Each player makes a move by drawing a curve that joins two spots, or that loops from a spot back to itself, without crossing any lines drawn earlier, and … Continue reading Sproutology
ThatsMaths 