A Colloquium on Recreational Mathematics took place in Lisbon this week. The meeting, RMC-VI (G4GEurope), a great success, was organised by the Ludus Association, with support from several other agencies: MUHNAC, ULisboa, CMAF-IO, CIUHCT, CEMAPRE, and FCT. It was the third meeting integrated in the Gathering for Gardner movement, which celebrates the great populariser of … Continue reading Our Dearest Problems
Tag: Puzzles
The Two Envelopes Fallacy
During his Hamilton lecture in Dublin recently, Fields medalist Martin Hairer made a passing mention of the “Two Envelopes Paradox”. This is a well-known problem in probability theory that has led to much misunderstanding. It was originally developed in 1912 by the leading German number theorist Edmund Landau (see Gorroochurn, 2012). It is frequently discussed … Continue reading The Two Envelopes Fallacy
The Flight of the Bumble Bee
Alice and Bob, initially a distance l apart, walk towards each other, each at a speed w. A bumble bee flies from the nose of one to the nose of the other and back again, repeating this zig-zag flight at speed f until Alice and Bob meet. How far does the bumble bee fly? There … Continue reading The Flight of the Bumble Bee
Grandi’s Series: Divergent but Summable
Is the Light On or Off? Suppose a light is switched on for a half-minute, off for a quarter minute, on for one eighth of a minute and so on until precisely one minute has elapsed. Is the light on or off at the end of this (infinite) process? Representing the two states ``on'' and … Continue reading Grandi’s Series: Divergent but Summable
Leopold Bloom’s Arithmetical Adventures
As Bloomsday approaches, we reflect on James Joyce and mathematics. Joyce entered UCD in September 1898. His examination marks are recorded in the archives of the National University of Ireland, and summarized in a table in Richard Ellmann's biography of Joyce (reproduced below) [TM140 or search for “thatsmaths” at irishtimes.com]. The marks fluctuate widely, suggesting some lack of … Continue reading Leopold Bloom’s Arithmetical Adventures
Lateral Thinking in Mathematics
Many problems in mathematics that appear difficult to solve turn out to be remarkably simple when looked at from a new perspective. George Pólya, a Hungarian-born mathematician, wrote a popular book, How to Solve It, in which he discussed the benefits of attacking problems from a variety of angles [see TM094, or search for “thatsmaths” … Continue reading Lateral Thinking in Mathematics
The Ubiquitous Cycloid
Puzzle: However fast a train is travelling, part of it is moving backwards. Which part? For the answer, see the end of this post. Imagine a small light fixed to the rim of a bicycle wheel. As the bike moves, the light rises and falls in a series of arches. A long-exposure nocturnal photograph would … Continue reading The Ubiquitous Cycloid
Eccentric Pizza Slices
Suppose six friends visit a pizzeria and have enough cash for just one big pizza. They need to divide it fairly into six equal pieces. That is simple: cut the pizza in the usual way into six equal sectors. But suppose there is meat in the centre of the pizza and some of the friends … Continue reading Eccentric Pizza Slices
Speed Cubing & Group Theory
The article in this week’s That’s Maths column in the Irish Times ( TM038 ) is about Rubik's Cube and the Group Theory that underlies its solution. The Rubik's cube craze ran through the world like wildfire in the 1980s. This simple mechanical puzzle is made from small pieces, called “cubies”, in a 3x3x3 structure … Continue reading Speed Cubing & Group Theory
The Watermelon Puzzle
An amusing puzzle appears in a recent book by John A. Adam (2013). The answer is very surprising. The book argues in terms of simultaneous equations. A simpler argument, using the diagram below, should make all clear. The Watermelon Puzzle. A farmer brings a load of watermelons to the market. Before he sets out, he … Continue reading The Watermelon Puzzle
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
Sharing a Pint
Four friends, exhausted after a long hike, stagger into a pub to slake their thirst. But, pooling their funds, they have enough money for only one pint. Annie drinks first, until the surface of the beer is half way down the side (Fig. 1(A)). Then Barry drinks until the surface touches the bottom corner (Fig. … Continue reading Sharing a Pint
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