# Posts Tagged: puzzle

• stories

## the Reddit (after)effect

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Sunday january 2nd around 18hr NeB-stats went crazy. Referrals clarified that the post ‘What is the knot associated to a prime?’ was picked up at Reddit/math and remained nr.1 for about a day. Now, the dust has settled, so let’s learn from the experience. A Reddit-mention is to a blog what doping is to a… Read more »

• stories

## Olivier Messiaen & Mathieu 12

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To mark the end of 2009 and 6 years of blogging, two musical compositions with a mathematical touch to them. I wish you all a better 2010! Remember from last time that we identified Olivier Messiaen as the ‘Monsieur Modulo’ playing the musical organ at the Bourbaki wedding. This was based on the fact that… Read more »

• stories

## When was the Bourbaki wedding?

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It’s great fun trying to decode some of the puns contained in Betti Bourbaki’s wedding invitation. Below a photograph, taken on May 13th 1939, of three of the practical jokers (from left to right : Ralph Boas, Frank Smithies and Andre Weil), the others were Claude Chabauty, Weil’s wife Eveline and Louis Bouckaert (from Louvain)…. Read more »

• games, groups

## can -oids save group-theory 101?

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Can one base a group-theory 101 course on the notion of groupoids?

• games, groups

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About a year ago I did a series of posts on games associated to the Mathieu sporadic group $M_{12}$, starting with a post on Conway’s puzzle M(13), and, continuing with a discussion of mathematical blackjack. The idea at the time was to write a book for a general audience, as discussed at the start… Read more »

• geometry, groups

## the buckyball symmetries

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The buckyball is without doubt the hottest mahematical object at the moment (at least in Europe). Recall that the buckyball (middle) is a mixed form of two Platonic solids the Icosahedron on the left and the Dodecahedron on the right. For those of you who don’t know anything about football, it is that other ball-game,… Read more »

• featured

## exotic chess positions (1)

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Ever tried a chess problem like : White to move, mate in two! Of course you have, and these are pretty easy to solve : you only have to work through the finite list of white first moves and decide whether or not black has a move left preventing mate on the next white move…. Read more »

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## the King’s problem on MUBs

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MUBs (for Mutually Unbiased Bases) are quite popular at the moment. Kea is running a mini-series Mutual Unbias as is Carl Brannen. Further, the Perimeter Institute has a good website for its seminars where they offer streaming video (I like their MacromediaFlash format giving video and slides/blackboard shots simultaneously, in distinct windows) including a talk… Read more »

• stories

## Archimedes’ stomachion

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The Archimedes codex is a good read, especially when you are (like me) a failed archeologist. The palimpsest (Greek for ‘scraped again’) is the worlds first Kyoto-approved ‘sustainable writing’. Isn’t it great to realize that one of the few surviving texts by Archimedes only made it because some monks recycled an old medieval parchment by… Read more »

• stories

## censured post : bloggers’ block

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Below an up-till-now hidden post, written november last year, trying to explain the long blog-silence at neverendingbooks during october-november 2007… A couple of months ago a publisher approached me, out of the blue, to consider writing a book about mathematics for the general audience (in Dutch (?!)). Okay, I brought this on myself hinting at… Read more »

• stories

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Vacation is always a good time to catch up on some reading. Besides, there’s very little else you can do at night in a ski-resort… This year, I’ve taken along The Archimedes Codex: Revealing The Secrets Of The World’s Greatest Palimpsest by Reviel Netz and William Noel telling the story of the Archimedes Palimpsest. The… Read more »

• stories

## quotes of the day

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Some people are in urgent need of a vacation, myself included… From the paper Transseries for beginners by G.A. Edgar, arXived today : Well, brothers and sisters, I am here today to tell you: If you love these formulas, you need no longer hide in the shadows! The answer to all of these woes is… Read more »

• featured

## Chinese remainders and adele classes

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Oystein Ore mentions the following puzzle from Brahma-Sphuta-Siddhanta (Brahma’s Correct System) by Brahmagupta : An old woman goes to market and a horse steps on her basket and crashes the eggs. The rider offers to pay for the damages and asks her how many eggs she had brought. She does not remember the exact number,… Read more »

• stories

## sobering-up

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Kea’s post reminded me to have a look at my search terms (the things people type into search engines to get redirected here). Quite a sobering experience… Via Google Analytics I learn that 49,51% of traffic comes from Search Engines (compared to 26,17% from Referring Sites and 24,32% from direct hits) so I should take… Read more »

• featured

## tori & crypto : Diffie-Hellman or GCHQ?

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Boris Kunyavskii arXived the paper Algebraic tori – thirty years after dedicated to the 80th anniversary of V. E. Voskresenskii. The goal is to give an overview of results of V. E. Voskresenskii on arithmetic and birational properties of algebraic tori which culminated in his monograph “Algebraic Tori” published in Russian 30 years ago. As… Read more »

• featured

## mini-sudokube

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Via the Arcadian functor I learned of the existence of the Sudokube (picture on the left). Sudokube is a variation on a Rubik’s Cube in which each face resembles one-ninth of a Sudoku grid: the numbers from one to nine. This makes solving the cube slightly more difficult than a conventional Rubik’s Cube because each… Read more »

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## The M(13)-groupoid (2)

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Conway’s puzzle M(13) involves the 13 points and 13 lines of $\mathbb{P}^2(\mathbb{F}_3)$. On all but one point numbered counters are placed holding the numbers 1,…,12 and a move involves interchanging one counter and the ‘hole’ (the unique point having no counter) and interchanging the counters on the two other points of the line determined… Read more »

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## Mathieu’s blackjack (1)

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Mathieu’s blackjack is a two-person combinatorial game played with 12 cards of values 0,1,2,…,11. For example take from any deck the numbered cards together with the jack (value 11) and the queen (value 0) (btw. if you find this PI by all means replace the queen by a zero-valued king). Shuffle the cards and divide… Read more »

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## The Mathieu groupoid (1)

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Conway’s puzzle M(13) is a variation on the 15-puzzle played with the 13 points in the projective plane $\mathbb{P}^2(\mathbb{F}_3)$. The desired position is given on the left where all the counters are placed at at the points having that label (the point corresponding to the hole in the drawing has label 0). A typical… Read more »

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## The 15-puzzle groupoid (2)

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In the 15-puzzle groupoid 1 we have seen that the legal positions of the classical 15-puzzle are the objects of a category in which every morphism is an isomorphism (a groupoid ). Today, we will show that there are exactly 10461394944000 objects (legal positions) in this groupoid. The crucial fact is that positions with the… Read more »

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## The 15-puzzle groupoid (1)

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Before we go deeper into Conway’s M(13) puzzle, let us consider a more commonly known sliding puzzle: the 15-puzzle. A heated discussion went on a couple of years ago at sci-physics-research, starting with this message. Lubos Motl argued that group-theory is sufficient to analyze the problem and that there is no reason to resort to… Read more »

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## Conway’s puzzle M(13)

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In the series “Mathieu games” we describe some mathematical games and puzzles connected to simple groups. We will encounter Conway’s M(13)-puzzle, the classic Loyd’s 15-puzzle and mathematical blackjack based on Mathieu’s sporadic simple group M(12).

• featured

## NeverEndingBooks-games

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Here a list of pdf-files of NeverEndingBooks-posts on games, in reverse chronological order.

• stories

## the secret life of numbers

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Just read/glanced through another math-for-the-masses book : [The secret life of numbers](http://www.amazon.co.uk/Secret-Life-Numbers-Pieces-Mathematicians/dp/0309096588/sr=81/qid=1168541999/ref=sr_1_1/203-3776750-7074362?ie=UTF8&s=books) by [George G. Szpiro](http://www.citebase.org/search?submit=1&author=Szpiro%2C+George+G.). The subtitle made me buy the book : **50 easy pieces on how mathematicians work and think** Could be fun, I thought, certainly after reading the Amazon-blurb : Most of us picture mathematicians laboring before a chalkboard, scribbling numbers… Read more »

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## coalgebras and non-geometry 3

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Last time we saw that the _coalgebra of distributions_ of a noncommutative manifold can be described as a coalgebra Takeuchi-equivalent to the path coalgebra of a huge quiver. This infinite quiver has as its vertices the isomorphism classes of finite dimensional simple representations of the qurve A (the coordinate ring of the noncommutative manifold) and… Read more »