Posts In Category games
Seating the first few thousand Knights
on February 3, 2010 by lieven in games, groups, Comments (0)
The odd Knights of the round table-problem asks for a specific one-to-one correspondence between two realizations of ‘the’ algebraic closure of the field of two elements.
The first identifies the multiplicative group of its non-zero elements with the group of all odd complex roots of unity, under complex multiplication. The addition on is then [...]
The odd knights of the round table
on January 28, 2010 by lieven in games, geometry, groups, numbers, Comments (0)
Here’s a tiny problem illustrating our limited knowledge of finite fields : “Imagine an infinite queue of Knights , waiting to be seated at the unit-circular table. The master of ceremony (that is, you) must give Knights and a place at an odd root of unity, say and , such that the [...]
On2 : extending Lenstra’s list
on January 27, 2009 by lieven in games, numbers, Comments (0)
Hendrik Lenstra found an effective procedure to compute the mysterious elements alpha(p) needed to do actual calculations with infinite nim-arithmetic.
On2 : Conway’s nim-arithmetics
on January 26, 2009 by lieven in games, numbers, Comments (0)
Conway’s nim-arithmetic on ordinal numbers leads to many surprising identities, for example who would have thought that the third power of the first infinite ordinal equals 2…
On2 : transfinite number hacking
on January 8, 2009 by lieven in games, numbers, Comments (1)
Surely Georg Cantor’s transfinite ordinal numbers do not have a real-life importance? Well, think again.
5 years blogging
on December 31, 2008 by lieven in games, Comments (5)
A few recollections and a very quick number game by Hendrik Lenstra.
sporadic simple games
on July 13, 2008 by lieven in games, groups, Comments (0)
About a year ago I did a series of posts on games associated to the Mathieu sporadic group , 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 of [...]
Surreal numbers & chess
on April 8, 2008 by lieven in games, numbers, Comments (2)
Most chess programs are able to give a numerical evaluation of a position. For example, the position below is considered to be worth +8.7 with white to move, and, -0.7 with black to move (by a certain program). But, if one applies combinatorial game theory as in John Conway’s ONAG and the Berlekamp-Conway-Guy masterpiece Winning [...]
exotic chess positions (2)
on March 5, 2008 by lieven in games, Comments (10)
Juan de Mairena linked in the comments to last post to a truly great retro-chess problem ! In the position below white is to play and mate in three!
At first this seems wrong as there is an obvious mate in two : 1. Qe2-f1, Kh1xh2 2. Rg3-h3 The ingenious point being that black claims [...]
exotic chess positions (1)
on March 4, 2008 by lieven in games, Comments (4)
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. [...]
Hi, I'm a professor of mathematics at the University of Antwerp, in Belgium. My research areas are non-commutative algebra and non-commutative geometry. Sometimes, you can also find me here :
