Monthly Archives: November 2012

Geomagic squares

In 2001, Lee Sallows generalised the concept of a magic square, replacing the integers in each cell with subsets of the plane. He calls such a configuration a ‘geomagic square’ if the subsets in every row, column and diagonal can … Continue reading

Posted in Uncategorized | 3 Comments

Cipher 5: 99 problems or 23?

Due to popular demand, the frequency of Cipher Tuesdays has increased from every four weeks to its theoretical limit of every week. Also by popular demand, this cipher is given as both an image (for manual solvers) and delineated text … Continue reading

Posted in Ciphers | 4 Comments


Tsukamoto and Miyazaki of Kyoto University have discovered that three states are sufficient to enable gliders to exist on a Penrose tiling, rather than four. The following video demonstrates their discovery together with a periodic emitter in an augmented rule: On a … Continue reading

Posted in Uncategorized | 5 Comments

Outer automorphism of S6

Let’s consider the group S6 of permutations of {1,2,3,4,5,6}. For fairly boring reasons, we can find S5 living inside there — the subgroup which fixes the element ‘6’. More generally, S(n-1) is contained within Sn. S6 is special, though, since … Continue reading

Posted in Uncategorized | 3 Comments

Hyperboloid of one sheet

Suppose we took a solid unit cube and balanced it on a vertex. Next, we spin the cube really quickly about the vertical axis, producing a solid of revolution: Clearly, the top and bottom are two identical cones produced by revolving a line segment passing … Continue reading

Posted in Uncategorized | 5 Comments

Betts revisited

As a brief summary, I posted about the three-dimensional generalisation of a particular two-dimensional problem by Alexander Betts. In case you haven’t read it, or didn’t understand it, I’ll explain the ideas again here. A finite set S of n points in d-dimensional … Continue reading

Posted in Uncategorized | 6 Comments

Cipher 4: Think rationally

To make a welcome change from the monoalphabetic substitution ciphers embedded in images, I have decided to publish this particular cipher in a text-only format for ease of access. WII MJCVKWV FZN ZQLHWMH HA ZLH GMFKTJQ DKOQXT XM UNN LAADANPNFT EOWZXJRX … Continue reading

Posted in Ciphers | Leave a comment