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Monthly Archives: August 2013
Cipher 41: Caesar cipher
I’ve incorporated a few classical ciphers before, but generally avoided the Caesar cipher due to how trivial it is to bruteforce. This one should present more difficulty: When you have the password, use it to access the protected area.
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Influential mathematicians
It has come to my attention that there is a maths camp taking place at Balliol College, Oxford, with the intention of subjecting young aspiring mathematicians to new ideas. Since one of the volunteers at the camp is advertising cp4space … Continue reading
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Growth of recursive string substitution
A Lindenmeyer system, or Lsystem, involves a recursive procedure applied to a string of symbols, where each symbol in the string is simultaneously replaced with a string, dependent on that symbol. For example, one of my favourite examples involves Easter eggs … Continue reading
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Analysing Escher
I have just been involved in the production of an action thriller about the International Mathematical Olympiad. Since certain intervals of time were inactive and unthrilling, I decided to pass the time by writing a few cp4space articles, amongst other … Continue reading
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Polynomials and Hamming weights
Let P(x) be a polynomial of degree n. Let H(i) represent the number of `1’s in the binary expansion of the integer i. Although reasonably easy to prove, it may seem surprising that the following identity holds: Does this theorem have a … Continue reading
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Cipher 40: Leversha’s paradise
Occasionally, mathematical olympiads contain no classical Euclidean geometry. One such example is the IMO paper in the action thriller X+Y, which encompasses discrete combinatorics, additive combinatorics and algebra. To compensate for this, I have designed a cipher based entirely on Euclidean plane … Continue reading
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Symmetric geometry theorems
Clark Kimberling’s Encyclopedia of Triangle Centres contains several thousand triangle centres, many of which are defined as intersections of three concurrent lines. For example, we have: The three medians of a triangle intersect at the centroid; The three altitudes of … Continue reading
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Kaleidoscopes
For the third time on cp4space, I’m going to refer to my Wythoffian polyhedron generator. This constructs a polyhedron by the use of some twodimensional fundamental region, bounded by mirrors meeting at predetermined angles. For example, a triangle with internal … Continue reading
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Cipher 39: Unknown location
The following image should be sufficient for you to determine the password to a reasonable degree of accuracy:
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Fair dice
(I’m testing out the functionality of the cp4space Facebook page. Hopefully, this post should be automatically published there.) In most familiar board games, cubic dice are used on the basis that each face is equally likely to face upwards. In … Continue reading
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