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Monthly Archives: April 2013
Cipher 27: Sunflower
I’m afraid that I’ve run out of inspiration for ciphers. I apologise if you’re disappointed, and hopefully this nice picture of a sunflower will cheer you up. In other news, the Balkan Mathematical Olympiad has changed its spacetime location. Rather … Continue reading
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Affine spaces over F3
The card game Set is played rather regularly at gatherings such as the MathsJam events held nationwide on a monthly basis. The original game involves trying to identify sets of three cards which form lines in the affine hyperspace . … Continue reading
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Recent discoveries in Conway’s Life
This is breaking news, by the way; hence, the article is somewhat rushed. (If you haven’t heard of Conway’s Game of Life, there is a summary on Wikipedia.) As of a few minutes ago, Mike Playle discovered a π/2 stable reflector with a … Continue reading
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Cipher 26: Spaced out
In many of the previous ciphers, the spaces between words have been omitted to increase difficulty. However, this results in a distinct loss of information. One such example is the following hashtag referring to my forthcoming birthday gathering (entitled Adam P’s Exposition). … Continue reading
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Ring of periods
Twelve years ago, Kontsevich and Zagier published an enlightening exploration of a set of real (or, more generally, complex) numbers known as periods. Firstly, let’s have a look at which sets are subsets of which other sets: The integers are a … Continue reading
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The nbody problem
With basic calculus, it’s possible to solve the problem of two masses orbiting under gravitational attraction. In particular, the only solution is for them to follow conic sections, sharing a common focus (the barycentre of the two particles). For example, Pluto and … Continue reading
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Cipher 25: My dear Watson
I encrypted this one manually, so please excuse me if there are any typographical errors in here. 220866632439789053161753150237+99155758+236839227408665332 532211921204447453909099391208080308099063+036825990722 7453902737+998460493122081253B292120444909984039216791166 2553419216+394205080316186334A52208A5920320527907B0+9903 99529099094913+995252A4080990995244493190991533+74084466 531627156828065392A1 Good luck!
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EGMO synopsis
I have returned from assisting at the Easter olympiad training camp at Trinity College, Cambridge. After we marked a selection test (the results of which I am not at liberty to divulge), a preliminary squad of nine people were selected, which … Continue reading
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Efficient computational matchings and lax sexual morality
Hall’s marriage theorem is wellknown and frequently useful, but it’s a nightmare from a computational perspective. The standard proof can be turned into an algorithm which finds a matching, but it’s impracticably slow. The reason for this is that the … Continue reading
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Onedimensional noughts and crosses
The ordinary game of Noughts and Crosses, also known as Tictactoe, features a board on which two players alternate placing symbols (O for the first player, and X for the second player) in unoccupied squares, attempting to form a line of three … Continue reading
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