Monthly Archives: April 2013

Cipher 27: Sunflower

Posted on April 30, 2013 by apgoucher

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

Posted on April 29, 2013 by apgoucher

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

Posted on April 26, 2013 by apgoucher

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

Posted on April 23, 2013 by apgoucher

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

Posted on April 21, 2013 by apgoucher

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 n-body problem

Posted on April 18, 2013 by apgoucher

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

Posted on April 16, 2013 by apgoucher

I encrypted this one manually, so please excuse me if there are any typographical errors in here. 22-0866-63-24397890531617-53150237-+99-155758+23683922-740866-5332- 5322-11-9212-0444-74539090993912-080803-08099063-+03-68-25-99-0722- 7453902737-+998460493122-0812-53B29212-0444-9099-84-03-921679-11-66 -25-5341-9216+3942-050803-16186334A5-22-08A5-9203205279-07B0-+99-03 -99-529099-094913+99-52-52A4-0809909952-44-4931-9099-1533+740844-66 -531627156828065392A1- Good luck!

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EGMO synopsis

Posted on April 14, 2013 by apgoucher

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

Posted on April 12, 2013 by jdcranch

Hall’s marriage theorem is well-known 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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One-dimensional noughts and crosses

Posted on April 12, 2013 by apgoucher

The ordinary game of Noughts and Crosses, also known as Tic-tac-toe, 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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