Monthly Archives: February 2013

Magic squares of squares

In 1770, Leonhard Euler sent this particular curiosity to Joseph Lagrange. It’s a 4-by-4 magic square, all of whose entries are perfect squares. Martin Gardner offered a prize for finding a 3-by-3 magic square of squares. Lee Sallows found a … Continue reading

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Cipher 16: The scenic route

Cipher Tuesday has been massively successful at coinciding with special occasions. We’ve had Christmas and New Year ciphers, and now this one lands on Shrove Tuesday (on reflection, I realise that will trivially happen every year!). So, to commemorate a rather exciting … Continue reading

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BMO2 marked

A group* of twelve of us congregated in London to mark† the second round of the British Mathematical Olympiad. After several hours of marking, punctuated with a surprisingly high-quality lunch, we were able to announce the scores. The high scores are available on the BMOC website; well done … Continue reading

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Langton’s ant revisited

Langton’s ant is a two-dimensional generalisation of a Turing machine, known as a turmite (a portmanteau of ‘Turing’ and ‘mite’, as well as being a pun on ‘termite’), renowned for its simple rules and interesting behaviour. Specifically, it has one state … Continue reading

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New perfect number discovered

A positive integer N is described as a perfect number if the sum of all of its proper divisors (that is to say, factors of N other than N) is equal to itself. For instance, the proper divisors of 28 … Continue reading

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Cipher 15: Shuffled

Neither of the last two ciphers have been solved yet; hence, I’ve made this one slightly easier for you. Good luck. The password is entirely lowercase and contains no spaces.

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|cp4space| = 100

This is the 100th article on cp4space, and is inspired by a discussion last night with Gabriel Gendler. Triangle centres with complex numbers Suppose we have a triangle in the Euclidean plane . We can identify the Euclidean plane with the … Continue reading

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