Author Archives: apgoucher

Cipher 65: Melencolia

Posted on April 15, 2014 by apgoucher

Firstly, congratulations to the British EGMO team (Olivia, Kasia, Katya and Eloise) for their impressive performance, coming eighth out of 29 competing teams. Apparently the competition was held in the same five-star hotel in Antalya enjoyed by a previous Balkan … Continue reading →

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Lifting the exponent

Posted on April 13, 2014 by apgoucher

I overheard mention of a particular problem on a recent British Mathematical Olympiad, namely the following: A number written in base 10 is a string of 3^2013 digit 3s. No other digit appears. Find the highest power of 3 which … Continue reading →

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Cipher 64: Sic transit gloria Monday

Posted on April 7, 2014 by apgoucher

Firstly, I have a few late items of news to discuss: Maria Holdcroft (former UK EGMO team member) and I survived our skydive on Wednesday, and have so far raised in excess of £886.77 (a large portion of which is from … Continue reading →

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Cayley-Menger determinants

Posted on April 2, 2014 by apgoucher

Niccolo Fontana Tartaglia, whom you may recognise from having discovered Cardano’s solution to the general cubic equation, also discovered a generalisation of Heron’s formula to compute the volume of a tetrahedron: As you may expect, this can be generalised to … Continue reading →

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Most difficult chess problem

Posted on March 28, 2014 by apgoucher

Neil Bickford has exhaustively searched the space of 5 × 4 sliding-block puzzles* to determine the one with the longest minimal solution. The unique result, which requires a whopping 235 moves, happens to be Bob Henderson’s Gauntlet puzzle: *subject to the … Continue reading →

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Cipher 62: Also untitled

Posted on March 25, 2014 by apgoucher

By the way, we’ve raised £463.00 so far for the Schistosomiasis Control Initiative (see this post for an explanation). This week’s cipher uses a couple of relatively simple ideas, although I could imagine it being difficult to cryptanalyse. DKGOQXIWSASPYKOWEEPLELTLELFSKTPITLJFCLXSANZRYYNTAAJDQC Good … Continue reading →

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Denser packing of pound coins discovered

Posted on March 20, 2014 by apgoucher

Until very recently, the densest known packing of pound coins in the plane was the hexagonal lattice packing of circles, which achieves a density of π/√12 ≈ 0.9069. This was proved by Axel Thue to be the densest arrangement of … Continue reading →

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Cipher 61: Discrepancy

Posted on March 17, 2014 by apgoucher

Slightly less major announcement: Stuart Gascoigne has now solved a total of 50 ciphers, earning the first ‘gold star’ icon on the solvers page. 00111101 11011100 11110011 00111110 00010110 11011110 00100000 11010111 10000001 00001000 11010111 10111111 11101101 00101110 11111010 00111110 00000010 10110001 … Continue reading →

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Rectangular hyperbolae and the orthocentre

Posted on March 16, 2014 by apgoucher

Firstly, a major announcement: Maria Holdcroft (whom you may remember from the cipher solvers page) and I will be performing a charity skydive on the 2nd April! If you wish to sponsor us, please specify the amount you intend to donate by commenting … Continue reading →

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Cipher 60: Tuesday comes between Wednesday and Friday this week

Posted on March 13, 2014 by apgoucher

The more astute observers amongst you may have noticed that this particular cipher is two days later than is usual, as a consequence of a particularly busy week. Hence, I had no choice but to officially postpone Tuesday by 48 … Continue reading →

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