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Showing posts from August, 2012

### 7.11

The problem that I read this week, and to spare you from the context behind it, is very easy to understand: in essence, you have 4 numbers that correspond to prices of products, where the price has a precision of two decimal points (i.e., the format is \$NN.nn). Call these numbers p1, p2, p3 and p4. The products are sold in a 7/11 store, and the coincidence at the heart of this problem is that these four numbers when multiplied altogether or when added up, the result is always 7.11. Mathematically speaking: p1+p2+p3+p4 = 7.11 p1*p2*p3*p4 = 7.11 Question becomes: what are the prices p1, p2, p3 and p4? Now, we have 2 equations and 4 variables which becomes extremely hard to solve. The book that I read this question at actually describes a 4-pages convoluted mathematical process to solve the problem, without any computers or algorithms. It is based on a number of very clever mathematical observations, but… I’d rather let the computer do the brute-force for me. The code to s

### Super Queen

In the chess literature amongst some of the most theoretical chess scholars there is a concept of the Super Queen, or in abbreviated form, SQ. SQ is a hypothetical variation of the game whereas we give an extra power to the already almighty queen: now in addition to the bishop- and rook-like moves, the queen also inherits the knight-like move (colloquially, the queen can now jump). Such a small variation of the game would actually cause a massive restructure of not only the overall dynamics of the game, but also every single strategy and fundamental would have to be revisited and reformulated: how would this impact the opening? The development phase? The gambits? The defense strategies, the clustering strategies, the tempo, the end game, the pieces promotion, the pieces sacrifice (the queen sacrifice), and so on so forth? An analogy to such an event can be draw in the realm of mathematics: when the root square of minus one was suddenly given a life in the form of the “number” i, a bran