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Diophantine equation

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This year's Abel Prize has been awarded to the German mathematician Gerd Faltings for work that brings together number theory and geometry to solve equations.

Mr and Mrs Magnus are a happy gnome couple. Unfortunately, foreseeing that they will be unable to keep up with their rising mortgage repayments, they've been forced to move into my back garden, where they've acquired a plot to build a house on. Gnome by-laws state that the total number of bricks used in any construction project must be 177 or planning permission will not be granted. How can they manage to stick to the rules?