Haunted Vault
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Haunted Vault is a numbers puzzle. If you turn one knob of the vault, the other knobs start turning too. The object is to turn the knobs such that the dials end at 00-00-00-00. The vault is filled with gears with gearing ratios like 21/34 and 34/43. The vault uses one-way bearings (type "CSK8") such that one can turn dials only clockwise, and the other driven dials can then turn counter-clockwise (anti-clockwise). The puzzle is based on the Non-Transitive Gears mechanism. However, a three-gear version is trivial to solve, as one can then move one dial by alternatingly nudging the other two. That solution does not work with four knobs. One solution approach is through linear algebra. The puzzle has four equations (dials) and four unknowns (knobs). One can invert this matrix to calculate how far each knob has to be turned to get all four dials right.
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