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Hilbert's twentieth problem - Hilbert's twentieth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It asks whether all boundary value problems can be solved (that is, do variational problems with certain boundary conditions have solutions).
Hilbert's nineteenth problem - Hilbert's nineteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It asks whether the solutions of Lagrangians are always analytic.
Boundary condition - In mathematics, boundary conditions are imposed on the solutions of ordinary differential equations and partial differential equations, to fit the solutions to the actual problem. In the problems most frequently considered, only one of the infinitely many solutions of the differential equation satisfies the boundary conditions.
Optimal solutions for Rubik's Cube/using the optimal solver - To use the solver linked to from the bottom of Optimal solutions for Rubik's Cube, the cube has to be turned into something that looks like this:
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