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We show and interpret three examples of nontrivial results obtained innumerical simulations of many-body systems: exponential convergence oflow-lying energy eigenvalues in the process of progressive truncation of hugeshell-model matrices, apparently ordered spectra generated by randominteractions, and regular behavior of complex many-body energies in a systemwith single-particle orbitals in continuum. The possible practical applicationsand new approaches are suggested.Comment: 12 pages, 4 figure

RANDOMNESS AND COLLECTIVITY IN NUCLEAR STRUCTURE: THREE THEORETICAL PUZZLES