We study Ising chains with arbitrary multispin finite-range couplings, providing an explicit solution of the associated inverse Ising problem, i.e. the problem of inferring the values of the coupling constants from the correlation functions. As an application, we reconstruct the couplings of chain Ising Hamiltonians having exponential or power-law two-spin plus three- or four-spin couplings. The generalization of the method to ladders and to Ising systems where a mean-field interaction is added

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... to general finite-range couplings is as well as discussed.