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You can solve this puzzle using a simple recursive program (see Enigma 1780), or with a more strategic based solver (see Enigma 1657), but here’s a program that uses PyMathProg to solve the puzzle using ILP. It runs in 69ms.

Solution:The letters in the second row are G E M N A I.There are two possible arrangements of the grid, but the PyMathProg solution stops when it finds a solution.