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Adding up both sets of equations shows everything solely depends upon E_{1}… So running an R code that checks for all possible values of E_{1} is a brute-force solution. However, one must first find what to check. Given that the sums of the triplets are of the form (16s,4s,s), the possible choices for E_{1} are necessarily restricted to

The first two values correspond to a second sum S_{2} equal to 188 and 192, respectively, which is incompatible with A_{1} being 193. Furthermore, the corresponding values for E_{2} and E_{3} are then given by