parmenides51 wrote: Examine if we can put the sixteen positive divisors of $2024$ on the cells of the table shown such that the sum of the four numbers of any line or row to be a multiple of $3$. $ \begin{tabular}{ | l | c | c | r| } \hline & & & \\ \hline & & & \\ \hline & & & \\ \hline & & & \\ \hline \end{tabular} $ If I'm not mistaken, this works: 1 4 2 8 22 1012 11 23 44 92 46 88 2024 506 253 184

Yes, since $2024 \equiv 2$ (mod $3$), its divisors come in pairs of the form $1$ mod $3, 2$ mod $3.$ So there are eight $1$ mod $3$ divisors and eight $2$ mod $3$ divisors. Place the divisors in the table in a checkerboard fashion so each row and column has two divisors of each type.