124. Progression. "If from nine digits, - said Professor Rackbrain, - you form three numbers $147, 258, 369$, you will find that each subsequent number differs from the previous one by 111 and that, consequently, an arithmetic progression has been formed."

Could you rearrange the nine digits in four different ways so that in each case the three numbers form an arithmetic progression, and the middle number remains the same?
124. The professor's answer was:

\begin{tabular}{lll}
297 & 564 & 831 \\
291 & 564 & 837 \\
237 & 564 & 891 \\
231 & 564 & 897
\end{tabular}

where the common difference of the progression is respectively \(267, 273, 327\), and 333. He pointed out that for each of the six permutations of the middle three digits, a corresponding solution can be found.

[V. Tebo in the book "Parmi les Nombres Curieux" showed that there are 760 such progressions. Besides 456 and its permutations, the middle number can be any permutation of the following groups of three digits: \(258, 267, 348\), and \(357\). -M. Γ.]