12.3. Can we select such digits $a, b, c$, so that the numbers $\overline{a b}$, $\overline{b a}, \overline{b c}, \overline{c b}, \overline{c a}, \overline{a c}$ are prime?

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(6-7 \text { grade })
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12.3. It is clear that among the selected three digits, there should be neither even digits nor the digit 5. Moreover, since the number 39 is composite, the digits 3 and 9 cannot be taken together. This leaves us to check two triplets: $1,3,7$ and $1,7,9$. In the first case, it is easy to verify that the numbers $13,31,17,71,37,73$ are all prime, i.e., the triplet $1,3,7$ will be the required one. As for the second triplet, it does not pass, as the number 91 is composite.