We have \( 12 \times 23 = 276 \). If we reverse the numbers, we get \( 672 = 32 \times 21 \), which is still a true statement.

Does there exist non-palindromes \( \overline{abc} \) and \( \overline{def} \) such that

\( \overline{abc} \times \overline{def} = \overline{ghijk} \) and \( \overline{kjihg} = \overline{fed} \times \overline{cba} \)?

Note: The letters do not represent distinct digits.

The first digit is non-zero.

Non-palindromes mean that \( a \neq c \) and \( d \neq f \).

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