Solution: Let $x \equiv 1 \pmod{7}$ and $x \equiv 1 \pmod{11}$. By the Chinese Remainder Theorem, $x \equiv 1 \pmod{77}$. The two-digit numbers satisfying this are $1 + 77 = 78$. Thus, the answer is $\boxed{78}$.

Sat, 02 May 2026 21:02:16 +0000

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