$$225-[42-\left\{25-(18-\overline{18+13})\right\}]=225-[42-\left\{25-(18-31)\right\}]$$
$$=225-[42-\left\{25-(-13)\right\}]$$
$$=225-[42-\left\{25+13\right\}]$$
$$=225-[42-38]$$
$$=225-4$$
$$=221$$
Hence, the correct answer is Option D
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