33 Find the largest positive integer that cannot be expressed as the sum of a positive multiple of 42 and a composite number.

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33. For any positive integer $n$ that cannot be expressed as a positive multiple of 42 and a composite number, consider the remainder $r$ when $n$ is divided by 42. If $r=0$ or $r$ is a composite number, then $n \leqslant 42$.

Now consider the case where $r=1$ or $r$ is a prime number.
If $r \equiv 1(\bmod 5)$, then
$$84+r \equiv 0(\bmod 5)$$

In this case,
$$n<3 \times 42=126$$

If $r \equiv 2(\bmod 5)$, then
$$4 \times 42+r \equiv 0(\bmod 5)$$

In this case,
$$n<5 \times 42=210$$

If $r \equiv 3(\bmod 5)$, then
$$42+r \equiv 0(\bmod 5)$$

In this case,
$$n<2 \times 42=84$$

If $r \equiv 4(\bmod 5)$, then
$$3 \times 42+r \equiv 0(\bmod 5)$$

In this case,
$$n<4 \times 42=168$$

If $r \equiv 0(\bmod 5)$, then
$$r=5,$$

In this case, since 5, 47, 89, 131, and 173 are all prime numbers, $n$ is at most 215.
In summary, the largest positive integer sought is 215.