The Easy, Smart Scholar's Solution

If there are ‘p’ people, there would be p*(p – 1)/2 handshakes. For about 30 handshakes, there must have been 8 people (excluding Captain Haddock), as the number of handshakes would be 8*7/2 = 28. To make it 31, Captain Haddock shook hands with the (three) ladies present. Thus, including Captain Haddock, there were nine, of whom three were women, making it 33.33 percent.

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