Q: Of these, how many came in their very first act of their career - i.e., before a spell in the field?
A :A little over half - 135 were in the match's first-innings, Bannerman's again being the first and the most recent Marcus North's 117 in South Africa in 2008/09.
Q: How many were converted to centuries?
A: 56 - and the first and most recent is the same as directly above.
Q: And - finally - how many whose careers are over ended-up averaging over 50?
A: 20 - Bannerman, Jack Hobbs, Herbert Sutcliffe, Walter Hammond, Alan Fairfax, Cyril Walters, Bryan Valentine, Dennis Compton, Victor Stollmeyer, Andy Ganteaume (both of whom played just the single Test innings), Deepak Shodhan, Sunil Gavaskar, Desmond Lewis, Rodney Redmond (who played only one Test), Javed Miandad, Taslim Arif, Rashid Khan, Brendon Kuruppu, Andy Flower and Naveed Nawaz (who like Redmond played just once, and that too in his case against Bangladesh). There are also 4 current players who made 50 or more in their maiden Test knock and currently average over 50 - Ricky Ponting, Rahul Dravid, Mahela Jayawardene and Virender Sehwag, and also Brad Hodge who appears relatively unlikely to play again. This list is a mix of some of the best batsmen of all-time who showed their class right from the very start, and players who performed well in their limited opportunity.
Q: Who scored the most consecutive unconverted half-centuries?
A: Sri Lankan captain Arjuna Ranatunga made his last Test century in 1993, but in the remaining 7 years of his career he passed fifty on 22 occasions, without turning a single one into a century.
Q: After the questions about hit-wickets a couple of weeks ago, I wondered if there have ever been two handled-the-ball dismissals in the same series? I imagine not.
A: No, indeed there have not been.
Q: And if not, when were the closest two?
A: The two most recent ones, in fact - in March 2001 Stephen Waugh was out in the unfortunate way, and in December Michael Vaughan repeated the trick. Both dismissals occurred in the final Test of a three-match series in India.