How many players have got a hundred and a hat-trick in the same T20?

Joe Denly scored a T20 hundred then took a hat-trick the other day. Has anyone else done this ? asked Graham Bowmer from the United States
Joe Denly's performance for Kent against Surrey at The Oval last week - after slamming 102 from 61 balls, he claimed a hat-trick with his legbreaks - was not only a first for senior T20 cricket; such a double has never been performed in List A cricket either. There have only been seven previous instances of a player managing a fifty and a hat-trick in the same T20 game.

In first-class cricket, which obviously offers much more scope for this feat, there have been 16 such doubles of a hundred and a hat-trick, including one in a Test, by Sohag Gazi for Bangladesh against New Zealand in Chittagong in 2013-14. The most recent instance at first-class level, by Kelly Smuts for Eastern Province against Boland in Paarl in 2015-16, was one of only three cases of a century and four wickets in four balls in the same game.

Shikhar Dhawan has now made a hundred in his first Test against five different countries - is this a record? asked Rahul Ghai from India
Shikhar Dhawan marked his overall Test debut with a superb 187 against Australia in Mohali in 2012-13, and since then has also scored centuries in his first Test appearances against New Zealand, Sri Lanka, Bangladesh and - most recently - Afghanistan in Bengaluru. He has yet to play a Test against Pakistan, Zimbabwe or Ireland, so he has a chance to add to his collection.

No one has made as many debut hundreds. Dhawan has nipped past a distinguished quintet who made centuries in their first Tests against four different opponents: Alastair Cook, Matthew Hayden, Kumar Sangakkara, Graeme Smith and Mark Taylor. Cook is yet to play a Test against Zimbabwe, Afghanistan or Ireland.

Who has the biggest difference between his highest Test score and his second best? asked Richard Bartlett from England
At the moment this peculiar record is held by India's Karun Nair, who amassed 303 not out against England in Chennai in December 2016. He was dropped for India's next Test, and his next-highest score is just 26, making a difference of 277.

Nair will obviously be hoping for a recall, and if he does get another chance his first target will be a score of 68 or more, which would restore the record to its long-time custodian Reginald "Tip" Foster of England. He had a difference of 236 between his highest Test score - 287 on debut against Australia in Sydney in 1903-04 - and his 51 against South Africa at The Oval in 1907.

KL Rahul scored 70, and then Ireland were all out for 70, in the recent T20 match. Has anyone ever actually beaten another side's score on his own in a T20 international? asked Colin Gunter from Ireland
That rapid 70 by KL Rahul set up a big Indian total of 213 for 4 in Malahide last month. Ireland only managed to equal his individual score in their disappointing reply. Aslam Siddiqui, an indefatigable researcher and contributor to the Ask Steven page on Facebook, revealed that there had been three previous uninterrupted T20Is where one man had outscored the opposition, and another one when the scores were equal. In October 2008 in King City, near Toronto, Hamilton Masakadza scored 79 for Zimbabwe, who then bowled Canada out for 75. Four years later, Luke Wright's 99 not out for England in the World T20 in Colombo easily outstripped Afghanistan's 80, then in Amstelveen in July 2015, Michael Swart's unbeaten 76 for Netherlands was seven more than Nepal managed in reply. In the first World T20, in Johannesburg in September 2007, Sanath Jayasuriya biffed 88 for Sri Lanka, who then dismissed Kenya for the same score. And only last week*, Aaron Finch, with a 76-ball 172, outscored Zimbabwe's 129 for 9 in Harare.

Has a captain ever declared in a Test and seen the opposition's openers pass his team's score? asked Keith Naismith from England
Only one Test captain has had his mortifying experience: in Georgetown in 1971-72, Garry Sobers declared West Indies' first innings at 365 for 7, but had to watch New Zealand's openers put on 387, still a national record. Glenn Turner scored 259 (after making 259 against Guyana the week before), while Terry Jarvis scored 182, his only Test century. A rain-affected match, it ended in a draw - like the other four matches of a rather forgettable series.

There have been 23 other occasions when the opening pair of the team batting second has passed the (all-out) total of the side that went in first. The most recent instance was in last week's Test in Antigua, when Kraigg Brathwaite and Devon Smith responded to Bangladesh's paltry 43 with an opening stand of 113.

*Thanks to Deepu Narayana for pointing out Finch's omission in the fourth answer