Is Karun Nair the only man who turned his maiden Test century into a triple? asked Ahmed Mithun from India
Karun Nair's unbeaten 303 against England in Chennai in December 2016 - in only his third match - actually made him the third batsman to convert his maiden Test century into a score of more than 300. So far, in five other matches, Nair's next-best score is just 26.
The first to achieve this was none other than Garry Sobers, who did not reach three figures until his 17th Test for West Indies, against Pakistan in Kingston in 1957-58. But he made it count when he did get there, going on to 365 not out, the highest individual score in Tests at the time; it remained the record for 36 years, until Brian Lara eclipsed it in 1993-94.
The other man to do this waited even longer. Bob Simpson had played 29 Tests - and was already Australia's captain - before he finally breached the hundred mark, against England at Old Trafford in 1964. He ground his way to 311, in a high-scoring draw. Like Sobers, who finished with 26 hundreds from 93 Tests, Simpson made up for lost time: he ended up with ten centuries in 62 matches.
Ben Foakes won the Man of the Match award in his first Test match and also his debut ODI. Was this a first? asked S Hari Narayanan from India
The England wicketkeeper Ben Foakes followed his award-winning Test-debut performance against Sri Lanka in Galle last November - he rescued England with 107 in the first innings - by making an equally vital unbeaten 61 earlier this month to help defeat Ireland in Malahide.
The only other similar double I can find was achieved by the Bangladesh left-arm seamer Mustafizur Rahman, who picked up the match awards in his first Test (against South Africa in Chittagong in 2015) and first one-day international (against India in Mirpur in 2015). Mustafizur must have been close on his T20 international debut, too, as he took 2 for 20 in his four overs.
Who has collected the most Test wickets without ever taking one in England? asked Kenneth Johnstone From England
The owner of this record used to be the Australian offspinner Bruce Yardley, who died earlier this year. Yardley took 126 wickets, none of them in England, which was the most when he played his final Test in 1983. But he has been overhauled since - first by the West Indian fast bowler Merv Dillon, whose 131 Test victims included none in England, and then by Stuart MacGill, who ended up with 208, but always missed out to Shane Warne in England.
Dilruwan Perera, the current Sri Lankan offspinner, has so far taken 153 Test wickets without any in England. Five others finished their careers with 100 or more Test wickets, but none in England: Bruce Reid of Australia (113), the Indian trio of Pragyan Ojha (113), Shivlal Yadav (102) and Irfan Pathan (100), and the South African slow left-armer Nicky Boje (100).
Rajasthan Royals fielded only one overseas player in their recent match against Delhi Capitals. Was this a first for the IPL? asked Savo Ceprnich from South Africa
That would indeed have been a record - but for the inconvenient fact that Rajasthan Royals' side for that match against Delhi Capitals last week actually included three overseas players - Liam Livingstone (England), Ish Sodhi (of New Zealand, although he was born in India) and Oshane Thomas (West Indies). ESPNcricinfo's database wizard Shiva Jayaraman has been able to find one solitary instance of a side fielding two overseas players in an IPL match (the maximum, of course, is four): Kolkata Knight Riders included Jacques Kallis and Eoin Morgan for their game against CSK in Chennai in 2011.
Which record, set in the inaugural Test in 1877, was broken last year by a Mexican? asked Debapriya Chakraborty from India
This was the record for the oldest international player on debut, held for nearly a century and a half by the Surrey slow bowler James Southerton, who was 49 years 119 days old when what is now recognised as the first Test of all began in Melbourne on March 15, 1877. However, during the South American Women's Championship last year, 53-year-old Sarah Hernandez played her first international, for Mexico against Brazil in Bogota, bagging a nine-ball duck. This was one of the first matches to benefit from the ICC ruling giving full international status to all T20 games between member nations.
The record for the youngest international player on debut has also changed hands recently: Samaira Dharnidharka was only 11 years 325 days old when she played for the United Arab Emirates in a T20 international against Thailand in Bangkok in January. She was about two months younger than her compatriot Vaishnave Mahesh, who had made her debut as a 12-year-old against China the previous week.