How often has a Test innings started with one captain bowling to the other?

India's second innings in the WTC final started with Pat Cummins bowling to Rohit Sharma. How often has a Test innings started with one captain bowling to the other? asked Mahesh Dharmendra from India
You're right that India's chase in the World Test Championship final at The Oval at the weekend started with captain Pat Cummins bowling to skipper Rohit Sharma.

This pair had already done this twice already earlier in the year, in Nagpur and in Delhi in February. They were the 14th pair of captains to start a Test innings in direct opposition; The Oval was the 39th instance overall. The most recent one before Cummins/Rohit came in Mirpur late in 2018, when Shakib Al Hasan of Bangladesh bowled the first ball of both West Indian innings to his opposite number Kraigg Brathwaite.

The first pair to do it were Arthur Gilligan and Herbie Taylor, in the match at Edgbaston in 1924 in which England bowled South Africa out for 30.

I heard during the commentary that only two players in the World Test Championship final were under 30 - was this a first for a Test match? asked James Phillips from England
The two under-28s in the World Test Championship final at The Oval were the precocious pair of Shubman Gill, who's 23, and Cameron Green (24).

This was the 12th Test match to include only two players under the age of 28, but the third this year: Australians Todd Murphy (22) and Matt Renshaw featured against India in Nagpur in February, while in the match between New Zealand and Sri Lanka in Christchurch in March the only under-28s were Asitha Fernando (25) and Lahiru Kumara (26).

However, back in 1926 there were two Tests in the Ashes series in England that included just one man under the age of 28: Percy Chapman, 25, was the only "youngster" in the first Test at Trent Bridge and the third at Headingley. All the Australians in those matches were over 28: their opening partnership in the second Test at Lord's (where Chapman was joined for England by 21-year-old Harold Larwood), was the last occasion before David Warner and Usman Khawaja in the WTC final that Australia's openers were both at least 36 - Warren Bardsley was 43 and Bert "Horseshoe" Collins 37.

England lost wickets from the first two balls of an ODI in 2020. How many times has this happened - and has any team won after doing it? asked Michael Granger from England
In the match you're talking about at Old Trafford in September 2020, Jason Roy and Joe Root were dismissed by the first two balls of the match, from Mitchell Starc. Even so, England looked like winning that game, before a sixth-wicket partnership of 212 between Alex Carey and Glenn Maxwell turned the tables.

There have been four other ODIs in which wickets fell to the first two balls of an innings, and only one of them was then won: New Zealand bounced back to beat Ireland in Malahide in July 2022 despite losing Martin Guptill and Will Young from the first two balls of their chase, bowled by Mark Adair.

There have also been six T20Is in which wickets fell to the first two deliveries. Five of them were lost, and the other ended as a no-result. And apart from Ireland's win mentioned above, there have been four ODIs and 11 T20s won by a team which was 0 for 2 early on (not necessarily after two balls).

Kumar Sangakkara and Ricky Ponting both ended their Test careers with their last two three-figure scores being double-centuries. Are there any others? asked Tim Malin from Australia
You're right that Kumar Sangakkara's last two Test centuries were doubles - 221 against Pakistan in Galle in August 2014 and 203 vs New Zealand in Wellington in January 2015. But Ricky Ponting doesn't quite qualify for this list - the 40th of his 41 Test hundreds was 134 against India in Sydney in 2011-12 (he did make 221 not long afterwards, in Adelaide).

Three other batters achieved this impressive farewell feat. Vinoo Mankad's last two Test centuries for India were 223 in Bombay and 231 in Madras (now Chennai) against New Zealand in 1955-56. Pakistan's Qasim Umar made only three Test centuries, but the last two were 210 against India in Faisalabad in 1984-85, and 206 against Sri Lanka in 1985-86, also in Faisalabad. And the New Zealander Stephen Fleming signed off with 202 against Bangladesh in Chattogram in 2004-05, and 262 vs South Africa in Cape Town in 2005-06.

What is the longest duck in Test cricket, by balls faced? asked Alex Cardew from England
The longest duck in a Test match, by any measure, was achieved by the New Zealand fast bowler Geoff Allott against South Africa in Auckland in 1998-99. Allott lasted for 77 balls, and 101 minutes, before giving a catch off Jacques Kallis: he'd helped Chris Harris, who finished unbeaten on 68, add 32 for the last wicket.

Jimmy Anderson had a 55-ball duck in 2014, which just failed to stave off defeat by Sri Lanka at Headingley - he was out from the penultimate ball of the match, after batting for 81 minutes). And the West Indian fast bowler Miguel Cummins came close to Allott's time record against India in Antigua in 2019 - he survived for 95 minutes (45 balls) before falling for nought, and hasn't played another Test since.