What are the highest and lowest Test totals featuring four or more ducks?

Jimmy Anderson and Stuart Broad, with a combined age of 74, opened the bowling in the first Test against India. Was this anywhere near a record? asked Phil Wiseman from England
The combined age of England's new-ball pair at Trent Bridge in the first Test - Jimmy Anderson turned 39 less than a fortnight ago, while Stuart Broad was 35 in June - was not quite the oldest for England. Back in 1947-48, Harold Butler (almost 35) and Gubby Allen, the 45-year-old captain, took the new ball against West Indies in Port-of-Spain.

Butler and Allen were the oldest pair of fast(ish) bowlers to open any Test innings, but there have been three older combinations involving spinners. The remarkable Australian slow left-armer Bert Ironmonger features in the top two: he was 48 when he took the new ball with medium-pacer Ron Oxenham (39) in the second innings against West Indies in Sydney in 1930-31. Two seasons earlier, Ironmonger (making his debut at 46) had opened with legspinner Clarrie Grimmett (nearly 37) against England in Brisbane, again in the second innings. The other instance came for South Africa at Lord's in 1951 when, with England needing just 16 to win, skipper Dudley Nourse (40) opened the bowling with Eric Rowan (41).

The oldest new-ball pair since that 1951 match involved two more spinners - Rangana Herath (40) and Dilruwan Perera (who celebrated his 36th birthday during the match) for Sri Lanka against South Africa in Colombo in 2018.

I believe that "caught Marsh bowled Lillee" is still the most prolific fielder-bowler combination in Tests. Is anyone close, and who holds the records for one-day and T20I? asked Kieron McKenna from Australia
You're right that "c Marsh b Lillee" is still top of this list in Tests: there were 95 such dismissals. Also for Australia, "c Gilchrist b McGrath" came close with 90, but the leading current combination is some way down the list - there have been 52 instances of "c de Kock b Rabada" so far. That assumes that New Zealand's BJ Watling really has retired - he caught 75 off Tim Southee, 57 off Trent Boult, and 55 off Neil Wagner (all including a few in the field, not as wicketkeeper).

The record in ODIs is 75 instances of "c Boucher b Ntini", just ahead of Glenn McGrath and Adam Gilchrist, who combined for 72 catches - and, surprisingly, a stumping. The victim was New Zealand's Craig McMillan, who strayed out of his crease in Wellington in 2004-05. Some suggested McGrath might not have been too pleased that the keeper had moved up to the stumps, after spotting McMillan leaving his ground: "I believe he is trying to have it withdrawn from the record books," joked Gilchrist a few years later.

In T20Is the most prolific pair is Mushfiqur Rahim and Shakib Al Hasan of Bangladesh, who have so far shared six catches and 11 stumpings; the Pakistan wicketkeeper Kamran Akmal took 14 stumpings and one catch off Saeed Ajmal.

There were four ducks in England's total of 183 on the first day of the first Test. I was wondering what the highest and lowest Test totals were with four or more ducks? asked Mrinal Sinha from India
The four ducks in England's first-innings 183 at Trent Bridge was a long way from either record. The highest total which has included four players who were out for nought was 501, by West Indies against India in Georgetown in 2002 - the local pair of Carl Hooper (233) and Shivnarine Chanderpaul (140) made up for the other failures. When South Africa totalled 429 against Bangladesh in Centurion in 2008-09, their total included five ducks (and centuries from Ashwell Prince and Mark Boucher).

The lowest is, perhaps not surprisingly, the lowest Test total of all - New Zealand's 26 against England in Auckland in 1954-55 included four ducks (and a highest score of 11).

Further to the recent questions about birthday performances, has anyone scored a T20I century on the big day? asked Tim Johnstone from New Zealand
The only man to achieve this distinction is Australia's David Warner, who smacked 100 not out from 56 balls against Sri Lanka in Adelaide on his 33rd birthday in October 2019. The next-highest is a more modest 60 not out, by Yuvraj Singh for India against Sri Lanka in Mohali on his 28th birthday in December 2009 (he also took 3 for 23).

The highest score in one-day internationals by a player on his birthday is 134, by Sachin Tendulkar for India against Australia in Sharjah on the day he turned 25 in April 1998. Three others - Ross Taylor (131 not out on his 27th birthday in March 2011), Sanath Jayasuriya (130 on his 39th in June 2008) and Vinod Kambli (100 not out on his 21st in January 1993) - have scored ODI centuries on their birthdays.

Who holds the record for the most runs before lunch - in Tests and in first-class cricket? asked Keith Waterfield from Scotland
The most runs in a pre-lunch session in a Test match is 130, by England's Ben Stokes, who zoomed from 74 to 204 on the second morning against South Africa in Cape Town in 2015-16. He finished with 258, including 30 fours and 11 sixes. Stokes beat the old record of 123, set by Les Ames, also for England, against South Africa at The Oval in 1935.

The most on the first day of a Test match is 112, by Charlie Macartney for Australia against England at Headingley in 1926. Macartney came in at No. 3, after Warren Bardsley had been dismissed by the first ball of the game. There have been only five other centuries before lunch on the first day of any Test.

The first-class record is held by the South African Test player Russell Endean, who smashed a scarcely believable 197 runs before lunch on the first day for Transvaal against Orange Free State in Johannesburg in 1954-55. One explanation, though, is that it was a three-hour pre-lunch session. Endean was deprived of the chance of a unique double-century before lunch when his batting partner, Cyril Tayfield (the brother of Test offspinner Hugh), saw out the last over before the interval. That onslaught broke the mark set by the magical Indian KS Ranjitsinhji, who stroked 180 runs before a declaration at lunch on the second day of Sussex's match against Surrey in Hastings in 1902.