What is the closest Test series ever played, by average runs per wicket scored by each team?

What is the closest Test series ever played, in terms of average runs per wicket scored by the two teams? asked Arpit Agarwal from India
There have so far been 506 series comprising three or more Tests. The closest of all in this particular respect was the three-match Border-Gavaskar Trophy series between India and Australia in 2000-01, which included India's famous victory in Kolkata after following on, mainly thanks to the heroics of VVS Laxman and Rahul Dravid. India, who ended up winning the series 2-1, averaged 34.164 runs per wicket overall, while Australia averaged 34.160 - a difference of just four-thousandths of a run.

When West Indies beat India 2-1 at home in 1975-76, they averaged 37.32 runs per wicket against 37.34, a negative difference of 0.02. And when England (34.04) and South Africa (34.10) drew 1-1 in England in 1994, the difference was 0.06 of a run.

At the other end of the scale, in the five-match Ashes series of 2009, England won 2-1 despite averaging 34.15 runs per wicket to Australia's 40.65, a record negative difference of 6.49. England also beat South Africa 2-1 in 1998 despite averaging 29.34 runs per wicket to their opponents' 35.37 (a difference of 6.03). And back in 1891-92, Australia (21.69) beat England (27.68) 2-1, despite a negative difference of 5.99 runs per wicket.

Has anyone ever been out for a pair in a Test by being lbw twice, offering no shot? asked Graham Clarke from Australia
I believe the only man to suffer this strokeless fate was the Australian Ken "Slasher" Mackay, against India in Kanpur in 1959-60. In the first innings he was lbw padding up to the offspinner Jasu Patel, who was on his way to figures of 9 for 69 (and 14 for 124 in the match): you can see that dismissal in this clip (Mackay is the second of the two left-handers dismissed). In the second innings Mackay escaped Patel, but offered no shot to Polly Umrigar, who was also bowling offbreaks, and was out for another duck as India neared their first-ever Test victory over Australia.

Mackay doesn't describe the dismissals in detail in his 1964 autobiography, Slasher Opens Up, although he does say that Patel and Umrigar "presented me with an appropriate Christmas gift, a pair of ducks" (the match ended on Christmas Eve).

I was lucky enough to see Scotland beat Zimbabwe the other day. How often have Scotland beaten a Test-playing nation in ODIs or T20s? asked Kevin McKenzie from Scotland
Scotland's seven-run victory over Zimbabwe in Edinburgh last week was only their third victory over a Test-playing nation in a T20I. They also beat Bangladesh in The Hague in July 2012, and Ireland in Al Amerat in February 2019. (And they beat Ireland twice in 2015, before they gained Test status.) In all, Scotland have won 30 of their 67 T20Is, including seven victories over Netherlands and five against Kenya.

In one-day internationals, Scotland have recorded three victories over Test-playing nations, defeating Zimbabwe in Edinburgh in June 2017 and, the following year, famously beating England at The Grange as well. They also defeated Afghanistan in Bulawayo in March 2018 - this was after Afghanistan had been elevated to Test status, but before they'd actually played a Test.

In all, Scotland have won 43 of their 117 ODIs, including four against Ireland and three more against Afghanistan before they had Test status. They have beaten Canada and Netherlands seven times each, and Kenya, Papua New Guinea and United Arab Emirates five times.

I noticed there were 19 lbws in the Championship match between Durham and Essex this season. Was this anywhere near a record? asked Brian Turner from England
You're right that there were 19 lbw dismissals in the County Championship match between Durham and Essex in Chester-le-Street in May 2021. That turns out to be a new Championship record, beating 18, which had happened five times previously - all since 2010 - including a month beforehand, in Cardiff, in the match between Glamorgan and Sussex. Nine of those fell to Ollie Robinson, which equalled the first-class record for a single bowler.

There had been two previous instances of 19 lbws in a match, both in India, but the overall first-class record is two cases of 20 - both at the new Providence Stadium in Guyana. In 2011, there were 20 lbws in the Test between West Indies and Pakistan there; and in 2019-20 there were 20 more in the match between Guyana and Jamaica.

How many people have lost a Test in which they scored a century in each innings? asked SM Nazmus Shakib from Bangladesh
Eleven men have suffered this bittersweet experience in a Test match. The first was the great England opener Herbert Sutcliffe, whose 176 and 127 were not enough to stave off defeat against Australia in Melbourne in 1924-25. The most recent instance was by Brendan Taylor, for Zimbabwe against Bangladesh in Mirpur in 2018-19.

Brian Lara hit 221 and 130 against Sri Lanka in Colombo in 2001-02 - but West Indies still lost. Lara's 351 runs in that match is a record for a Test defeat, just ahead of Andy Flower's 341 - he scored 142 and 199 not out - for Zimbabwe against South Africa in Harare two months beforehand, in September 2001. For that list - which features Lara four times in the top 30 - click here.

One of the odder stats concerns Andrew Strauss. England never lost any of the 19 matches in which he scored a century - but they did lose the Test in which he made two, against India in Chennai in 2008-09. For the full list, click here.