Have England ever been bowled out twice more quickly than they were in Perth?

Mitchell Starc improved his best bowling figures in his 100th Test, against West Indies, and improved them in his 101st Test at Perth. Has anyone done this later in a Test career? asked Ekamabaran Raveendran from India
Australia's Mitchell Starc took 6 for 9 - his best figures at the time - as West Indies were skittled for 27 in Kingston in July. That was his 100th Test - and in the first innings of his 101st, against England in Perth, Starc took seven wickets in a Test innings for the first time, finishing with 7 for 58.

Unsurprisingly, this is easily the latest stage of a career at which a player improved his best Test figures. Two Pakistanis come next: Wasim Akram had best figures of 6 for 62 after 50 Tests, but took 6 for 43 against New Zealand in his 51st, and improved that to 7 for 119 in his 52nd, in February 1994. Abdul Qadir started his 48th Test with a best return of 7 for 142, but took 7 for 96 against England at The Oval in August 1987, and improved that with 9 for 56 in his 49th, against England in Lahore in November 1987.

The latest a batter has improved his highest score in successive Tests was by Australia's Ricky Ponting in December 2003. After 72 Tests his highest score was 206, but he scored 242 against India in Adelaide in his 73rd, and improved that with 257 against them in Melbourne in his 74th match. His successor as captain, Michael Clarke, improved his previous-best of 151 with 166 in his 58th Test, against Pakistan in January 2010, then made 168 in his 59th, against New Zealand in Wellington two months later.

Travis Head scored a century on the second (last!) day in Perth. Has anyone else ever made a fourth-innings century before the end of the second day of a Test before? asked Martin Bennett from Australia
That stunning innings by Travis Head, which decisively wrenched the first Ashes Test Australia's way in Perth, was indeed the first time anyone had made a century in the fourth innings of a Test by the end of the second day. The only other time a team has reached 100 in the fourth innings on the second day of a Test was at Headingley in 1912, when South Africa made 105 for 7 against England - but the highest individual score was Louis Tancred's 38 not out (he was out for 39 next morning).

Head reached his century in just 69 balls, the fastest in the Ashes apart from Adam Gilchrist's 57-ball hundred at the WACA in Perth in December 2006. The only other faster century for Australia in a Test was in 67 balls, by Jack Gregory against South Africa in Johannesburg in November 1921. David Warner also reached three figures in 69 balls against India at the WACA in January 2012.

England faced only 67.3 overs in both innings in Perth. Have they ever been bowled out twice more quickly? asked Jon Morrison from England
England were bowled out twice in 67.3 overs - 405 balls - in the first Test in Perth. They have only been bowled out twice more quickly in Tests they lost on two occasions, the most recent of which was in March 1904, when they faced just 54.1 overs (325 deliveries) in being dismissed for 61 and 101 by Australia in Melbourne. Before that England were bowled out for 53 and 62 in 388 balls (97 four-ball overs) by Australia at Lord's in July 1888.

The fewest balls to be bowled out twice and lose by any side in a Test is 248 (49.3 five-ball overs) by South Africa (93 and 30) against England in Port Elizabeth (now Gqeberha) in February 1896.

Shai Hope has scored international centuries against all 11 possible Test-playing opponents. Has anyone else done this? asked Marlon Hoyte from Barbados
Shai Hope's 109 not out in an ODI against New Zealand in Napier last week completed this particular full set: he's scored individual international centuries (in Tests, ODIs or T20Is) against his 11 possible Test-playing opponents. Hope has scored four against England and India, three against Bangladesh, two against Pakistan and Sri Lanka, and one against Afghanistan, Australia, Ireland, New Zealand, South Africa and Zimbabwe. Only three of his hundreds have come in Tests: two against England at Headingley in August 2017, and one against India in Delhi in October.

Seven players have scored international centuries against ten of their 11 possible Test-playing opponents: Hashim Amla (no hundreds against Afghanistan), Shikhar Dhawan (none against England), Martin Guptill (missing Afghanistan), Mahela Jayawardene (Ireland), Virat Kohli (Ireland), Rohit Sharma (Ireland) and Marcus Trescothick (never played against Afghanistan).

How many times in Tests have a team won the toss, decided to bat first, been bowled out on the first day, have a deficit on the first innings but gone on to win the Test against the host nation, as South Africa did in the first Test in India? asked Andre Terblanche from South Africa
That's probably the most specific question I've ever received! South Africa did do all this in the first Test against India in Kolkata earlier this month, but actually it was the third time it had happened this year - Australia did it against West Indies in Bridgetown in June, and Ireland did it to beat Zimbabwe in Bulawayo in February. This particular set of circumstances appears to have happened 32 times in all in Tests now. The first time was in August 1882, when Australia beat England at The Oval in the match that spawned the Ashes legend.

There's also an update from a question a couple of weeks ago:
In this column I answered a question about the players with the best averages in their last 25 Tests. In calculating the answer we considered only players who had won at least 50 caps - but actually that probably wasn't the right way to do it. Two or three readers pointed out that the great England bowler Sydney Barnes took 170 wickets at 16.49 in his last 25 Tests - but he hadn't shown up in our searches as he played only 27 matches in all.

And so… we widened the search to include everyone's last 25 Tests, even if they only played 26 (or 27 like Barnes). The efforts of Jasprit Bumrah in the first Test against South Africa actually gave him a better average than Barnes ahead of the second match of the current series - 125 wickets at 16.38 - but that may change: and in any case there's someone who beats both of them, as the England offspinner Jim Laker took 120 wickets at 15.93 in the last 25 of his 46 Tests. Alec Bedser (136 at 18.68) and Curtly Ambrose (99 at 18.78) are fourth and fifth.

Among batters Don Bradman remains way out on top (3468 runs at 105.09), but the West Indian Clyde Walcott comes in second, with 2651 at 67.97 in the last 25 of his 44 Tests, ahead of Kane Williamson (currently 66.67), Kumar Sangakkara (64.05) and Andy Flower (63.83).