Has anyone averaged more than Muttiah Muralitharan's six wickets per Test?

Sri Lanka scored 345 in a recent one-day international, without anyone hitting a six - was this a record? asked Daniel Stockill from South Africa
Sri Lanka amassed 345 for 8 against West Indies in Hambantota last week without the aid of an individual six. That did break the previous record, which was England's 333 for 6 against Australia in Sydney in 2010-11. There have been four other ODI totals of 300-plus without an individual six, one each by South Africa (321 for 8 v Pakistan in Nairobi in 1996-97), India (309 for 5 v Australia in Kochi in 1997-98), Sri Lanka (307 for 6 v India in Colombo in 2009) and Pakistan (302 for 9 v India in Centurion in 2009-10).

The highest total without a six in T20Is is Australia's 164 for 6 against India in Sydney in 2018-19. That was equalled in July 2019 by Jersey, with 164 for 3 against Guernsey in Castel.

I spotted that Muttiah Muralitharan averaged more than six wickets per Test. Is this a record? asked Amitha Fernando from Sri Lanka
Muttiah Muralitharan took exactly 800 wickets in his 133 Tests, an average of 6.01 per match. Given a minimum of 50 wickets, that's a modern-day record, although it is exceeded by four bowlers who played before the First World War. Best of all is England's SF Barnes, whose 189 wickets came in just 27 matches, at an average of exactly seven per Test. The 19th-century trio of Jack Ferris (6.77 wickets per Test), Tom Richardson (6.28) and George Lohmann (6.22) are the others who shade Murali.

Leading the way for current bowlers is Yasir Shah, who has so far taken 213 wickets in 39 Tests, an average of 5.46 per match, which puts him tenth overall. R Ashwin is 15th, with 5.14 wickets per Test (he had 365 from 71 matches after the first Test in New Zealand).

How many people have scored a hundred and a fifty in their debut Test? asked Jamie Morton from England
Thirteen men have started their Test careers with a hundred and a half-century in the same game, the first being KS Ranjitsinhji, who made 62 and 154 not out for England against Australia at Old Trafford in 1896.

The list also includes the unfortunate Rodney Redmond, who made 107 and 56 in his only Test, for New Zealand against Pakistan in Auckland in 1972-73. Pakistan's Azhar Mahmood, with 128 and 50, both not out, against South Africa in Rawalpindi in 1997-98, is the only one to do it without being dismissed. The most recent batsman to start his Test career this way was Faf du Plessis, with 78 and 110 not out for South Africa against Australia in Adelaide in 2012-13.

Tamil Nadu won a T20 game earlier this season with 15.5 overs to spare. Is this the most in any T20 match? asked Ram Prakash Mehta from India
Tamil Nadu needed only 4.1 overs to surpass Manipur's 55 all out in their Syed Mushtaq Ali Trophy match in Thiruvananthapuram last November, winning with 95 balls to spare. The same day, in Surat, Gujarat bowled Sikkim out for 55 and won with 94 balls to spare.

But the overall list is headed by two official T20Is from last year's Romania Cup. Austria beat Turkey with 104 balls to spare after bowling them out for 32 in Ilfov County, two days after Luxembourg skittled them for 28 (also in Ilfov) and won with 101 deliveries in hand. In the Mushtaq Ali Trophy in 2009-10, Jharkhand beat Tripura (30 all out) with 100 balls to spare in Dhanbad, while in Kampala in May 2019, Namibia had 97 balls remaining when they overhauled Botswana's 46.

Mushfiqur Rahim has now scored three Test double-centuries, yet averages below 40. Is this the lowest? asked Thomas from Germany
Mushfiqur Rahim scored 203 not out - his third Test double-century - in the one-off match against Zimbabwe in Mirpur. That left him with an average of 36.77 - indeed the lowest for anyone with three 200s. Next comes Brendon McCullum, who averaged 38.64 despite hitting four scores of 200 or more, one of them a triple-century. The only other batsman with three or more who averaged under 40 was Sri Lanka's Marvan Atapattu (39.02), who hit no fewer than six Test double-centuries.

The lowest average of anyone who scored two Test double-hundreds is 31.47, by India's Vinoo Mankad - both against New Zealand at home in 1955-56 - while the lowest for anyone with one is the 18.74 of Australia's Jason Gillespie, who hit 201 not out after going in as nightwatchman in what turned out to be his final Test, against Bangladesh in Chittagong (now Chattogram) in 2005-06.

And finally there's an update to last week's question about tall New Zealand Test players, from the Indian journalist Bipin Dani:
"I spoke to Kerry Walmsley, who is mentioned at the end of last week's article, and he said: 'I'm not quite as tall as Kyle Jamieson. I'm six foot six inches. I have met Kyle, as I am a selector for the Auckland Aces. I haven't spoken much about his height to be honest - it's just nice to look up to someone when you're as tall as I am!"