How often has a player scored a hundred and a duck in the same Test?

In a recent IPL game, Kieron Pollard was Player of the Match though he only meaningfully participated in 14 deliveries in the entire game. What's the lowest number by someone who received the award in a T20 match? asked Nathan from Australia
You're right that Kieron Pollard was only actively involved in 14 deliveries during Mumbai Indians' IPL victory over Punjab Kings in Abu Dhabi on September 28 - he faced seven balls, bowled one over, and took one catch. Pollard was the third man to win the award having been involved in only 14 deliveries in an IPL game, after Nuwan Kulasekera, for Chennai Super Kings against Pune Warriors in Chennai in 2012, and Munaf Patel, for Mumbai Indians against Pune Warriors in Mumbai in 2011.

But they're not top: there are two cases of 13 by IPL match award-winners - Mark Boucher for Royal Challengers Bangalore against Kolkata Knight Riders in Durban in 2009, and James Faulkner for Rajasthan Royals against KKR in Abu Dhabi in 2014. Boucher faced 13 balls and didn't take a catch, but he was keeping wicket, so would undoubtedly have been actively involved in rather more deliveries.

The record for all T20 matches, as far as we can establish, is active involvement in just eight deliveries before lifting the match award. This was achieved by the South African David Wiese, for Titans against Dolphins in Centurion in 2012-13, and Dinesh Karthik for India vs Bangladesh in the Nidahas Trophy final in Colombo in March 2018. The scorecard for Yorkshire against Leicestershire at Headingley in 2014 suggests that Adam Lyth was involved in only eight deliveries, but he shared the award in that match with Aaron Finch after a spectacular relayed boundary catch - and since Finch ended up with the ball, Lyth doesn't feature on the scorecard. But he thus played a major role in at least one other ball in addition to the eight he faced while batting.

There are a few caveats with these figures. First, we only have full statistics for around 70% of T20 games. Most significantly, we can only consider scorecard entries - so a player who, for example, received the award in part for outstanding fielding wouldn't show up. We've also ignored matches reduced by rain or other reasons. So Shiva Jayaraman of ESPNcricinfo's stats team had a fun time totting up the rest!

What's the highest Test score by a batter outside his home country? asked Kevin Millard from England
The highest individual score away from home in a Test remains Hanif Mohammad's epic match-saving 337 - in a record 970 minutes - for Pakistan against West Indies in Bridgetown in 1957-58. That just edged out Wally Hammond's 336 not out for England against New Zealand in Auckland in 1932-33.

In all, there have been 11 triple-centuries by batters in overseas Tests, two of them by Don Bradman at Headingley, in 1930 and in 1934. (There are 12 if you count Azhar Ali's unbeaten 302 for Pakistan against West Indies in a "home" Test in Dubai in 2016-17.)

How often has a player scored a hundred and a duck in the same Test? asked Bevan McAllister from New Zealand
In all, this has now happened 172 times in Test matches. The most recent instance involved Najmul Hossain of Bangladesh, against Sri Lanka in Pallekele in April. The first time it happened was in the first ever Test in England, at The Oval in 1880, when Australia's captain, Billy Murdoch, made 0 and 153 not out.

Two men have done it three times: Shivnarine Chanderpaul for West Indies, and England's Andrew Strauss. A further 22 batters managed it on two occasions.

I noticed that Matthew Hayden outscored Pakistan's match aggregate on his own in his only innings of a Test in 2002. Has anyone else done this? asked Abdul Shabeer from India
Matthew Hayden was the fifth man to exceed the opposition's aggregate score on his own in his only innings of a Test with a definite result: Pakistan made 53 and 59, while Hayden hit 119 for Australia in Sharjah in 2002-03. The others to achieve this were Bobby Abel (120) for England against South Africa (43 and 47) in Cape Town in 1888-89, Len Hutton (364) for England vs Australia (123 and 201) at The Oval in 1938, Don Bradman (185) for Australia vs India (98 and 58) in Brisbane in 1947-48, and Inzamam-ul-Haq (329) for Pakistan vs New Zealand (73 and 246) in Lahore in 2002.

For batters who went in twice, Justin Langer (191 and 97) outscored Pakistan (179 and 72) in Perth in 2004-05, while Gordon Greenidge (134 and 101) made more than England (71 and 126) managed at Old Trafford in 1976, as did Patsy Hendren (169 and 45) vs Australia (122 and 66) in Brisbane and Dimuth Karunaratne (158 not out and 60) vs South Africa (126 and 73) in Galle.

I read that Dwight Eisenhower was the only American president to attend a Test match. But is it right that he was also a member of MCC? asked Syed Iliyas Hussain from England
President Eisenhower witnessed at least part of a somewhat somnolent day's play in the third Test between Pakistan and Australia in Karachi in 1959-60. During the day, which was uninterrupted apart from a break while the teams were introduced to Eisenhower, Pakistan scored 104 for 5 in 65 overs, so it's unlikely the distinguished visitor was terribly excited.

This was the last Test played on a matting pitch. Australia's captain in that match, Richie Benaud, in his book Willow Patterns, wrote that Eisenhower "made the remark that he thought this cricket game was supposed to be played on grass rather than mat. The Pakistan president [Mohammed Ayub Khan] then said, 'This is the last time a Test match will be played on matting in this country', and he gave orders to that effect."

It's also true that Eisenhower was a member of the Marylebone Cricket Club, although it wasn't because of any particular liking for the game. General Eisenhower, as he then was, was one of 11 leaders given honorary life membership of MCC in 1946, in recognition of their efforts in the Second World War. Eisenhower was the only American; the other ten were all British. Winston Churchill, the wartime prime minister, was one of those honoured, along with the top brass from the army, navy and air force. Arguably the most famous of the others were Field Marshal Montgomery of Alamein, and Admiral Lord Louis Mountbatten, the Queen's second cousin and uncle of the Duke of Edinburgh.