## 48

A special post to celebrate my 48th birthday.

This post looks at the number 48 for reasons which will become apparent.

THE NUMBER 48

48 has the most factors of any number under 50, nine other than itself (24, 16, 12, 8, 6, 4, 3, 2, 1). It is therefore an ‘abundant number’ – abundant numbers are those whose factors add up to more than the number itself, while deficient numbers have factors that add up to less than the number itself, and perfect numbers have factors that add up to exactly that number. In the case of 48 its factors add up to 76, giving it an abundance of 1.583.

48 squared is 2,304, and 2*3!*4+0 = 48, while 48 cubed is 110,592, and ((11+0)*5)-(9-2) = 48.

48 IN CRICKET

As a cricket fan I look at occurrences of the number 48 in the game. In 1907 Colin Blythe, Kent’s left arm spinner of the era, conceded just 48 runs while claiming 17 Northamptonshire wickets in one single day’s play. This is the cheapest ever match haul of 17 wickets, and the joint most ever taken in a day in first class cricket.

In the 1925 first class season Nottinghamshire skipper Arthur Carr hit 48 sixes. The following season he would captain England in the first four matches of the Ashes series, before Percy Chapman was brought in as skipper for the last match of the series.

In 1896, WG Grace scored 301 against Sussex at the age of 48, still the oldest ever first class triple centurion.

In the ‘Jubilee Match’ early in 1980 Ian Botham claimed 7-48 in India’s second innings, noteworthy as he had already taken 6-58 and scored 114*, the first man to combine a century and a ten wicket match haul at test level, although a few months earlier Enid Bakewell had achieved the same feat for England Women against West Indies Women.

At Edgbaston in 1981 against Australia England captain Mike Brearley managed the highest individual score of the match with 48 in England’s first innings. This was the first completed test match since 1935 to not feature an individual half century. Australia had the better of most of it, but then collapsed from 87-3 to 121 all out in the final innings to lose by 29 runs.

Why I have I produced a post the text part of which focuses on the number 48? Because today is my 48th birthday.

PHOTOGRAPH

I have decided to select a single image with which to end this post…

## Surrey In Control

A look at Surrey v Gloucestershire, a mathematical teaser, an article and some photographs.

Although I am giving some details from a cricket match and have used that as my title this is not exclusively a cricket article. I also wish to take the opportunity to welcome any new readers who may come to the site as a result of an article about me in the Lynn News, a screenshot of which is the feature image of this post. Also, I am going off on holiday later today, to northern Scotland (I will be travelling on an overnight train for some of the journey), and posting may be limited for the next eight days for that reason.

SURREY V GLOUCESTERSHIRE

This match has seen some dramatic swings in the just over four sessions it has been going for. At 105-1 Surrey looked in control, at 183-5 the pendulum had swung towards Gloucestershire, and by the close yesterday at 285-5 it was evenly poised. Hashim Amla, the former South African international, had a ton to his name by the close and Jamie Overton at n07 reached 50 off the final ball of the day. Overton fell to the first ball of the morning, which brought Sean Abbott to the crease. Gloucestershire then made a very odd call, seeking to keep Amla off strike to attack Abbott who is a decent lower order batter and had been sent in ahead of someone with 10,000 FC career runs to his name. This backfired horribly, Abbott making 40 out of a stand of 61. His dismissal at 346 brought Rikki Clarke (he of the 10,000 FC runs) to the crease, and at the moment he and Amla are still together. The score is now 385-7, with Amla closing in on 150. To come are the two specialist spinners, Virdi and Moriarty. Gloucestershire have been excellent thus far this season, but it is hard to see any way for them to win this game from here.

A MATHEMATICAL TEASER

I regularly feature problems I have encountered on the website http://www.brilliant.org here, sometimes adapated, and I do so again today:

A small additional question: can you identify the four mathematicians after whom Carl, Leonhard, Emmy and Sophie are named (answers to both parts of this question in my next post).

PHOTOGRAPHS

I always include photographs in my blog posts, and I have some for you now:

## England’s Number Three Slot

A look at the England number three position where for once there are a number of good options, the reverse of the usual situation through my time following the team.

In this post I deal with a topic well known to all who have followed the England men’s cricket team for any length of time: who will bat at number three going forward? However, this is time the question is apposite for the reverse of the usual reason.

ENGLAND’S NUMBER THREE

The number three position has traditionally been a very tough one for England to fill. In the 1960s it was usually either Dexter at three and Barrington at four or vice versa, but since then it has been an almost continual problem. David Steele did well there in 1975-6, Chris Tavare did what was asked of him in the early 1980s – namely give the order something in the way of backbone, David Gower had one superb series there against Australia in 1985, Michael Vaughan made the position his own in the early 2000s, and a decade later Jonathan Trott was as good a number three as England have had in my lifetime. More recently we have seen Joe Denly there playing a holding role to ensure that the opposition bowlers were not instantly into England’s middle order, and this winter in India with Burns recently returned from a layoff we saw Jonathan Bairstow batting there and failing horribly. Suddenly however there appear to be a wealth of options.

NUMBER THREE PRESENT AND FUTURE

The current incumbent is Zak Crawley, who will bat there against New Zealand behind the opening pair of Burns and Sibley. Crawley scored 267 from no three against Pakistan last summer, but has done little since with Lasith Embuldeniya having his number in the Sri Lanka series, and save for one fifty India giving him a thoroughly miserable time. If Crawley does not produce significant runs against NZ then his place is definitely in jeopardy. There are at least three players who are in the running for his slot by dint of batting superbly there for their counties:

• Tom Abell: The Somerset captain was placed at number three with two other Toms, Banton and Lammonby, opening at the start of this season. Banton has already been dropped from opening though did subsequently feature as keeper in one match. Lammonby has played one decent innings this season, and his strong start in first class cricket (459 runs at 51.00 in his first six matches) has been badly tarnished. He is young enough to bounce back, but currently an England call up looks a long way away. Abell at number three, and often with the innings beginning to disintegrate around him has scored over 500 runs this season at an average of better than 60 and is looking every inch an England number three in waiting.
• James Bracey: The Gloucestershire batter and occasional wicket keeper was on the fringes of the England squad last season, spending a lot of time in bio-secure bubbles as a reserve. He has continued to impress from number three this season and has been named in the squad for the New Zealand series.
• Nick Gubbins: The gritty Middlesex batter has had a superb season batting at three, and his masterly 124 on the final day of the last match against Surrey turned a situation in which Middlesex were hoping to avoid defeat and fearing the worst into one in which Middlesex had a definite sniff of victory before the rain made its final intervention, rendering the chase just too steep.

Of the three named, Abell and Bracey (already in the squad) are both in with a strong chance of being selected. Gubbins is an outside shot, but there seems little doubt that given the opportunity he could do a solid job for England.

SOLUTION TO A TEASER

In my last post I included the following teaser, adapted from brilliant.org:

This post looks at such play as there has been in the latest round of championship fixtures, which have been heavily affected by the weather â€“ there have been bands of rain sweeping across Britain, coming in from the west although by some freak my corner of northwest Norfolk has largely escaped, with only Friday being really wet.

THE EARLY GAME

Hampshire v Leciestershire was supposed to run from Wednesday to Saturday. In fact only a tiny amount of cricket was possible. Hampshire scored 233 in the first innings, bowled Leicestershire out for 84, and forfeited their second innings, leaving Leicestershire 22 overs to score 150 to win. Leicestershire made no serious effort to take on this chase on the game was drawn.

AROUND THE GROUNDS

A number of games have been so badly hammered by the weather that there is no real chance of a result. Kent v Glamorgan and Northamptonshire v Lancashire have already been confirmed as draws, though the former saw an amazing performance from Darren Stevens. Kent at low water mark were 93-7 in their first innings, but ended up tallying 307. Stevens, at the age of 45 scored 190, with 15 sixes and 15 fours. He shared a ninth wicket stand of 166 with Miguel Cummins, whose share of that partnership was one not out. Stevens then added the wicket of Marnus Labuschagne to his share of the spoils. Nottinghamshire v Worcestershire, Durham v Derbyshire and Essex v Warwickshire are all headed the same way, and it will take miracles for any of those games to yield definite results. Gloucestershire v Somerset is likely to be a draw as well, but the way Gloucestershire are collapsing means that it is not dead yet â€“ Somerset scored 300-8 declared, with Tom Abell scoring his first century of the season (overall he now has over 500 runs at an average of more than 60 for the season), and Gloucestershire are 27-6 in reply. That leaves the London derby, in which the Surrey openers, Burns and Stoneman have been utterly dominant â€“ they put on 135 in each innings, equalling the highest ever identical opening stands in FC history, a record set in 1979 by Kepler Wessels and John Barclay of Sussex. Surrey declared just before lunch today at 259-2, setting Middlesex 290 (full scores, Surrey 190 and 259-2 dec, Middlesex 160 and 28-1). Burns completed his first century of the season.

A POTENTIAL ENGLAND NO3

Somerset started this season with a plan for their top order â€“ three guys all answering to Tom, Lammonby, Banton and Abell at 1,2 and 3. Banton has already fallen by the wayside, his career as a first class opener over almost before it began. Lammonby has managed one good score all season, and his dismissal in the game currently in progress, run out going for one that was never there, was the product of a scrambled mind. The one to prosper has been Tom Abell who is handling batting at no3 like one born to perform that task. Crawley remains the man in possession for England, but if he does not score runs against NZ then England may decide that change is needed, and Abell would surely be the logical person to turn to in that case: he is just entering the prime years of a cricketerâ€™s career, he is batting superbly at no3 and several of his best scores have come in very testing situations, all of which give him the appearance of a test no3 in waiting.

A MATHEMATICAL TEASER

This problem comes from brilliant.org, but I have added a bonus element as well as slightly tweaking the setting:

A brief note on â€˜concatenationâ€™: in a mathematical context it is represented by an equals sign flipped through 90 degrees and it means that the two digits between which it appears are joined to form a single number.

Additional â€˜bonusâ€™ question: Once you have worked out the answer to the main problem, if one of the two sums cannot be solved under the given conditions what extra operations would need to be permitted to make it solvable? Full explanation in my next blog post.

The first part is quite easy: problem A is resolved simply by using the concatenation symbol to turn the 1 and 2 into 12 and adding the three to get 15. Problem B cannot be resolved (the biggest number you can get without concatenation is 7 (3 x 2 +1 = 6+1 = 7) and the only numbers you can generate by concatenating are 321 (all numbers used, obviously hopeless), 32 which leaves with with one which enables you to finish with either 31, 32 or 33 and 21, which leaves the three, which appears at the beginning. The only integers you can generate with the three and the 21 this way round are 24 or -18.

For the second part you need to allow a minimum of three more operators: square roots and floor or ceiling functions (you only need the latter, but the two operations come as a package). The floor and ceiling functions are respectively the nearest integer below an actual answer and the nearest integer above an actual answer. With these you can concatenate the two and the one to form 21, the square root of 21 is approximately 4.58, the ceiling function of which is 5, and you have the three unused to multiply and make 15.

PHOTOGRAPHS

My usual sign off…

## County Championship Washouts

This post looks at such play as there has been in the latest round of championship fixtures, which have been heavily affected by the weather – there have been bands of rain sweeping across Britain, coming in from the west although by some freak my corner of northwest Norfolk has largely escaped, with only Friday being really wet.

THE EARLY GAME

Hampshire v Leciestershire was supposed to run from Wednesday to Saturday. In fact only a tiny amount of cricket was possible. Hampshire scored 233 in the first innings, bowled Leicestershire out for 84, and forfeited their second innings, leaving Leicestershire 22 overs to score 150 to win. Leicestershire made no serious effort to take on this chase on the game was drawn.

AROUND THE GROUNDS

A number of games have been so badly hammered by the weather that there is no real chance of a result. Kent v Glamorgan and Northamptonshire v Lancashire have already been confirmed as draws, though the former saw an amazing performance from Darren Stevens. Kent at low water mark were 93-7 in their first innings, but ended up tallying 307. Stevens, at the age of 45 scored 190, with 15 sixes and 15 fours. He shared a ninth wicket stand of 166 with Miguel Cummins, whose share of that partnership was one not out. Stevens then added the wicket of Marnus Labuschagne to his share of the spoils. Nottinghamshire v Worcestershire, Durham v Derbyshire and Essex v Warwickshire are all headed the same way, and it will take miracles for any of those games to yield definite results. Gloucestershire v Somerset is likely to be a draw as well, but the way Gloucestershire are collapsing means that it is not dead yet – Somerset scored 300-8 declared, with Tom Abell scoring his first century of the season (overall he now has over 500 runs at an average of more than 60 for the season), and Gloucestershire are 27-6 in reply. That leaves the London derby, in which the Surrey openers, Burns and Stoneman have been utterly dominant – they put on 135 in each innings, equalling the highest ever identical opening stands in FC history, a record set in 1979 by Kepler Wessels and John Barclay of Sussex. Surrey declared just before lunch today at 259-2, setting Middlesex 290 (full scores, Surrey 190 and 259-2 dec, Middlesex 160 and 28-1). Burns completed his first century of the season.

A POTENTIAL ENGLAND NO3

Somerset started this season with a plan for their top order – three guys all answering to Tom, Lammonby, Banton and Abell at 1,2 and 3. Banton has already fallen by the wayside, his career as a first class opener over almost before it began. Lammonby has managed one good score all season, and his dismissal in the game currently in progress, run out going for one that was never there, was the product of a scrambled mind. The one to prosper has been Tom Abell who is handling batting at no3 like one born to perform that task. Crawley remains the man in possession for England, but if he does not score runs against NZ then England may decide that change is needed, and Abell would surely be the logical person to turn to in that case: he is just entering the prime years of a cricketer’s career, he is batting superbly at no3 and several of his best scores have come in very testing situations, all of which give him the appearance of a test no3 in waiting.

A MATHEMATICAL TEASER

This problem comes from brilliant.org, but I have added a bonus element as well as slightly tweaking the setting:

A brief note on ‘concatenation’: in a mathematical context it is represented by an equals sign flipped through 90 degrees and it means that the two digits between which it appears are joined to form a single number.

Additional ‘bonus’ question: Once you have worked out the answer to the main problem, if one of the two sums cannot be solved under the given conditions what extra operations would need to be permitted to make it solvable? Full explanation in my next blog post.

PHOTOGRAPHS

My usual sign off…

Nottinghamshire v Worcestershire has progressed while I have been preparing to put this post up – Worcs, all out for 80 in the first innings are 106-4 in their second, still 214 away from avoiding an innings defeat, and suddenly definitely looking at defeat.

## Action Underway In All Championship Fixtures

A look at the county championship, solution to yesterday’s mathematical teaser and plenty of photographs.

The game between Somerset and Surrey has just got underway after the first four sessions fell victim to the weather which means that all matches now have some play. This post scouts round the grounds to see what is going on.

AROUND THE GROUNDS

Essex v Derbyshire: Essex batting first are 138-1 after 34.5 overs (no play yesterday). Sir Alastair Cook is unbeaten on 58, while big Billy Stanlake has the one wicket to fall but has been expensive, going at almost five an over. Nick Browne, the man out, scored 59, and Westley is at the crease with Cook.

Durham v Worcestershire: Durham scored 246 batting first and Worcestershire are 98-4 in response. Ben Raine has 2-11 and Chris Rushworth 2-38 for Durham and Tom Fell 40 not out for Worcs. Lees made 99 for Durham, with Brydon Carse second top scorer with 38 not out. Tongue claimed 5-39 for Worcs.

Sussex v Kent: Sussex are 177-4, already 32 ahead of Kent with six first innings wickets still standing. Tom Clark is 36 not out and Ben Brown 21 not out. Stiaan Van Zyl made 52. Darren Stevens who made his FC debut five years before Clark was even born, has 2-45 and Nathan Gilchrist 2-46.

Glamorgan v Yorkshire: Glamorgan are 96-7, play having started a day late due to the weather. Harry Brook, mainly a batter, has 3-15 with his medium pace, Steven Patterson 2-15 and Ben Coad and Jordan Thompson each have a wicket. David Lloyd made 31 and Billy Root 23. At the moment Michael Neser and Andrew Salter are batting for Glamorgan. Glamorgan’s other Aussie, Labuschagne, managed just 10. Glamorgan were 69-2 at one point before slumping to 82-7.

Middlesex v Hampshire: Middlesex are 163-9. This match saw one session of play yesterday and most of today’s scheduled play although there was an interruption for bad light. Gubbins made 51 for Middlesex, his fourth 50+ score of the season, while Blake Cullen scored 27. Kyle Abbott has 5-44 and Mohammad Abbas 3-42.

Somerset v Surrey: Surrey are 14-0 in the fifth over. There is no brother v brother element in this game as Craig Overton is not playing for Somerset. Leach is also rested, which means that Roelof van der Merwe is playing. Burns has 6 not out, Stoneman 7 not out. Gregory and Davey are bowling for Somerset, with De Lange first chance and Tom Abell possibly bowling ahead of van der Merwe in the circumstances. Craig Overton has been rested at the request of the ECB, which suggests that an England recall beckons for the Devonian giant.

#BBCCRICKET SELECTION GAME: PICK XI FOR 1ST TEST

The XI I picked is shown below (go here to try it yourself), and then I provide some supplementary notes:

You are given a list of options for each position, and some of the choices they provide are obviously flawed. My own selection is uncontroversial as regards the top seven – Woakes has to be an automatic pick in England, and absent Stokes who is recovering from injury, he is the only one fitted to play the role of genuine all rounder. I opted for Craig Overton at eight, because Oliver Edward Robinson was not available to be selected there, though Archer was. I could have picked Archer at eight and Robinson at nine and then explained that I would actually reverse their batting positions but decided to go for Overton instead and explain the situation in more detail. Overton is in magnificent form and I am not too worried about this personnel change. Archer bowled beautifully for Sussex yesterday and is clearly fit and firing, though Olly Stone could also be awarded that slot and the Durham duo of Mark Wood and Brydon Carse are also both possibles. Leach has to play if fit (if not Parkinson comes in), and I have gone for Anderson out of the veterans.

SOLUTION TO YESTERDAY’S MATHEMATICAL TEASER

Yesterday I presented the following:

The answer to the above is 18. I offer two of the published explanations, first a masterpiece of brevity from David Vreken:

David Vreken
May 11, 2021

By casting out the nines, (E+A+R)+(E+R+A)âˆ’(A+R+E)=A+R+E(E + A + R) + (E + R + A) – (A + R + E) = A + R + E(E+A+R)+(E+R+A)âˆ’(A+R+E)=A+R+E must be divisible by 999.

Out of the given options, only 181818 is divisible by 999, so A+R+E=18A + R + E = \boxed{18}A+R+E=18â€‹.

For those who prefer a more thorough approach here is a complete explanation from Inesh Chattopadhyay:

PHOTOGRAPHS

Time for my usual sign off:

As I prepare to put this up, Surrey have moved on to 50-1, Stoneman back in the hutch, Burns in to the 20s, continuing his strong start to the season, and Amla just starting.

## All Eyes On Durham

A look at such action as there has been in the county championship, a teaser, a few links and plenty of photographs.

There has not been much action in the county championship due to poor weather in various areas but I look at the little there has been.

GAMES NOT STARTED YET

Four of the six games have yet to see any action: Essex v Derbyshire, Yorkshire v Glamorgan, Middlesex v Hampshire and what should be the tie of the round, Somerset v Surrey.

Sussex v Kent did get underway but they have gone off for the light (inexcusable – find a ball of a colour that is easier to see under floodlights and keep playing). Kent are 74-3. Jofra Archer claimed two wickets in a fiery new ball burst and has subsequently bowled a second spell of four overs (his opening burst was also of four overs, suggesting that someone from England’s management has told Sussex to use him in short spells), while the third wicket, that of Jordan Cox, went to Oliver Edward Robinson who produced a corker of a ball that uprooted the youngster’s off stump. That brought Oliver Graham Robinson, the Kent keeper and middle order batter to the crease, but before there was time for a duel between the two almost homonymous cricketers the light intervened.

This means that the only game in progress is up at Chester-le-Street where Durham are 97-3 against Worcestershire. Bedingham, the South African born batter who has been scoring very heavily for Durham went for just 24 today, but Lees, the former Yorkshire left hander, is on 39 and Jack Burnham has 5. Charlie Morris has two wickets and Joe Leach one.

A MATHEMATICAL TEASER

This one from brilliant.org is not too difficult, though I am removing the multi-choice options, deeming them unneccessary. Solution/ explanation in my next post:

Three interesting links before my usual sign off:

This piece from the space academy details the discovery of the first planet to have been identified outside our galaxy. Click here to read the full piece.

Richard Murphy has put up a piece on his blog, Tax Research UK, about Green Recovery Bonds, as well as a link to a more detailed report on the same subject.

Now for those photographs:

Durham have moved on while I have been working on this post to 121-3, and Lees has reached 50, the 50th time in his FC career he has done as much, but he has only converted 17 of the previous 49 into 100s.

## County Championship Round Up

A look at the county championship at half way in it’s ‘conference’ stage, solutions to a couple of mathematical teasers and plenty of photographs.

Although two teams, Derbyshire and Durham, did not play in the last round of the championship which concluded yesterday most have played five matches which makes it halfway through the ‘conference’ stage of the season. Thus it is an appropriate time to look at the groups in detail.

SOMERSET CLOSE OUT HAMPSHIRE

After I finished yesterday’s post only one match had a definite result, Somerset beating Hampshire by 10 wickets. Josh Davey and Craig Overton each took five wickets in the second Hampshire innings, and Byrom needed only one delivery to score the two runs Somerset required for victory. Felix Organ for Hampshire scored seven off 108 balls, one of the slowest innings in the history of the championship. The slowest non-duck (ducks by definition don’t have a scoring rate!) in championship history was Brian Hardie’s four singles in 142 minutes for Essex in the 1970s, while Lancashire stonewaller of the 19th century Dick Barlow (the Barlow of “my Hornby and my Barlow, long ago”) twice played innings of five in 150 minutes. Ever since Gloucestershire prevented them from making it three wins out of three Hampshire have done very little right. Here Organ’s abandonment of any attempt to score runs cost them, as they only just avoided the innings defeat and simply could not put Somerset under time pressure. When Gloucestershire saved the match against Hampshire the draw was accepted because Gloucestershire were about 60 ahead and Hampshire would only have had three overs in which to chase them even had they taken the final Gloucestershire wicket. Hampshire’s approach in their second innings basically left them only one route out of trouble: bat for the whole of the remainder of the match.

THE GROUPS AT HALFWAY

All tables copied from www.cricinfo.com:

Group 1

Durham and Derbyshire were not involved in the last round of fixtures. From the point of view of 5th place Essex, stuffed by Nottinghamshire in the last round, a victory for Derbyshire in that match would be preferable even though it would temporarily put them last: if Derbyshire won they would have between 56 and 64 points depending on bonus points, and Durham between 53 and 61, meaning that Essex would be 15 points off second place, while a Durham win would mean they have between 69 and 77, and Derbyshire between 40 and 48, giving a worst case scenario of Essex being 21 points behind second place. Also, the Durham win would mean that Worcs on 66 points, 14 better than Essex are in fourth, making even the modest achievement of a place in division two for the closing stage of the season tough for Essex, whereas a Derbyshire win would mean that at worst 4th place is on 61 (if Durham score full bonus points in defeat), nine better than Essex and not too much of a challenge to overhaul. The anomaly in this group, caused by the decision to award extra points for the draw this season in that Worcestershire, yet to win a game, are third out of six. For the group as a whole, a big win for Durham in that game in hand would probably be the best result, sending them top and effectively making it three clubs battling for the top two spots and three clubs fighting to avoid ending up in division three.

Group 2

A clearer picture in this group, with Gloucestershire and Somerset looking likely to hold on to the top two places, Hampshire and Surrey third and fourth and Middlesex and Leicestershire bringing up the rear. Somerset’s position is especially meritorious as they started on minus eight due to a particularly graceless complaint from Essex being acted on by the ECB (the pitch, for a game that Somerset had to win to become champions in 2019, was a poor one, but no action was taken during the game, and Essex did enough to take the title, which makes their subsequent action in putting in an official complaint especially mean spirited). Middlesex have been good for long periods of most of their games, but when they go off the rails it tends to be in a big way – crashing through the protective barriers and down into a deep ravine littered with boulders. They had the better of the first innings in each of their games against Somerset but had two horror batting collapses in the second innings of those games which gave Somerset two chases that were stiff but manageable and both of which they pulled off. Leicestershire have decent batting but a calamitous lack of bowling. Hampshire started excellently but after being baulked by Gloucestershire in their third match have been able to do little right. Surrey have had their moments, such as their utter destruction of Hampshire in round four but also handed Middlesex their only win of the season, at Lord’s. Gloucestershire have been superb.

Group 3

The roses counties are dominating this group, though Northamptonshire are still just about in the hunt for second place. Kent’s struggles are mysterious – they have what looks a decent squad, but no one has been performing consistently. The batting in particular has been poor, while their bowling has been over reliant on the veteran Darren Stevens. Sussex are struggling with the bat – they have some very impressive bowlers. It is very likely that Oliver Edward Robinson will be involved with England and so miss quite a few games which will make their already tough task even tougher.

SOLUTIONS

Each of my previous two posts contained a mathematical teaser from brilliant.org. I now present solutions and explanations:

From two days ago:

The answer is that Saed wins. Here is Saya Suka’a published explanation:

There are only 14 maximum legal moves possible with this arrangement, so the player taking the even turns will win (if they can preserve it up to the very last turn).

Okay, so they can go rook but no castling allowed. The spaces are 1-2-1-2-1, and it’s a game of “Go East”, so we are only interested with the 2-1-2-1 part of the spaces. The leftmost token has a twin in the second one from the right, and the other two are also likewise. The magic incantation is “Mirror, mirror until you hit the wall”.

From yesterday:

I asked you to name a five minute time frame for Ivan’s return, because brilliant had given a set of multi-choice options that basically killed the problem. When Ivan sets out the time is between three and four, so the hour hand is somewhere between those two numbers on the clock face. We are then told that he returned between seven and eight and noticed that the position of the hour and minute hands were reversed from when he went out, which means that the hour hand is between seven and eight and the minute hand is between three and four. When the minute hand is positioned at three it is fifteen minutes past the hour, and when the minute hand is positioned at four it is twenty minutes past the hour. Thus if we call the exact time of Ivan’s return T, then in mathematical notation 7:15<T<7:20 – Ivan got home some time after 7:15 and before 7:20.

Brilliant’s four multi-choice options were 7:15, 7:18. 7:35 and 7:37, and as you can see only one of those is actually within the time frame – 7:15 is one edge of said frame and not actually quite a possible time. This poor selection of possible answers spoiled a really good problem.

My thanks to Charlotte Hoather, who commented with her answer, a good effort, yesterday.

PHOTOGRAPHY

My usual sign off…

## Somerset Against The Clock

A look at Hampshire v Somerset and the rest of the closing stages of the fifth round of Championship matches, plus a teaser, plus some photographs.

Welcome to this post, which looks at the closing stages of the current round of County Championship fixtures, with particular attention on the game at Southampton.

SOMERSET ON SONG

Yesterday was a near universal washout in the County Championship, but this game did see some action, during which Somerset claimed the wicket of Sam Northeast. When the light closed in Hampshire were 110-4, still 147 to the bad. Hampshire have dug in and fought hard, but their inability to score with any speed means that they are still highly likely to lose this match. Joe Weatherley fell for 44 after 279 minutes and 209 balls of resistance, James Vince made 42, and Liam Dawson and Lewis McManus have also come and gone. Hampshire are currently 198-8, still 59 short of avoiding the innings defeat, with Felix Organ and Keith Barker batting together and only Mohammad Abbas, a genuine no11, to come. Craig Overton has bowled magnificently, his current figures being 34-16-45-5. Josh Davey has 3-27 from 21 overs. Hampshire are going at 1.8. If this had been a first innings performance Hampshire would have batted the whole 110 over bonus point period and not accrued a single point, while Somerset would have two of a possible three. The trouble with this ultra-attritional approach of Hampshire’s is that if they do not bat right through the day they will certainly lose the match – there is no runs/time equation for Somerset to worry about.

AROUND THE GROUNDS

Three matches have already concluded. Middlesex were beaten by Gloucestershire yesterday, consolidating the latter’s hold on top place in the group. Middlesex had conceded a first innings lead of 63 (210 plays 273) and a second innings batting collapse then left Gloucestershire needing only 90 to win, a feat they accomplished without much trouble. Middlesex have been in the game or even ahead of the game at some point or other of most of their matches, but have had a tendency to have a horror session that costs them the game.

Nottinghamshire have beaten Essex by an innings and 30 runs. Essex managed just 99 and 194.

Northamptonshire routed Sussex by an innings and 120 runs. Sussex slumped to 106 all out in the first innings, Northants declared on 441-9 and Sussex could do no better than 215 at the second attempt. Only Oliver Edward Robinson, with 49 not out in the first Sussex dig and bowling figures of 5-58 had a decent match for Sussex.

Barring miracles all the other games are going end in draws due to the intervention of the weather.

A MATHEMATICAL TEASER

With Somerset’s main opposition being the clock this one seemed appropriate for today. I have reframed the problem slightly from the brilliant.org version because their version opened up a hack, of which I duly availed myself. I reproduce most of the problem below before ending with my own formulation:

Brilliant offered four possible answers, and their choices spoiled the problem by making it impossible not to solve. Instead I ask you to give a five minute window within which Ivan got back. Solutions to both this and yesterday’s teaser in my next blog post, and a full explanation of the flaw in the brilliant multi-choice options.

PHOTOGRAPHS

My usual sign off…

## England Potential Bowlers

A look at potential bowling options for England, a couple of links, a mathematical puzzle and some photographs.

Welcome to this post which features a few bonus features. The weather has ensured that developments in the County Championship do not warrant a post today, so I am looking at possible bowling options for England.

ENGLAND BOWLING PICKS

I am going to work through the options starting with out and out speedsters and ending with four players, two of them very much future rather than present prospects, who would not be picked purely for their bowling but might be used a few overs here and there.

The are four out and out fast bowlers who the selectors might well pick: Jofra Archer, Brydon Carse, Olly Stone and Mark Wood. Three of these have already played test cricket, while Carse has been making waves over the last couple of years. Personally given his injury history and his value in limited overs cricket I would be chary of picking Wood for test matches. Archer and Stone could both easily play, and Carse is an extra option. On home tracks I do not see more than one bowler from this bracket being warranted, but some overseas tracks may well warrant two or more out and out speedsters (Perth and Johannesburg spring to mind).

Right arm medium-fast/ fast-medium: There are many English bowlers in this bracket with excellent FC records, but to me six have definite England claims. The two veterans Anderson and Broad will probably rotate, though there may be situation in which both get selected. Oliver Edward Robinson and Craig Overton are both having storming seasons, have superb career records and would seem to be in a head to head for the no8 slot. With Stokes currently injured it is quite likely that an all rounder will be selected to bat at no7, and the two main candidates for that role in this bracket are Chris Woakes and Ryan Higgins. Woakes if definitely fit would be the first choice, especially with the first test taking place at his northwest London fiefdom, aka Lord’s.

Left arm medium to fast-medium: Sam Curran is the obvious bowler of this type for England to turn to, and could possibly bat as high as seven, though eight seems more realistic for him at present. George Garton is another promising talent in this bracket, and Sussex have him batting at no7 at the moment.

Spinners: Jack Leach is the man in possession, and it is wildly unlikely that a home pitch will warrant the selection of two specialist spinners. Matt Parkinson (leg spin), Jack Carson and Amar Virdi (both off spin) have all had big performances this season, and given the slim pickings England off spinners have generally had in Australia Parkinson is probably the current no2. Finally, there remains the possibility of offering Sophie Ecclestone who has an extraordinary record in women’s internationals her opportunity to perform alongside the men.

Batters who bowl: Obviously Stokes (LHB, RF) would if fit be preeminent in this category, but he is currently injured. Matt Critchley of Derbyshire (RHB, LS) is having a superb season with the bat and it is quite possible that England would select him and give him a few overs here and there in addition to using his batting. A couple of youngsters who will be on the radar in the near future are Lewis Goldsworthy of Somerset (RHB, SLA) and Luke Hollman of Middlesex (RHB, LS). Goldsworthy hasn’t yet bowled in FC cricket, but has scored 39, 41 not out and 24 in his three innings, and the last two were knocks played under considerable pressure on pitches that were not straightforward.

Myself given that the next test match is at Lord’s I would be going with Woakes and Oliver Edward Robinson at seven and eight, with commiserations to Craig Overton. My team would look something like: Sibley, Burns, Crawley, *Root, Pope, +Foakes, Woakes, OE Robinson, Stone, Leach, Anderson. Archer, Carse or Wood could take Stone’s place and of course Broad could play ahead of Anderson depending on form or fitness.

The Lynn News are running a poll for who should be their Charity of the Year, and NAS West Norfolk, of which I am branch secretary, are among the nominees. Please read the article and vote for us by clicking here.

Phoebe has one again opened up her blog for people to promote their own blogs, and I urge you to visit and check out some of the blogs advertising themselves there. Please click here to do so.

A MATHEMATICAL PUZZLE

This is a fun problem from brilliant.org:

PHOTOGRAPHS

Leaden sky and persistent rain are not the best conditions for photography, but I do have some pictures to share with you:

## Day Two Championship Action

A look at goings on in the county championship, a solution to yesterday’s teaser and some photographs.

We are just in to the afternoon session on day two of the current set of county championship games. This post looks at what is going on.

SURREY V HAMPSHIRE

This is the game I have been focussing on today. Yesterday Surrey dismissed Hampshire for 92, and were going well in response, with Burns and Amla established at the crease. Today Surrey have been hugely impressive, although Burns fell for 80. Amla is past his century, 137 not out, and Ollie Pope is on the verge of reaching 50. Surrey, 278-2, are already 186 to the good.

AROUND THE GROUNDS

Sussex v Lancashire: Lancashire cleaned the Sussex tail up quickly this morning, restricting them to 328 all out, and have reached 55-0 in reply. Tom Bailey and Danny Lamb each took three wickets, and Saqib Mahmood, Matt Parkinson and Liam Livingstone picked up one apiece. Keaton Jennings and Alex Davies are both in the 20s for Lancashire.

Notts v Derbyshire: Nottinghamshire scored 256 batting first, and had Derbyshire 86-8 at the end of yesterday. This morning they winkled out the last two, Derbyshire reaching 105. Nottinghamshire then declined to enforce the follow on, an understandable but cautious decision. Notts are 115-1 in their second innings, 266 to the good. Haseeb Hameed and Ben Duckett are going well for them. Luke Fletcher took five wickets in the Derbyshire innings, and Stuart Broad and Dane Paterson two each.

Worcestershire v Essex: Essex are 393-4, with Cook and Westley having scored centuries and Dan Lawrence 90. Alzarri Joseph has 2-92.

Durham v Warwickshire: By the close yesterday Warwickshire were already in the lead with all 10 wickets standing. They have lost one wicket today, and are currently 212-1 in response to Warwickshire’s beggarly 87. Lees has 86 not out, while Will Young has just gone for 124. Liam Norwell has the one wicket Warwickshire have taken.

Gloucestershire v Leicestershire: Leicestershire are 393-7, Ben Mike having just reached 50. Sam Evans and Lewis Hill both scored centuries. Daniel Worrall has 4-79 and Ryan Higgins 2-65.

Somerset v Middlesex: Middlesex batted first and made 357, Somerset are 14-0 in reply. Robbie White scored 92 for Middlesex, while Davey and Overton each took three wickets.

Glamorgan v Kent: Kent were all out for 138, and Glamorgan are 170-8 in reply, having resumed today on 109-2. David Lloyd followed his four cheap wickets with 62, and birthday boy Darren Stevens has 5-53, while Matt Milnes has 3-46. Were Stevens to get an England call up he would be the fourth oldest test debutant ever, behind James Southerton (49years 19 days old when the first ever test started), Miran Baksh (47 when called up in 1955) and Bert Ironmonger (46 when called up in 1928). If he went on to get selected for the Ashes tour he would be the oldest Ashes tourist since Hobbs in 1928-9 and the oldest to make a first trip to Australia since Southerton.

Yorkshire v Northamptonshire: Yorkshire reached 206 in the first innings, helped by a half century from Dominic Bess. Northamptonshire are 137-5 in response, Saif Zaib 31 not out and Tom Taylor 21 not out. Steven Patterson has three wickets and Jordan Thompson two. Wayne Parnell took five wickets for Northamptonshire and Gareth Berg three.

While I have been typing this Surrey have cruised on to 308-2, Amla 147 not out, Pope 68 not out.

SOLUTION TO TEASER

Yesterday I posed this from brilliant.org:

192 + 162 + 122 = 476. There 30 x 3 students = 90 doing two languages at least. 476-90 = 386. There are 404 students in total and 404 – 386 = 18, thus 18 students must be studying all three languages.

PHOTOGRAPHS

As I go to publication Surrey have moved on to 324-2, Amla 156, Pope 75.