Congratulations to England on a Series Win Against the World Number One Ranked Test Nation

Congratulations to England on their series win, a farewell to Alastair Cook who has announced his impending retirement from international cricket, some maths problems and solutions and some photographs.

INTRODUCTION

This is going to be a long post because there is a massive story to cover concerning the cricket in addition to the match itself. I will also be including some mathematical problems and solutions and of course some of my own photographs.

ENGLAND WIN A THRILLER TO TAKE THE SERIES 3-1 WITH A MATCH TO GO

On Thursday when England stumbled to 86-6 after winning the toss and batting I was not expecting to be writing a piece of this nature. England failed to polish off the Indian first innings when they had a chance of a lead. When Stokes stuffed skipper Root (run out 48) it was 122-5 and England led by only 97. Then came another lower order fightback, and with Curran adding 46 to his first innings 78 England set India 245 to win. The match was settled while I was at the Mencap Beach Hut, Old Hunstanton on an NAS West Norfolk day out. As usual the key wicket was that of Kohli, and once he had gone India never got back into contention, Moeen Ali adding four wickets to the five he took in the first dig (he is very much a bowler who likes being at home – 91 wickets at 31 in England, 51 at 52 abroad) to help settle things. In neither innings did England’s top order deliver sufficiently (a recurring problem). Aside from Root’s 48 from his preferred no 4 slot in the second innings, the highest score from an England player in the top four was Jennings’ second innings 36. I am now going to through England player by player.

A N Cook – see next section
K K Jennings – a failure in the first innings, and in many ways a worse story in the second – an opener who gets as far as 36 should be settled in for the long haul. I believe that with the series safely won and the situation ripe for experimentation he should be dropped.
J E Root – the skipper dropped himself to no 4 in the second innings and it took a run out to get rid of him then.
J M Bairstow – he was sufficiently injured to prevent him from keeping but not apparently from batting, but if he is to play as a specialist batsman it should be at no 3.
B A Stokes – the new, responsible Stokes played well up to a point in this match but in the second innings he overdid the blocking to the point of handing the initiative to India. Also running out the skipper never looks great (save perhaps at Christchurch in 1978 when Botham, allegedly acting on instructions from vice captain Willis to do whatever was needed to up the run rate, stitched up skipper Boycott).
J C Buttler – one of only two England batsmen to have topped the 250 run mark thus far in the series (the other being the wunderkind Curran) and competent behind the stumps.
M M Ali – a useful batting effort after England’s disastrous start on day 1 and two good bowling performances. His mid-match promotion to number three (where he did recently hid a double century for Worcestershire v Yorkshire) shows how desperate England are to find a way for Root to bat at four.
S M Curran – about the only thing the youngster hasn’t done in this series is walk on water! He is establishing himself as a star player.
A U Rashid – a poor match with both bat and ball, but he is too good not be firing again soon.
S C J Broad – a solid match for the veteran new ball bowler. He has now drawn level with Sir Richard Hadlee in the all-time test wicket takers list.
J M Anderson – a quiet match for one of the all-time great swing bowlers, but even though he did not take many wickets he continued to command respect.

I will end the cricket part of this post by naming my team for The Oval.

FAREWELL ALASTAIR COOK

Alastair Cook, after 160 test matches, the last 158 in sequence (the longest unbroken run of appearances in test history, and not likely to be challenged any time soon) has announced that the last match of this series, at The Oval, will be his international swansong. This marks the end of an epoch not just for England but for test cricket – in many ways Cook is the last true test match batsman, having made his debut before T20 was a really major thing and unlike many who get seduced by the bright lights and big money at tournaments such as the IPL he abandoned short form cricket to concentrate on his test match career. His achievements in test cricket placve him firmly among the greats of the game, and I think he has timed his announcement exactly right, bowing out on his own terms (which he had more than earned the right to do) and before too many people began to ask just why he continued to be picked.

On the 2010-11 Ashes tour Alastair Cook had to most successful visit to that part of the world by anyone named Cook since Captain James called by in 1770, and the most successful by an England batsman since Hammond in 1928-9. He played three monumental innings in that series, a match saving 235 not out at the Gabba (also sometimes referred to as the ‘Gabbatoir’ on account of what often happens to visiting sides there), his 148 at Adelaide that set the stage for the Pietersen innings that put Australia right out of that game and the 189 at Sydney in the final game that ensured that the final scoreline for the series would reflect England’s dominance (a 2-2 draw would have been an utter travesty, and even 2-1 to England after a drawn final match would have looked better than Australia deserved).

I have no doubt that there will be occasions in the near future when England find themselves wishing for Cook’s cool head and fighting qualities. It will be hard to get used to an England order without the name Cook at the top of it.

From this huge cricket fan and devotee of test cricket the message is “Well done Alastair, and thanks for some fabulous memories, especially of the Aussies being humbled in their own backyards”.

THE TEAM FOR THE OVAL

HI do not expect that thsi team will actually be picked (!) but it is what I would do in these circumstances, with the series already won: A N Cook, R J Burns, T T Beaumont, *J E Root, O J D Pope, S M Curran, +J C Buttler, M M Ali, A U Rashid, S C J Broad, J M Anderson.

PROBLEMS AND SOLUTIONS

I begin with the solutions to the two problems I posed in my last post:

AKSHATHA AND DEV

I give you a beautiful published solution from David Vreken:

1001 PROBLEM

Here is the answer:

I published a solution to this problem, which although more than half of all solvers got it wrong is actually very easy. My solution:

1001 is odd, and the only even prime number is two.
1001 – 2 = 999, which is obviously divisible by three (full prime factorization is 3 x 3 x 3 x 37)
Negative numbers do not apply to these questions as with them no number matches the definition of a prime, but even if they did, 1,003 (1,001 – -2) is composite anyway (17 x 59).

WHAT IS THE AREA OF THE QUADRILATERAL?

This is first of two new problems from brilliant.org for you:

There are two ways to solve this one, the official method and a hack (no bonus points awarded for guessing which method I adopted!).

HOW MANY ITEMS?

Incidentally this question should not be taken as suggesting that I approve of this method of pricing – the reverse is actually the case, I think it is utterly ridiculous and very irritating.

PHOTOGRAPHS

Church, North Norfolk — A church in North Norfolk

The new ‘Sandcruiser’ wheelchair at the beach hut.

Sandcruiser in action — The sandcruiser in action

Dolphin kite — No – not a real dolphin performing a record breaking acrobatic feat – merely a flashy kite being flown in the breeze.

Bentley I — A vintage Bentley (six shots in total)

Amber — Possibly a small piece of amber with something preserved inside it.

You Are Cordially Invited… 💛

Phoebe is hosting a meet and greet today – why not come and join in the fun…

HEALTH | INSPIRATION

Dear friends,

It is no secret that I value this WordPress community and that I enjoy each one of your wonderful blogs. Therefore, today will be a Meet-and-Greet, where I welcome each of you to promote yourself on my blog.

The guidelines are simple and are as follows:

Leave a comment on this post with your blog’s name, a description, and a link to either your homepage and/or your favorite post.
Take a minute to browse the other comments and to visit some of the blogs listed.
If you would like, share this post with others so that your readers can participate as well.

As you know, WordPress is filled with wonderful bloggers and talented writers. I encourage everyone to be open to meeting someone new today and to help support one another.

Let’s make this an awesome Meet-and-Greet!

Love,
Phoebe

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Cricket and Other Stuff

Cricket, in the course of which I make a very radical suggestion for dealing with England’s top order woes, and a few other things, including Maths and Public TGransport.

INTRODUCTION

As well as some stuff about the state of play in the current England vs India series I have a couple of mathematical problems for you and some of my own photographs at the end.

ENGLAND’S DREADFUL START

England won the toss yesterday morning before the fourth test match of the five match series against India at the Ageas Bowl, ~~Botley~~ Southampton. This was the last thing they managed to do right for some considerable time. At last, with the scoreboard reading a barely credible 86-6, Sam Curran, inexplicably dropped from the last test match and now returning to the fray, emerged from the pavilion. Much of the carnage was more due to good Indian bowling than bad batting, although Jennings (already on borrowed time for my money) will not want to see replays of his LBW (however good a piece of bowling it may have been padding up to one which would have uprooted the middle stump otherwise never looks good). Fortunately England’s tail managed to produce a diplodocid (see picture at end of this paragraph) proportion of the innings. Curran, making the ridiculous decision to drop him from the previous game look positively ludicrous, racked up 78 before he was last out, the total hvaing reached a semi-respectable 246.

Diplodocus — This is why I described the contribution of the England tail as being of diplodocid proportions.

India are currently 135-2 in response. Only once in test match history has a side come back from 0-2 down to take a five match series, in 1936-7 when Australia’s comeback was fuelled by scores of 270, 212 and 169 from Don Bradman in the course of those last three matches. In 1894-5 Australia levelled the series at 2-2 after being 0-2 down but Andrew Stoddart’s England rallied to win the decider.

England’s continuing top-order woes need to be addressed if they are to avoid surrendering a series on which they seemed nto so long ago to have a vice-like grip. Rory Burns must come into the side in place of Jennings. I would also bring Pope back but place him lower in the order. brief interjection – BIG NEWS – Kohli Is Out! Also, thinking about the need for top order runs I now tender a suggestion far more radical than Rory Burns – there is one England opener who has making stacks of runs all over the place of late – the one and only Tammy Beaumont! The way they have performed thus far none of the current top order are entitled to object to that suggestion.

Yes going with two new openers would be a colossal gamble, but they could scarcely fare much worse than Cook and Jennings have in this series.

A COUPLE OF MATHEMATICAL TEASERS

Both of these, from my usual source, are very easy problems which have tripped a number of solvers up. I give them in the reverse order to which they appeared:

And

HERITAGE OPEN DAY

Heritage Open Day this year is Sunday September 16th. There will be some 60 sites open in the King’s Lynn area, and if you there on the day do make sure you visit. If you happen to visit the cellars at the Bank House between 12 noon and 2PM I will be one of the volunteers you encounter.

TWO STORIES OF BRITISH PUBLIC TRANSPORT DAFTNESS

I start this section with the more minor but also more personal of these stories. Today I made my travel arrangements to Sheffield for a cousin’s wedding. I checked bookings from King’s Lynn to Sheffield, and the cheapest ticket would have cost me £68.20. Knowing that a ‘plan B’ was available I then checked out bookings from Peterborough to Sheffield and lo and behold up came a ticket for just £38.50, which when the two bus tickets on the ExCel are added in amounts to £51 all up. In other words to have travelled by train from King’s Lynn all the way to Sheffield would have cost me 33% more than the combined bus/ train route I am actually taking. Now of course not everyone booking this journey would have known of the alternative, and I wonder how many people have been swindled in this.

My second story of public transport daftness is that The Elizabeth Line (aka Crossrail) will not now be coming into service until nearly a whole year later than planned (more here).

PHOTOGRAPHS

The pictures here are of items I purchased at our auction on Wednesday (it was reasonably successful, with a few big sales, and a lot of items finding buyers).

Lot 121 – I scanned these items rather than photographing of them.

Under a viaduct and over a bridge — A photograph of the item taken this morning

360 — Two of the four items in this lot were of sufficient interest for me to consider bidding, the Nobel Prize cover, and the one that really settled it, the Classic Locomotives.

Classic Locomotives FDC — The main cover photographed this morning.

Classic Lcomotives stamps II — The first of two close-ups of the stamps (the reflectivity of the protective covering makes this a challenge).

Classic Locomotives other side — The ‘cover’ part of this item contains a lot of information when opened up (see also next picture for the other side).

A Mixed Bag for Monday

Solutions to my last two maths problems, some sciencey pieces, a petition and some photographs.

INTRODUCTION

This post includes solutions to the problems I posed on Saturday, and a few other things from various sources.

SPACE STATION DODECAHEDRON

Here is the question as a reminder:

Here is the answer:

Here is a splendidly concise solution from David Vreken:

A VARIARION ON THE MALFATTI THEME

Here is the question:

Here is the answer:

In the 19th century Malfatti conjectured that the way to maximise the area of a triangle you could fill with three circles was to fill in the three largest circles that touch specifically two of the three sides. Although he was not alive to be humiliated it turned out that he was not merely wrong, his proposed solution has been proved not to work for a single triangle. The solution that always works is first put in the largest single circle that touches all three sides that you can, then fill in the largest circle you can in the remaining space and then do so again. In an equilateral triangle the difference is small, but in a long thin isosceles triangle it is quite substantial.

Here is Jeremy Galvagni’s published solution:

SCHOOL REFUSAL SYNDROME PETITION

This on the official site for petitions to the UK government, which means that you have be a UK citizen to sign it. Please click the screenshot below to sign and share it if so minded:

A TRIO OF SCIENCE PIECES

First a fascinating piece from the National Geographic titled “Can Today’s Whale Species Survive the age of Humans” which covers the past and present of the cetaceans and speculates about their future.

David Quammen, a good writer and a useful scientist to know about if you are planning an A to Z post, has a new book out on the subject of evolution, and Jerry Coyne of whyevolutionistrue has provided a very detailed review of it.

Finally, a letter to the Guardian signed by 60 well known environmental campaigners declaring their unwillingness to debate with climate change deniers, and why they are unwilling to do so. Below is the opening to the letter (please click to visit the original) and a list of signatories:

SOME FINAL PHOTOGRAPHS

To finish here are some of my recent photographs:

Book Review: The Mitford Murders

A review of “The Mitford Murders” by Jessica Fellowes.

INTRODUCTION

I was in King’s Lynn Library on Friday when I saw a copy of this book, by Jessica Fellowes, on the shelves and decided to take a punt. The fact that today is the following Monday and I am posting this review gives a clue as to what I made of the book.

THE SETUP OF THE BOOK

This book is based on a real life murder, that of Florence Nightingale Shore, god-daughter of “The lady with the lamp” and like her famous godmother a war-time nurse. At the heart of the story is a fictionalised account of goings on in the aristocratic Mitford Family. The heroine is Louisa, who takes a job in the household helping to look after the children. Crucial to the development of the story is the friendship she forms with Nancy, the eldest of the Mitford children (16 when the story opens to Louisa’s 18).

Spanning just over two years, and taking in two countries the story is developed with expert touch, and the revelation of the true murderer is a gobsmacker.

This is a splendid story, combining its other merits with giving a panoramic view of immediate post WW1 life, covering the full range of society.

CLOSING THOUGHTS

I understand that a second book in the series is due soon, and I say “Bring it on”. I follow that by saying that if you see a book with Jessica Fellowes’ name on the cover you should definitely pick it up. Rating *****.

Will The 2019 Aspi.blog Calendar Be All Cornish?

Presenting an idea for the next aspi.blog wall calendar and inviting suggestions in response.

INTRODUCTION

Those of you familiar with this blog will know that a photographic wall calendar has become something of a tradition – the 2019 effort when I finally do it will be number four. I have started thinking about and this post is intended to show one possibility.

A CORNISH THEMED CALENDAR

Those of you who saw my “A Grockle’s Eye View of Cornwall” series (you can access them all from here) will be aware of the amazing scenery I saw while I was down there. Since it was obvious that a number of those pictures would have to feature I then started thinking about how a Cornish gallery calendar might work, and this is where I have reached so far.

THE FRONT COVER

To provide a clue of what is within this is my envisaged front cover pic if I go the “pure Cornish” route:

OTHER POSSIBLE PICTURES

January would be this one:

The other pictures that I have identified as possibles, in no particular order are these:

The Brunel bridge — This bridge is so iconic that my shot of it would have to feature.

St Michael's Mount panorama — After a number from St Ives, we move on St Michael’s Mount and its surroundings.

WHAT DO YOU SAY?

Do you think the “pure Cornish Calendar” idea works? If so do you have any other of my Cornish pictures that you would like to see featured? If not feel free to suggest others of my pictures that should be there.

England Versus India

An account of the first three matches of the test series between England and India plus some photographs

INTRODUCTION

I have not written about the goings on in the current England versus India Test series as yet, because I have been busy writing about other stuff. This post repairs the omission.

MATCH 1 AT EDGBASTON

This was a nail-biter of a game, with fortunes swinging constantly as it progressed. When India were 115-6 in response to England’s 287 it looked like the home side were firmly in the driving seat, but Virat Kohli marshalled the lower order to such purpose that India trailed by only 13 on first innings. When England then slumped to 87-7 in their second innings it looked settled in India’s favour, but Sam Curran played a fine innings to give England a target of 194 to defend. England took wickets consistently, but not until Kohli was finally dislodged by a Ben Stokes yorker that trapped him plumb in front to make it 141-7, leaving nos 8, 9, 10 and 11 needing to cobble together a further 53 did the home side actually look favourites. They managed only 20 of those runs, and England were one up in the series. Curran was deservedly named player of the match (Kohli’s contribution of 149 and 51 was not enough to save his side from defeat, so it would have been wrong for him have got the award).

SECOND TEST MATCH AT LORD’S

India batted first in very difficult conditions. Nevertheless, and magnificently as England’s seamers bowled in conditions made to measure for them, a tally of 107 all out looked pretty definitively inadequate. When England were 131-5 themselves it looked less so, but a monster partnership between Bairstow and Woakes (in in place of the unavailable Stokes) effectively settled the outcome of the match. Woakes completed his maiden test century, being 137 not out when England declared, while Bairstow missed adding to his own tally of such scores by a mere four. India collapsed again (130 all out this time) and England were 2-0 up in the series. Anderson became the first bowler to take 100 test wickets at Lord’s in the course of this game, and only the second ever to 100 at a single venue anywhere (the first, Muttiah Muralitharan, did so at no fewer than three different venues). Woakes’ century meant that joined the select list of cricketers to feature on batting and bowling honours boards at Lord’s (Ian Botham is there, and among overseas cricketers Keith Miller is the sole person on both boards).

THE THIRD TEST AT TRENT BRIDGE

Before this match got underway England perpetrated a blunder, setting the scene for four and little bit days in which such things would become routine, by dropping Sam Curran after two matches in which he performed excellently to make way for Ben Stokes, now cleared of all criminal charges, to return to the squad. I personally would not have selected Stokes at all, but even had a gun at the head proposition forced me to do so nothing would have induced to me to drop Curran (yeah, pull that trigger if dropping Curran is the price to pay for you not doing so!).

Perhaps feeling after the first two matches that they could bowl India out on anything England put them in after winning the toss. India tallied 329, helped by some butter-fingered English fielding. The match was won and lost in the space of an hour and a half on day two when England being 54-0 in reply to 329 became England 128-9 in reply to 329. Buttler and Anderson got the final England first innings total up to 161. In their second innings India reached 352-7 before declaring leaving England two days and a mini-session to negotiate or 521 to score. Kohli had his second century of the series, having misssed out by three in the first innings. Cook and Jennings did the first part of their mammoth task, getting England to the close without losing a wicket. Both then fell early on day four, and two more quick wickets followed, at which point Buttler and Stokes joined forces. Their partnership at least showed some belated fight, and Buttler completed his maiden test hundred, while Stokes batted for a long time in largely defensive manner. Another clatter of wickets followed the breaking of the partnership and it was only some bloody-mindedness on the part of Rashid and Anderson (who had earlier in the game become only the second bowler to record 100 wickets in test matches against India, behind Muralitharan) took the game into a fifth day.

Somewhat bizarrely the Trent Bridge authorities decided to charge £10 for admission on a day that could have lasted for one ball (actually it managed to last for 17, meaning that anyone who paid to get in did so a rate of just under 59p per delivery). At the MCG in 1982, when again the final day could have lasted one ball, but there was also an outside chance of a home victory (37 needed with one wicket left BUT at the crease with no 11 Jeff Thomson was a certain Allan Robert Border) the authorities there did not charge admission. On that earlier occasion those who took advantage of the freebie got 85 minutes of gut-wrenching tension and one of the closest finishes of all time (England won by three runs after Thomson nicked one from Botham that would have had the umpire spreading his arms had the no11 simply ignored it, Tavare palmed the ball upwards and Geoff Miller took the rebound. Here, with in excess of 200 required and nos9 and 11 together at the crease there could only be one result (the largest number of runs that a last wicket pair have ever knocked off to win a first-class match is 76 way back in the fifties). Thus England were well beaten and lead the series 2-1.

LOOKING AHEAD

England’s top four is their major current problem area. At Trent Bridge those positions were filled by:

England’s all-time leading test run scorer but also someone who has not had a decent score since the Melbourne featherbed in December.
Someone who is clearly out of his depth at this level (Jennings)
One of the three best batsmen currently eligible for test cricket (Root – Kohli and kiwi Kane Williamson are the other two) to be found anywhere in the world.
A fine young batsman who at this stage of his career is not a test match number four.

The above situation, India managing a decent first innings total and the fact that Root for once had a poor game put a lot of pressure on the middle order, and Buttler and Stokes kin the second inninsg apart, they folded under it.

My suggested squad for the fourth test is: A N Cook, R J Burns (someone with a magnificent record as an opening batsman who is probably ready for elevation to the test match ranks), B A Stokes, J E Root*, O Pope (I did not say that he is not a test match batsman, and I believe that he can be, and should be persevered with, just not as high as number four, a position he never occupies even for his county), J C Buttler+, C Woakes, S Curran, A Rashid, S C J Broad, J M Anderson. If two spinners are warranted then Bess comes in for Broad, with Curran sharing the new ball with Anderson (the latter being a change I might make anyway, having Broad as third seamer). When recovered from his injury Bairstow comes in to the squad, probably replacing Stokes at no 3, just possibly coming as opener, bringing down the curtain on Cook’s illustrious career. Some of these suggestions, especially even considering dropping Cook might be seen in certain quarters as heretical.

I still just about make England favourites for the series (after all, they are still ahead), but they need to respond better to opponents making decent totals – this not the first time in recent years that they have folded in response to a respectable but not massive total – it happened twice against South Africa last year.

PHOTOGRAPHS

For you hardy souls who have made it to the end of this post, here are some of my photos:

Pride in the Park from afar II — The first of a number of shots here featuring the inaugural King’s Lynn and West Norfolk Pride – I found out about the event which took place a week ago too late to take part, as I already had other commitments, one of which I was on my way to honour when I took this.

Muntjac II — I had to photograph this muntjac from long range – as soon as they spot a human they flee.

A Solution and Some New Problems

A solution and a couple more problems from brilliant.org.

INTRODUCTION

On Wednesday I left you with a problem from brilliant.org to tacke having presented solutions to several others. Today I start with a solution and then present you with some new problems.

SOLUTION TO WEDNESDAYS PROBLEM

Here is the problem again:

Here is the answer:

And now here is Mark Hennings’ published solution:

As a side issue various commenters on brilliant.org demonstrated their failure to read the question by bringing up examples of numbers that are both square and cube (e.g 64), but these are utterly irrelevant since the question was about a number that is both one more than a square and one less than a cube.

NEW PROBLEMS

Two new problems for you, one easy, especially if you are familiar with the story of Signor Malfatti, and one slightly more difficult but quite fun.

CAN YOU OUTDO MALFATTI?

SPACE STATION DODECAHEDRON

A Massively Successful Auction

An account of yesterday’s splendidly successful auction.

INTRODUCTION

On Wednesday James and Sons had a small but very important auction featuring gold coins and proof sets. We were anticipating a very considerable success, because we knew that there were bids of sufficient size on every lot that everything would sell, and we also knew that some of the items had a very large number of watchers online (one had no fewer than 17). The rest of this post tells the story of a truly amazing auction.

TUESDAY – FINAL PREPARATIONS

In view of the high value of the gold the only items that were set out on display were as many of the proof sets as I could lay out on one large table. I also made sure that the IT was all fully functional, as the last thing we wanted was for a glitch to affect this auction. I was able to enjoy the NAS West Norfolk Steak Night at The Globe later that evening in the knowledge that all had gone as smoothly as it could have (I restricted myself to a modest two pints of Ringwood Fortyniner in view of the importance of the following day).

WEDNESDAY – A DAY OF TRIUMPHS

I awoke a few minutes before my alarm was due to go off (not uncommon with me – the alarm is more insurance policy than necessity) and left my flat precisely as intended at 6:45, ensuring that there was no chance of missing the bus. Arriving at the shop, I unlocked, deactivated the alarm, then relocked the door as in view of what was in the shop I did not want customers coming in while I was there on my own. I then began to set up for the day. The auctioneer arrived not very long after me, and I was able to complete the setup, verify that everything was working and take some photographs. Before nine o’clock customers started arriving, and by 9:30 it was standing room only in the shop, as no fewer than 16 potential room bidders were present, in addition to over 60 online bidders and not a few who had put commission bids in in advance of the sale.

P1190889 — The proof set display, with lot 135 front centre

P1190886 — One of the two significant coins from lot 139…

P1190888 — The setup before anyone else had arrived.

P1190892 — Potential room bidders (three pics)

: Lot 139 on the big screen.

THE AUCTION STARTS

The first five lots were 1974 Krugerrands which were expected to make approximately £800 each and did exactly that. Then came lot 6, the James II Guinea which was one of two items that had been the subject of a query the previous day as a result of which it had extra images above the regular image gallery for such an item. Estimated at £500-750 the interest it had attracted saw the final hammer price reach exactly £1,000.

The first three images constitute my regular image gallery for a single coin.

6-c — One of the questions asked about this coin related to the edge, and to help back up my own comments on the edge of this coin I took two photographs that between showed it in its entirety.

Lot 7 was a William III Half Guinea, which in relative terms fared even better since with an estimate of £300-500 it actually went for £900!

Lots 8 to 24 inclusive were half sovereigns, and all sold well, most going for around the £100 mark. Lots 25 to 90 incluisve were…

SOVEREIGNS FROM VICTORIA THROUGH ELIZABETH II

These we knew would sell respectably, because a major and long standing client whose job is to sell gold items had put in commission bids of £180 a time on the whole lot, confirming our auctioneers valuation was on the mark. Most of the sovereigns actually sold for more than that, £190 being a common figure and a few of them going to and in some cases beyond £200. Then came…

LOTS 91-5 – THE HUGE SUCCESSES

The first four of these lots were high value gold proof sets which we were expecting to be on or around the four figure mark. Actually, and barely believable they went for £1,600, £2,000, £2,000 and £1,600 respectively!!

Lot 95 was a sovereign in a gold mount with a gold chain and 8 1mm diamonds (in otherwords a very fancy necklace). Estimate at £300-400 it eventually sold for £550.

After these it was time for…

THE REGULAR PROOF SETS

Of course after what gone before the proof sets were a little bit “after the Lord Mayor’s show”, but there were still a handful of highlights to come.

LOTS 113 AND 114

These were respectively a Scottish and Welsh proof set (hence the split colouring of the heading) each expected to make £8-12. The Scottish set went for £20 and the Welsh for £18

These were a mere curtain raiser for…

LOT 121

A 1992 proof set featuring an EEC 50p coin the rarity of which turned a £10-15 estimate into a £50 hammer price!

The next big success was…

LOT 128

This 1999 proof set featuring a Diana Princess of Wales £5, a bimetallic rugby £2 and Scottish coins from £1 down to 1p had an estimate of £15-20 and ended up going for £32.

Then came two successive monster successes with…

LOTS 135 and 136

Lot 135, a 2009 proof set, featuring as it did the highly prized Kew Gardens 50p, the Henry VIII £5, and the Darwin and Burns £2 coins was estimated at £100-120 but ended up going for £220!

135-d — A close up of this one was mandatory.

135-e — I also deemed the Darwin £2 worthy of a close-up

Lot 136 was a 2010 proof set featuring a Restoration of the Monarchy £5 (350th anniversary thereof), A Florence Nightingale £2, a London £1 and a Girl Guiding 50p. Estimated at £20-25 it sold for £100!!

Not long later came…

LOT 139 – A BITTERSWEET IMAGER’S TRIUMPH

This London Underground 150th anniversary proof set had been badly misdescribed, with one of the £2 coins mentioned as featuring trains, and the roundel coin not even mentioned, but the imager’s efforts more than compensated for this. Estimated at £25-30 it attracted sufficient interest to push the final price up to £52 (and inter alia out of the imager’s reach, hence the heading of this section).

139-c — The ’roundel’ coin which is fairly rare.

139-b — The other London Underground 150th anniversary coin, which is much less rare.

That was the last of the yearly proof sets, but there were still a few lots to go, and two of them provided noteworthy results.

LOT 148 – A SENEGALESE STUNNER

This 1975 Senegal Triple Crown, solid sterling silver, Euroafrique 150 franc coin, boxed and with a certificate was estimated at £15-20, but a lively bidding battle pushed the final price up to £48.

Finally, came…

A STRONG FINISH

Lot 151, the final lot in this small sale, was an accumulation box containing a few good bits and some ordinary stuff. Estimated at £40-50 it ended up going for £95.

Once the auction setup had been dismantled and the last room bidders had gone it was time for me to attend to other matters. You can view a catalogue for the general collector’s auction we have next Wednesday here.

THURSDAY – PUTTING TOGETHER A PRESS RELEASE ABOUT THIS AUCTION

Yesterday morning I produced a PR piece about the success of this sale, going big on the images as well. I conclude this piece with a link and a screenshot:

GOLD COIN AUCTION GIVES FAKENHAM AUCTIONEER BEST RESULT IN YEARS

Solutions to Good and Bad Mathematical Problems

Solutions to the problems I put up here on saturday and some new problems.

INTRODUCTION

On Saturday I produced a mixed bag of offerings from brilliant.org, promising to provide solutions in a later post, and now that time has arrived.

THE WORST SET PROBLEM I HAVE EVER ENCOUNTERED ON BRILLIANT

I got nowhere close to solving this for reasons which will soon become obvious.

Here is the official “correct” answer:

My beef is with that diagram. The answer given works on the red section being the largest part of the parallelogram whereas the diagram shows it as the smallest, which was the basis on which I worked. This is way beyond a diagram being “not to scale”, which I have no great issue (the most famous of all such schematic diagrams, variations of which can now be seen representing transport systems in cities everywhere in the world is of course H C Beck’s London Underground diagram), but showing what is actually the lagrest single area of the diagram as the smallest is a bridge too far (Beck enlarged the central area so the stations were easier to see, but he did not actually make it cover a larger area than the surrounding suburbs, merely a less small area than was actaully the case, which to me is what if the approach is to have any validity is what “not to scale” should mean). The diagram in this question was literally worse than useless – wkith no diagram at all it would be have been a better question than it was with the actual diagram.

ANSWERS TO THE TWO FABULOUS PROBLEMS

First, what I now call the “Mendrin Circles Problem” after its creator:

Here is Albert Lau’s published solution:

Second, the problem of Mr Mediocre’s Lawn:

First the answer:

Jeremy Galvagni’s published solution was worthy of this splendid problem:

The ‘chessboard shading’ in this diagram is the key to the excellence of this solution – it rules out A and D, while B’s location rules it out, leaving only C as an option.

THE BONUS PROBLEM

The answer:

Attaching the leash to an edge or a corner introduces restrictions which are not there if it is attached to the centre of a face. At full extent Honey can be diametrically opposite her starting position, which means that the entire surface of the cube is available to her.

A NEW PROBLEM

This is a very old problem indeed:

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