England Selectors’ Ostrich Impression and Other Stuff

Some thoughts on the (in)action of the England selectors this week, some mathematical teasers and a few pictures.


A couple of days ago I wrote about England’s series win over India and presented some problems and solutions. This post is on similar lines, dealing with the actual behaviour of the England selectors and my thoughts thereon.


England, with the series already in the bag, had a diamond-encrusted golden opportunity to experiment with options to fill gaping holes in their top order. Cook’s announcement of his impending retirement from international cricket should have acted as an extra spur. Instead of which we see very little in the way of forward planning or of experimentation of any sort. Even with the certain knowledge that a new opener will have to come in to replace Cook the selectors persevere with the proven failure Jennings.

Three individuals who can feel more aggrieved than most by this behaviour are Rory Burns (another 90 against Essex yesterday after the latter won the toss and chose to bowl first), Dan Lawrence and Liam Livingstone

In view of Cook’s impending retirement I would have recognized openers at 1,2 and 3 (not a bad approach in test cricket anyway), with a view to the two other openers than forming a partnership in future matches. This is why in the previous post I mentioned Tammy Beaumont, a recognized opener who has been scoring stacks of runs recently. Batting is at least as much about timing and placement as it is about brute power, and that is why I believe (unlike in the case of fast bowling) a woman could mix it with the men even at the highest level, similarly with slow bowling and possibly wicket-keeping (for my money the best user of the gauntlets in world cricket across the board at the moment is Sarah Taylor). A number of the all-time greats of test match batting have been of diminutive stature (Bradman, Gavaskar, Tendulkar, Sehwag, Hanif Mohammad and several of the finest Sri Lankans spring to mind instantly). I am well aware that this super-radical option will not happen, but the alternatives that that leaves with are:

  1. Two brand new openers, neither of whom have any experience of international cricket.
  2. One new opener and one opener who has shown already that they are not actually good enough (Jennings)
  3. Two openers who gave failed to prove themselves (presumably Jennings and a recalled Stoneman). 

Of those three options, none of which massively appeal, my choice would number 1, which might end up working out well, and then the question is who to choose to open alongside Burns (whose case for selection is undisputable in the circumstances). 

Having taken the “ostrich option” re their top order difficulties the only outcome from this game that could be acceptable is not merely a win to make it 4-1 for the series but a win by a massive margin. The timidity of the England selectors means that at least one and possibly two England openers will be starting their careers on overseas tours, with their first home test series being against those well known softies, the Aussies.


I will start as usual with answers and solutions to the previous problems (all from brilliant.org) before offering up some new problems.


Screenshot 2018-09-03 at 5.08.56 PM

First the answer:

quad answer

The hackers solution is that there are only two really serious possibilites since the shape is a square, namely 67 (giving an area of 289 = sides 17 units long) and 102 (giving an area of 324 = sides 18 units long), and since the question gave one three tries just enter those values for the first two tries (if your first entry does not come up right). Here, courtesy of Jeremy Galvagni is an elegant genuine solution:



First the answer:

Screenshot 2018-09-05 at 3.09.42 PM

The figure in front of the .99 part of the price can vary, so all we need to know is how many .99s add up to answer ending in .89, and the answer is 11 (11 x 99 = 1,089, so 11 x 0.99 = 10.89), and the next number of items after 11 that would give us an answer ending in .89 is 111, the lowest price total for which would be $109.89. Thus Marie purchased 11 items.


First an astronomy themed problem:


Now a question that has got almost three-quarters of those who tackled in on brilliant, but is not actually difficult:



Swimming MoorhenMoorhen on branchTwo MoorhensMoorhensMagpie

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.


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 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.

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.

Beaumont on the attack

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.


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:

Canteen problem.jpg




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.


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).


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

148148-a148-bBlizzard conditions

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 stamps I

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).

Locos fact sheet


A Solution and Some New Problems

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


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.


Here is the problem again:

Fermat Challenge

Here is the answer:

Fermat 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.


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.


Malfatti Mistake question


Space station Dodecahedron

Good and Bad Mathematical Problems

Two splendid problems, one terrible one and one intermediate one, all courtesy of brilliant.org.


This week on brilliant.org I have encountered two of the finest mathematical problems that I have seen on that site, and also unequivocally the worst. In the rest of this post I will share these problems with you – solutions and explanations will appear in a later post.


This is the terrible problem referred to in the introduction. In almost 15 months og being a brilliant.org solver I have complained about precisely one problem – this one:

bad problem

The “correct” answer when I give it will make it clear precisely why I was so annoyed by the setting of this problem.


These two problems were beautifully set, very fun to solve, and one has a published solution that I consider to be quite superb. First:~
Mendrin Circles

I tackled this one this very morning:

Mr Mediocre question II


Can you give Honey the ant maximum possible access to the surface of the cube?

Honey the ant

Walk for Wildlife

Advertising the Walk for Wildlife and attending to mathematical matters.


The centrepiece of this post comes courtesy of the team4nature twitter account. I have also included the solution to a prnblem from brilliant.org and a new problem from the same source.




Here is the answer the problem I posed last week:

3 and 2 answer

carrying out the subtractions in thte brackets above gives us (2 * 3^22)(2 * 3 ^23)(2 * 3^24). This becomes (2^3)(3^(22+23+24))= (2^3)(3^69). Thus m = 3 and n = 69, and 69 + 3 = 72.

bridging the lake

As a supplement to this little problem, would you have an observation platform where the three bridge segments meet at the centre of the lake? This latter of course, unlike the mathematical question is purely a matter of opinion. I would go for a circular platform just below the level of the bridges, accessible by lifts and stairs.

A Solution and A Couple of New Problems

A solution and two new problems by way of a quick post before setting off for Marxism 2018.


I am writing this immediately before setting off for Marxism 2018, a four-day political festival taking place in London. I should be able to do some posting at the event and at my accommodation. In my recent “An A-Z of Me” I included a mathematical problem from brilliant.org, and I now post the solution to that problem and offer you a couple of others.


The problem I posted earlier was this:


The answer is that there is not, because it turns out that the perimeter of a plus-plus is always a multiple of four, which 2018 is not.


These are also both from brilliant.org. One is easy but generated a bit of controversy, while the other is very hard to solve properly, but by applying logic it can be easily worked out what the correct answer is. First, the hard problem:

clock problem

The easier problem which generated some controversy is this one:


Answers to Puzzles and Notice of Absence

Notice of my imminent departure for a week’s holiday and solutions to Wednesday’s puzzles.


A couple of days ago I set some puzzles for you, and in this post I will be answering them. Also, I am off to Greece for a week’s holiday later tonight (I fly out of Gatwick at 5:40AM, so am envisaging taking the 21:36 train out of Lynn, connecting to a Thameslink service at St Pancras and arriving the airport just after 1AM – the second latest set of connections available to me, and I know British public transport too well and trust it too little to rely on the last possible connections) and although I will take any opportunities that arise to go online I will still have comparatively little access to the internet, so you will hear little from me between now and a week tomorrow evening when I shall be back home.


Dr Frankenine

Here is the most elegant of the official solutions, posted by Callum Cassidy-Nolan:



Fuel Tank

As you can see from the above graphic, almost half of those who attempted solutions on brilliant.org got it wrong. A perusal of the comments section revealed a degree of reluctance on the part of some of the errant solvers to admit to being wrong (never mind arguing with the umpire, some of these folk were metaphorically following that up by arguing with TV replay umpire) so I am to explain the whole process of getting the right answer (though it took me milliseconds to work out and not much longer to enter the correct answer):

  1. After stage 2) half of the original fuel remains and is then topped up with new fuel, and we are told to assume that perfect mixing occurs…
  2. After stage four one quarter of the tank of perfectly mixed fuel has gone, and as it is perfectly mixed one half of that fuel is original, meaning that a further one eighth of total tank full of original fuel has been used.
  3. One half plus one eighth = five eighths of the original tank full of fuel has been used, leaving three eighths of the original tank full still there.
  4. As a percentage three eighths is 300/8 = 37.5 per cent, and the question has asked for that figure. 

One particularly offensive complainant attempted to use the fact that the question had said decimals allowed to claim that an answer of 0.375 should have been permitted. This is wrong – the question specifically asked for a percentage, and the reason for mentioning the a decimal figure was OK was so that people did not think they needed to round to the nearest whole number, which in correct mathematical notation would have been 38 (the figure being rounded away is five or greater so you round up, had it been four or less it would have been correct to round down). 

Another complaint people made was being marked wrong for including the percentage symbol – I am less unsympathetic to this than I am to the indefensible claim that 0.375 should have been marked as right, as this latter has missed out turning the answer into a percentage, but including the symbol is still a mistake as the way the question is asked renders it needless to do so. 

Please note that I did not create this problem and had nothing to do with deciding what answer should be marked as right – I have treated it at length because I was annoyed on the composers behalf that so many solvers rather than attempting to see by looking at correct solutions, of which plenty of good ones were posted, why their chosen answer was wrong instead opted for the ‘argue with the umpire’ approach, in some cases being very unpleasant about it. Here to end this little post is David Vreken’s published solution: