UCAS End of Cycle data – the Whitty effect and getting lost in the (Boston) Matrix

In February the good people at UCAS released their end of year report along with some lovely dashboards allowing people to look into the major trends around applications and accepts for the UK HE system. They also released their massive range of data sets which gave the VizHE folks something to do in lock down.

With their shiny dashboards UCAS had pretty much covered the basic summarisation of the data so we wanted to see what else we could extract that piqued our interest.

With the current world situation we talked through looking at subject trends from a position of what are the popular subjects and to what degree had they been influenced by the brilliant scientists and doctors who have been a large part of the collective effort in the past year or so.

We each followed separate lines of enquiries and came up with three fantastic vizzies – one using the Boston Matrix approach to review subject trends, one digging into the Whitty effect and one looking at the choices both within subject and ethnic group around clearing and adjustment.

The Boston matrix is a tool used to look at the portfolio of products to see how they are performing. It effectively places the products into four quadrants:

Star (High market growth, high market share)

Question Mark (High market growth, low market share)

Cash Cows (Low market growth, high market share)

Dogs (Low market growth, low market share)

The quadrants are created by plotting the change in market share against the market share for the current year based on the applications for each subject. It is possible to look at the data by different date ranges and by individual institution performance.

The visualisation is available here: https://public.tableau.com/views/UCASApplications-BostonMatrix/InstitutionBostonMatrix?:language=en&:display_count=y&:origin=viz_share_link

Jennie – The Chris Whitty Effect – Analysing the increase in UCAS applications for health and social care courses

I decided to focus on the increase in applications for health and social care courses coinciding with the COVID-19 pandemic, termed ‘The Chris Whitty Effect’ by WONKHE in their recent blog available here (Tracing the Chris Whitty effect in the 2020 end of cycle admissions subject data | Wonkhe).

Delving into the data more closely I could see straight away the increase in JACS subject area ‘Subjects allied to Medicine’ which has a big jump from 2019 to 2020 and it stands out amongst other JACS subject groups. The trend over time is also interesting for this subject; applications dropped in 2017 and 2018 coinciding with the change in removal of bursaries from 1st August 2017 for students taking pre-registration nursing, midwifery and allied health courses. This year though, main scheme applications (the main UCAS application scheme whereby students can apply for up to five institutions or course) are up by almost 9%.  Medicine and Dentistry has also seen a 5% increase in applications, but by far it is Subjects allied to Medicine that has seen the biggest increase.  When looking at total accepted places, again it is these two subject areas that are ranked on top, with a 17% increase in accepted places for Subjects allied to Medicine and a 9% increase for Medicine and Dentistry.  Conversely Non-European Languages and Literature has seen the biggest drop, with a 15% decrease in main scheme applications and an 11% decrease in total accepts, so it would be interesting to delve further into this data in future analysis.

Looking specifically at Subjects allied to Medicine I wanted to focus on individual providers to see if an increase in applications is also reflected in an increase in accepts. As I expected, the majority of providers that saw an increase in applications from 2019 to 2020 also saw an increase in total accepts. Of interest though are those providers for which applications increased but accepts either stayed static or even decreased. I wondered if this was due to caps on the numbers of places available at these providers so I looked at applications and accepts across all JACS subject areas for these particular providers.  Although I couldn’t see any obvious pattern here, some of these providers did see an increase in applications and accepts for certain subjects (see University of Bath).  This could mean that caps on places for Subjects allied to Medicine might be the issue, however more in-depth knowledge of courses at the provider would be needed to know for sure.

This time I experimented with using a long form dashboard which I haven’t used before.  I usually like to see everything all in one go, however I do think it works and helps tell the story.  I also played with the golden yellow colour across the dashboard, I don’t think it looks too bad, but let me know what you think 😊. If I had more time I would have liked to repeat the bottom chart for all providers in scatter plot to see if this pulls through any patterns when comparing across different subject areas.

The visualisation is available here: The Chris Whitty Effect – Analysing the increase in UCAS applications for health and social care courses – Jennie Holland | Tableau Public

Sasha – Widening Participation – Exploring changes in relationships of ethnic groups in UCAS application stages

I set out to investigate the difference between applications and acceptances recorded for each acceptance route against measures of widening participation in HE. The first challenge was to combine the files: there was one file containing applications, another acceptances and a set for each of the WP metrics. Starting with the ethnic group data I noticed that there was a huge difference in numbers; far more acceptances than applications. The crux being the applications file only contained main scheme applications whereas acceptance also included others (see below). Not a big issue as you can use this field to join the data. However what you end up with is only three acceptance routes: Firm, Insurance and Other, and not many insights to draw.

Back to the drawing board, I looked at the initial question that interested me. I wanted to look at the differences in groups of people going to university at the opposite end of the scale acceptance scale: adjustment and clearing. I dropped the combined file altogether and focused solely on acceptances. The below DNA chart shows the few groups going for adjustment and their subject choice by year. It also compares the popularity of these subjects when it comes to clearing.

The visualisation is available here: TBC



Blog number 2 for the 2020 VizHE team which now includes the skills of Rhodri Rowlands and Jennie Holland both visualisation masters and data wrestlers extraordinaire.

The standard data returns that UK HE institutions have to complete is focused on the estate that University inhabits.  This data set is not always the most exciting (although VizHE have covered it before here and here) but with the current position the sector, country and world are in the estate and it’s make up suddenly becomes an important topic.

The initial discussion for the VizHE team was to look at to what extent social distancing would be possible on campuses.  In the data set from HESA we have students, staff as well as internal and external space for each institution so a couple of calcs and we would have the answer….

As we talked it through though we realised we were getting caught up in the jump to an overly simplistic view of a complex problem.  There are many factors that the metric does not take into account such as how the spaces are configured, what groups the students are in and also to what extent the data focuses on students and staff who would be on campus!

So changes in direction needed – luckily this data set had plenty of options.Within the data set there is a wealth of information around the environmental credentials of the HEIs.  From waste to energy to emissions to travel.It was in travel that Dave decided to explore and to see how the UK HE staff get to work.  In this Viz Dave has defined four categories:

  • Great – where staff cycle or walk to work

  • Not too bad – where staff get the bus, train or car share

  • Bad – where staff travel via motor bike or single occupancy car journey

HEIs were then ranked by how great they were.  There were some unsurprising results with many Oxford and Cambridge near the top and a lot of London and big city HEIs doing well.  Within this though there was a contrast between how many were really great against how much they were just not too bad.Interactive viz – click hereHow do staff get to work_

Jennie’s visualisation is titled ‘Uni-cycling – which institution is #1 for cycle spaces?’, and looks at the total number of cycle spaces at each institution against the number of staff and students to build a cycle space ranking.  The visualisation is split into two halves.  The left-hand gears control the ranking and can be used to flick through the ranking list.  The right-hand gears are used to highlight institutions and look for patterns based on groupings such as Million Plus, Russell Group etc. (data sourced from learning-provider.data.ac.uk), as well as their geographical location.

Unsurprisingly Oxbridge do well, with approximately 5 people per cycle space on average (2018/19) compared to 29 people on average across all other institutions.

To expand the analysis further it would be interesting to source some additional datasets and see if there are differences in the number of cycle spaces based on institution type (city, campus etc.), as well as how well the surrounding area is equipped for cycling based on the number of cycle routes. 

View the viz here!

Jennie Viz

Hopefully that has shown that there are some interesting insights in the Estates data!

Let us know what you think

VizHE crew

VizHE 2020 – starting with Finances

Hey up – it has been a while since the Visualising HE crew have got together.  Since the last post Elena has moved to Sweden so we have roped in Sasha from the Information Lab to bring much needed energy and skills to the project.

As with the post last year we have picked up the Finance data to see what interesting insights we could identify.  The talented bunch at WonkHE have been pulling the Finance HESA data apart in recent weeks in particular looking at the potential impact the current situation may have on the sector and indeed individual institutions – if you have not read their stuff then you really should.

We each took different routes through the data which brought the opportunity to try out new chart types.

Adam and Sasha both looked at the income streams for Universities to see how diverse they are.  Adam wanted to be able to the see the whole sector whilst also being able to see the individual Universities within the sector.  His Viz also allows the user to change the sort order if there is one income stream you are more interested in.

Adam’s Viz

HE Income by category

Link to interactive viz

Sasha wanted to focus on the individual University so you can see how diverse the income is and which of the income streams dominates by University.  The visualisation also has the ability to see the information for previous years as well.

Sasha’s Viz

How diverse is the income portfolio of HE providers_

Link to interactive viz

Dave decided to focus on the picture of the sector as a whole and using basic quadrant analysis spit out the Universities into what degree their income is made up of tuition fee income and out of that tuition fee income how much is from non UK or EU students.  The visualisation paints quite a stark picture given the current position.

Dave’s Viz

VizHE April 2020 HEI Tuition fees

Link to interactive viz

Well that is the first post for Visualising HE for 2020 – let us know what you think

National student survey – how happy are they?

So this year there was a change with the national student survey (NSS). This time it was not changes to the survey itself (last year the questions were changed and new themes introduced) but, rather, changes that it now came under the custody of the Office for Students (OfS) since they replaced HEFCE.

The changes were not dramatic but represented a subtle shift towards the students’ interests.  The data was not shared with Higher Education Institutions (HEI) before publication so that the students got to know the performance of the HEI at the same time as the Institutions themselves.

The other changes have been that the data has been presented in a slightly different, more accessible format.  It is a long way off dashboards with visualisations but the data is there for people to easily review.

So we at #VizHE decided to pick up from where we left off last year (NSS 2017: One data set, many dataviz approaches.) and pull out a few interesting nuggets for you.

The starting point was to see how the students had responded on a national level looking at the themes.  This was also tied into the monthly story telling with data challenge which was on dot plots.

NSS Theme score comparison (1)

The interactive viz: is here!

The main takeaway is that it really has not changed that much and where changes have occurred, they have been negative.  The only exception is Wales where the students have responded much positively this year compared to last.

Adam decided to reviz the headline theme performance overview originally posted on the OfS pages because he wished to make it easier to compare satisfaction with the themes rather than themes and years mixed up together.




NSS2018 themes.png

Following on from revizzing the headline NSS theme results Adam wished to dig a little deeper into the student satisfaction with the separately reported question 26 – ‘Students’ union’ part of the ‘Student Voice’ theme, highlighted above as very much lagging in student satisfaction compared to the sector theme scores.

Which unions are getting it right?

Which unions are getting it right

The interactive viz is here!

The main takeaway is that Alternative Providers (AP’s) appear to be getting it right more than Higher Education Providers and Further Education Colleges when taking the median score for each the provider types as a reference point. However, the populations are small for AP’s and this could be causing the volatility and wide distribution of scores seen in the figures. Hover over the box plot distributions to see which providers are getting a thumbs up from the students and who are in the dog house!

So that’s all from us for now. Thank you for reading and we hope you enjoyed exploring our  visualizations!

Dave and Adam

Team #VisualisingHE

Shining a light on business and community interaction in HE

One area of UK higher education which is not much talked about is the work that is undertaken working with businesses and the community, whether that be through research, consultancy or training.

The lovely people at HESA collate all the terrific detail of this work through the annual Higher Education Business and Community Interaction (HE-BCI) survey.

The data and associated visuals produced by the splendid people in Cheltenham are here: Lovely data and visuals.  For this post team #VisualisingHE focus on just a couple of aspects.

HE Market Leaders

Firs is Dave’s take on the business and community services provided by HE provider. He looked at which institutions are providing the bulk of activity (and, therefore, the income) in this area, and how it is changing over time.

HEBCIS - Market Share

The interactive visualisation shows the data in quadrants and allows the user to split the data by the type of service and also the type of organisation that the HE provider was working with.

The size of the square is the total income for the selection and the colour provides shows the region of the provider.

The main takeaway from this visualisation:

In all the categories there are only a few HE providers who dominate the area (Oxford for Contract Research, University of Leeds for Facilities and equipment) with the exception of Consultancy which is shared a bit more across the sector.

Engagement with the General Public

The second take on the HE-BCI data is Elena’s interactive visualisation that shows how universities engaged with the community in the 2016/17 academic year in one of 5 categories.

HEI Social Engagment.png

The screenshot above shows details just for free Museum education type of events. Each HEI is plotted in the scatter and is coloured based on the region it belongs to. For consistency, Dave and Elena used the same colours for the regions. T

he scatter plot shows the scope of the HEIs’ activities measured by number of attendees and number of staff days. The totals for the entire sector can be seen just above the scatter.

The main takeaway from this visualisation:

The main insight can be seen when switching between the different types of events: usually universities are clustered quite closely and very few outliers can be seen in any of the categories.

Thank you for reading and we hope you enjoyed exploring our visualisations.

Dave & Elena


‘Non-continuation’, ‘continuation’, ‘retention’, ‘drop out’, ‘no longer in HE’… blah blah blah. There are many words for it and they are all slightly different but they basically come down to how good is the sector and higher education institutions (HEI) at keeping students in the system so that they can flourish and achieve.

One of the most established metrics in this area is used in the UK performance indicators which is produced annually by HESA (full details here).  This metric focuses on the extent to which the students have been retained within the system (i.e. have they left but gone to another institution) and looks at not only if they dropped out throughout the year but also if they returned following the summer.  There is also allowance given for the fact that going to University itself can present challenges for the stufents so those that leave in the first few months are not counted in the metric.

For this post we focused on two simple but key questions (HESA provide a lot of additional insight on their site)

How have things changed over time?

How do the very different HEIs perform?

For the first question Adam looked at the full time, first degree, first year, non-continuation trend in the sector as a whole over the last 10 years. In particular, the visualisation focuses on the UK domiciled entrants enrolled on a full-time mode and shows how the rate is different for young and mature students.

Interactive viz here!

Non Continuation rate_UK HE 20067-20156

For the second question Dave focused on just the latest year’s data.  When producing the metric HESA also arrive at a benchmark which takes into account the make up of the particular HEI student body.  It is a nod to the fact that not all HEI have the same challenges when it comes to retaining students.

It’s a long one! This visualisation lists all the HEIs with the non continuation rate (lower is better) coloured by the variance to benchmark and the width of the line showing how many students make up the non continuation.

Interactive viz here!Non Con HEI Summary

I hope that was of interest and please do dig into HESA’s analysis.

Dave, Adam and Elena

Students in HE – some interesting bits..

Hey up – it is a new year and at Visualising HE towers we made a new year’s resolution that we would keep up with the latest HE data releases. So we were pleased that HESA provided us with an early new year present in the form of some summary student statistics loveliness.

The lovely people in Cheltenham have taken a slightly different tact with this release with an approach guiding the reader through the analysis and allowing the draw down of the data that supports each chart so that you can revisit the story for additional insight.  This approach has not had universal acclaim (a superb WonkHE article on the subject) but it gave us rich pickings for our Visualising HE fun.

So where to start? With all the discussions around Brexit and the widening discussions around the value international students have on the UK economy it was felt that looking at where the students come from would be worth a peak.

Take 1: UK vs. Non-UK Enrolments

The first viz uses data from figure 6 and focuses on Higher Education Institutions (HEI) and to what degree their enrolments come from the UK against non UK enrolments.

UK vs Not UK (1)

The interactive viz is here and the vispiration came from the great Ben Jones blog post.

The main takeaways from this is that (unsurprisingly) the number of UK enrolments is quite spread with most HEI taking in sizeable cohorts.  When looking at non UK enrolments there are many HEI taking small amounts then a few taking in the larger numbers.

In terms of interesting HEI the University of Manchester stands out just through its sheer size both for UK and Non UK enrolments where it is among the largest in both categories. Imperial College has a slightly different balance with nearly as many non UK enrolments as UK.  Then the reverse of that is Sheffield Hallam who have a large UK cohort and a small non UK cohort.

Take 2:  UK, Other EU and Non-EU 1st year enrolment Trends

The second viz uses data from figure 8 and builds onto the international question by separating the EU and Non-EU entrants to deliver a quick insight into the general trends across the sector. Figure 8_visualisingHE

The interactive viz is here.

The main takeaways from this visualisation are the predominance and continued growth of UK domiciled students entering at first degree in UK HE in 2016/17, and the continued proportional decline of the Non EU first degree postgraduate research (PGR) and postgraduate taught (PGT) student populations.

The filters on the top right of this dashboard allow us to delve further into the data set and see the trends at country level. It appears that the the decline of the Non EU entrants at a postgraduate level is most prominently observed at HEIs in Wales, where first year enrolments on both PGT and PGR programmes have experienced the sharpest decline during the last four years.Adam's UK-EU-NonEU Enrolmentspng.png

Take 3: Subjects’ Popularity and the Gender Gap

The third viz uses the data from figure 12 and presents an overall view of the new enrolments in the sector with a slight focus on the subjects’ popularity (science vs. non-science enrolments) and the gender gap (male vs. female enrolments).


The interactive viz is here.

The main takeaways from this dashboard are that enrolments in the science subject areas, represented with blue diamonds, have increased more than enrolments in the non-science subject areas, shown as grey circles, since 2012/13.

A further insight is available through the in-built #VizInTooltips available on hover. From these we can see that first year enrolments on ‘Computer science’ related programmes have increased at both First degree and Postgraduate Taught (PGT) levels.

Summary - Computer Science.png

The dashboard also highlights that the ‘Business & administrative studies’ appear to attract similar numbers of male and female students. All of the subjects dominated by male enrolments are from the science field. However, the gender gap has been gradually decreasing for some of them: ‘Architecture, building & planning’ is a good example where the difference has decreased from 28 to 20 percentage points.

Summary - Architecture.png

Take 4: Top 10 Non-EU Domiciles

The last take on HESA’s SFR for 2016/17 uses data from figure 11 and is the colourful  #Coffetableviz style visualisation of the Top 10 Non-EU Domiciles for First Year enrolments in the UK.

Non EU international dom first year enrolments to UK HE_white

The interactive viz is here.

The main takeaways here are the solid first position for enrolments from China and the fact that the top 10 domiciles have remained the same since 2011/12. Other more noticeable changes include Nigeria’s decline from 4th to 6th position (shown in orange) and Hong Kong’s rise from a steady 6th to a 4th position from last year (shown in light green).

That’s it for now from us. Thank you for reading and we hope you enjoyed exploring our data visualisations!


Dave, Adam and Elena

The potential TEF metric – sustained employment from LEO

Back in 2016 the government released its first experimental LEO data (or Longitudinal Educational Outcomes to give it its full given name) and it has now matured to be considered under the TEF (Teaching Excellence Framework to give it its birth name) with TEF 2 including an element of it as a supplementary metric.

Unlike the salary data (which Adam did a superb job vizzing here) this metric is not going to grab the attention quite as easily. The metric is sustained employment 3 years after graduation.  The data is sourced form HM Tax returns and does have challenges (lack of self employment, maternity leave etc etc) but it does provide some interesting patterns by subject.

The first viz is a simple view showing where the HEI (Higher Education Institutions to give it its name that its Mother would use when telling it off) sit by its metric outcome grouped by subject.

The interactive viz is here

LEO 3 Year

As you can see the GB average is around 75% for most subjects with just Languages and Combined subjects falling below that. Economics, Education, Mathematical Sciences, Medicine and Dentistry and Nursing all have a GB average above the 75% seen in the other subjects.

At the moment this is just a supplementary metric which will only be used for context when selecting the TEF outcome (another excellent blog explaining TEF here) but it shows the direction of travel and HEIs need to get a handle on where they sit in this metric.

To aid that understanding Adam has created a magnificent more exploratory viz which allows the data to be split by sex, years after graduation (1, 3, 5) as well as region. It can then be viewed by subject with the ability to highlight your institution.

Take it for a spin here

LEO - Proportion of students in Sustained employment further study or both after graduating

Well I hope you enjoyed reading and found it informative – any questions, queries or feedback let us know.



The wonderful world of finance

It may be said that Finance data doesn’t always attract the big crowds in the world of HE. The HE main stage is often reserved for hotter topics like the Teaching Excellence Framework (TEF), Research Excellence Framework (REF) and external media focus from league tables often focus on the academic and student outcomes, rather than the support system sitting behind it. In our experience financial data struggles to get visualised and has a reputation for being dull and wedded to excel data tables. Cue #VisualisingHE…

We thought it would be a great idea to focus this post on the wonderful world of finance. We merrily went off and downloaded years of finance returns from HESA and combined them into a wonderful big data set, pulled on our finest Tableau viz gloves, poured a large coffee and readied ourselves to create some tableau masterpieces. We were thinking; small multiples, exploratory box plots and even the odd map.

All was going well until Adam pointed out:


Having just two years of data just made it a whole more tricky to do something interesting.  Most of the ideas we had fell by the way side.  The exploratory viz survived and Stephen joined the conversation and looked at mapping. Searching for ideas and filling a long string of twitter messaging, conversations took a bizarre twist with references to BANs. Dave was transcended back to his younger days where ‘just for fun’ he was tasked to build spreadsheets for his Dad in Supercalc – Adam felt it would be rude not to pay homage to this fond memory and attempted a retro spreadsheet viz to bring the memory back to life:


HESA Finance: 2014/5 & 2015/6 IN THE STYLE OF: SUPERCALC

On this finance focused folly we have honed in on Income, Expenditure and Surplus deficit, and here are the headline BANS:

Total income was £34.7 billion during the financial year to 31 July 2016. Overall expenditure was £33 billion in 2015/16. The surplus of income over expenditure was £2.3 billion in 2015/16, or 6.8% of total income.

The hard hitting stat (KFI) in the wonderful world of Finance, is Surplus deficit as a percent of total income, so our vizzes mainly explore this key financial indicator.

Below is an exploratory viz encouraging the viewer into the relationship between income, expenditure, surplus or deficit between providers, mission groups and years.

surplus deficit_explorartory.png

Link to viz: HESA Finance 2014/15 – 2015/16

The number of HE providers reporting a surplus was 142 out of 163 in 2015/16. Deficits in the financial year 2015/16 were reported by 20 providers.

So plenty of stuff there – one last roll of the dice…

Shape – the vizzes so far were great at looking at the providers and how they were performing but we wanted to have a play around and see if we could find something that shows the shape of the sector and a bit of how it has changed.

Income Expenditure Surplus

Link to viz: Income, Expenditure and Surplus for the UK HE Sector

Does it work?  Sort of we can see that the sector has made slightly more surplus in 2015/16 and we can see that only a few institutions make the bulk of the surplus.  We can also see that as a sector there has been a better financial performance with less providers having a negative KFI (Surplus/deficit as a % of total income).

There are definitely more effective ways of representing this (such as the exploratory view above) but we enjoyed trying something new.

Hopefully you have managed to get to the end and we have managed to convince you that it is possible to visualise HE finance data and find some useful insight.

An analysis of UCAS subject trends 2007-2016

For those that do not know UCAS is the main admissions service for entry to UK Universities.  Each year they produce an end of cycle report with associated data resources.

We have dug into these lovely resources and looked at the trends around Subject Groups.

For this blog we each looked at the same data but from slightly different angles and different chart types.

Is the UCAS application market evenly spread?

The first question we had was to what degree the UCAS applications are spread across the subject areas.  Are there a small group of subjects that have the majority of demand?

In order to answer this question Adam turned to the Pareto chart.  For those that have not come across this before it follows the Pareto 80/20 rule where by 80% is owned by 20% of the people.  This is a good way of visualising if an area is dominated by the few.

UCAS end of cycle report 2016Click on link to access the interactive viz: UCAS End of Cycle Report 2016: Pareto Analysis

As you can see from Adam’s viz, it is not quite fitting the Pareto rule but the sector is skewed towards 5 main subject areas which take up to 50% of all applications in 2016.

How has the demand changed over time?

For this question we wanted to look at the trends over time and to see the change we decided on a Bump chart.  Dave’s viz uses a bump chart which creates a rank then shows how the subjects change over time.  We have added in the number of applications as the size of the bubbles so you can see which are the larger and smaller subject areas.

UCAS Subject Popularity (1)Click on link to access the interactive viz: The Popularity of UCAS Subjects 2007-2016

As you can see at the top, there is not too much movement but the subject areas in the middle have seen some dramatic drops as well as some dramatic climbs over the last 9 years.

Which subject areas are on the rise, which – on the decline and which providers are the most popular ones? 

The third approach to analysing the UCAS data gives an extra dimension to the subject trend analysis. Elena used a scatter plot to compare the short term with the long term demand on the subject area groups and added an action filter to allow users to see the top [N] providers that attracted the highest amount of undergraduate applications.

UCAS Subjects vs. Top Providers (Highlight Kings College)

Click on the link to visit the interactive viz: UCAS Undergraduate Subjects and Providers: 2007-16

In the scatter plot above you can see that the bigger subject areas are experiencing a steady growth in demand. Looking at the 20 most popular providers shown in the rank chart, there isn’t much change in the top 5 institutions but King’s College London (highlighted) shows a steady increase over the 10-year period to move from 15th position in 2007 to 7th position in 2016 for the overall number of UG applications received.

So there you have it three different questions with three different solutions from three authors.

I hope you found it useful and of interest.  We would love to hear what you think.


Dave, Adam, Elena and Stephen