Some properties of Automorphic numbers

This post is a complete change from my usual subjects.

Many years ago a man named Mike Mudge wrote a monthly column for Personal Computer World called "Numbers Count". There seems to be very little about him on the web, except for other fans like me. One such column inspired the following paper written jointly by my father[1] and I.

This work has just come to light during a recent house move that caused me to search through old papers, and despite it being 20 years ago, a quick search of the web shows that it still contains some original stuff, so I thought it would be interesting to publish it here. I am publishing it here unaltered, though obviously computing power has improved a lot over the years. I have tried to reproduce it exactly, but I may have made some transcribing errors, and if you see any please let me know.

Nb 20 years ago this work was unique to the best of our knowledge, but I can't promise that is still so.

Some properties of Automorphic numbers

Abstract: 

An automorphic number is is a number whose square ends in the same digits as number itself. Automorphic numbers form two series ending respectively in the digits 5 and 6. Successive members of each series have the same sequence of trailing digits and are formed simply by appending a new leading digit to their predecessor. Corresponding numbers in the two series bear a simple numerical relation to one another and are co-prime. Consequently, the sequence of one series uniquely determines the sequence of the other series. Some properties of automorphic numbers are discussed and these properties used to develop rapid and efficient methods for the generation of automorphic numbers. One such method generates numbers of up to 32,000 digits in length in a run time of 75 minutes[2]. n-Automorphic numbers to bases other than 10 are briefly discussed.

Introduction:

The computer generation of automorphic numbers using a simple trial and error process soon indicates that there are only three n-digit automorphic numbers for any value of n. One of these consists of the digit 1 with a string of leading zeros and may be regarded as trivial. In the case of the other two, it is found that with the exception of the leading digit, each n-digit automorphic number is identical with the corresponding n-1-digit number, and it is therefore only necessary to determine the leading digit for any n-digit  automorphic number. The following describes some properties of automorphic numbers and which lead to more efficient methods for their generation.

Methods

The generation of automorphic numbers was carried out with a Packard-Bell 445 elite 486Ssx running at 33mHz using programmes implemented in turbo pascal.

Results

Theorem 1 : 
For any value of n, there exists only two n-digit automorphic numbers and these end in the digits 5 or 6.
Proof: Let n= 10a+b represent a two digit number. If n is automorphic then 
 n^2=100a^2+20ab+b^2=1000z+100y+10a+b   .............................  (1)
and b^2=b+10x
where x is an integer. Only b=5 or b=6 satisfy this condition and therefore all 2 digit automorphic numbers must end in 5 or 6.

Substituting b=5 in equation (1) above gives
100a^2+90a=1000z+100y-20
90a must end in the digits 80 and therefore a=2 and n=25.
Substituting b=6 in equation (1) above gives
100a^2+110a=1000z+100y-30
110a must end in the digits 70 and therefore a=7 and n=76.

Let n=100a+10b+c represent a 3 digit number. If n is automorphic then 
n^2=10^4*a^2+2ab*10^3+b^2*10^2+2ac*10^2+20bc+c^2=10^5z+10^4y+10^3x+100a+10b+c ........ (2)
and c^2=c+10j where j is an integer, therefore the digit c must be either 5 or 6.
Substituting c=5 in equation (2) gives us 
10^4*a^2+2ab*10^3+b^2*10^2+10^3a+10^2b+25=10^5*z+10^4*y+10^3*x+100a+10b+5 ...... (3)
and 90b must end in the digits 80, therefore b must have the value 2.
By the same procedure substituting b=2 into equation (3) gives the value a=6. Substitution of c=6 in equation (2) and repetition of the same procedure gives values of 7 and 3 for b and a respectively.
Therefore to digit automorphic numbers can only be 25 and 76, and 3 digit automorphic numbers can only be 625 and 376.

Conjecture A

If p and q are any pair of n-digit automorphic numbers then p+q=10^n+1

Conjecture B

If p and q are any pair of n-digit automorphic numbers then p and q are co-prime.

Theorem 2

If p is an n-digit automorphic number and q=p-1 then pq=100s where s is an integer.
Proof: Let pq=1000a+100b+10c +d and p^2=1000f+100g+p
Then p^2-pq=1000f+100g+p-1000a-100b-10c-e=p
1000f+100g=1000a+100b+10c+e
Therefore c and d must be zero, and a=f, b=g, and pq=100s where s is an integer.

Theorem 3

If p is an n-digit automorphic number and 10^nA+p is the corresponding n+1-digit automorphic number, then A(2p-1)+x=k*10^n-1 where k is an integer and 100x=p^2-p
Proof: Let p=10a+b. If p is automorphic then 
p^2=1000l+100m+10a+b=100(10l+m)+p
Let x=10l+m then p^2=100x+p and 100x=p^2-p
Let the 3 digit number be 100A+p, then if this number is automorphic
10^4A^2+200pA+p^2=10^5*z+10^4*y+10^3*x+100A+p and 200pA-100A=p-p^2+1000k
Therefore A(2p-1)+x=10k
By the same procedure it can be shown that for the 4-digit number 1000B+100A+10a+b the leading digit B is given by the expression
B(2p-1)+j=k*10^2 where p=100A+10a+b, j*10^3=p^2-p, and k is an integer.

Theorem 4

If k is the square of an n-digit automorphic number j ending with the digit 6, then the le4ading digit in the corresponding (n+1)-digit automorphic number is 10-m where m is the coefficient of 10^n in k. For the corresponding n-digit number ending with the digit 5, the leading digit in the corresponding (n+1)-digit number is m where m is the coefficient of 10^n.
Proof: Let p=10a+b where p is a 2-digit automorphic number, then p^2=1000l+100m+10a+b
Let the corresponding 3-digit automorphic number 100A+p
From Theorem 3 above we know
A(2p-1)+10l+m=10k where k is an integer
Substituting p=76 we get 151A+10l+m=10k and A*l+m=10
Therefore A=10-m
Substituting p=25 we get 49A+10l+m=10k and A*9+m=10k
Therefore A=m

Theorem 5

For any value of n there exists only three-n-digit tri-automorphic numbers and these end in the digits 2, 5 or 7.
Proof: Let n=10a+b then 3n^2=300a^2+60ab+3b^2
If n is tri-automorphic then:
300a^2+60ab+3b^2=1000z+100y+10a+b  ..................  (4)
and 3b^2-b=10x   ............................  (5)
where x is an integer. This condition is only satisfied by b=2, b=5, or b=7
Substituting b=2 in equation (4), it follows that a=9
Substituting b=5 in equation (4), it follows that a=7
Substituting b=7 in equation (4), it follows that a=6
Corollary: 
For di-automorphic numbers, equation (5) becomes
2b^2-b=10x and b=8
For tetra-automorphic numbers, equation (5) becomes
4b^2-b=10x and b=4
For penta-automorphic numbers, equation (5) becomes
5b^2-b=10x and b=5

Discussion

Initial computer studies were carried out by testing numbers in sequence for automorphic character. The programme listing is shown in Appendix 1 [3]. As might be expected run times were very long and only 16 automorphic numbers were generated in a run time of 3 hours [4]. These studies did however demonstrate two important properties of automorphic numbers.
1. Only two n-digit automorphic numbers exist for each value of n
2. Such numbers form two series in which successive members differ from their predecessors only in the leading digit.

The first 8 members are shown for example below

Series 1	5	25	625	0625	90625	890625	2890625	12890625
Series 2	6	76	376	9376	09376	109376	7109376	87109376
Total	11	101	1001	10001	100001	1000001	10000001	100000001

In order to convert an n-digit automorphic number into the corresponding (n+1)-digit automorphic number it is necessary only to test the digits 0 to 9 for suitability as the leading digit of the next number. This obviously facilitates the computer generation of automorphic numbers. Furthermore it appears from the above table that the sum of a pair of n-digit automorphic numbers is equal to 10^n+1 (see Conjecture A above), and therefore a sequence of automorphic numbers is uniquely determined by the corresponding pairing sequence.
Theorem 3 allows the calculation of the leading digit of the next automorphic number in the series. If for example p=625 then A*1249+390=10k implies A=0 giving 0625 as the next automorphic number in the sequence. If p=0625 then A*1249+39=10k gives A=9 making the next automorphic number in the sequence 90625.
Theorem 4 provides a simple alternative method for the calculation of the next leading digit in automorphic numbers terminating in the digit 6. If p=376 then p^2=141376 and m, the coefficient of 10^3 is equal to 1. Therefore A=10-1=9 giving 9376 as the 4 digit number.If p=9376 then p^2=87909376 and m the coefficient of 10^4 is equal to zero. Therefore A=10-0=10 giving 09376 as the 5-digit number. If p=625 then p^2=390625 and m, the coefficient of 10^3 is equal to zero giving 0625 as the 4-digit number.The same procedure gives 90625 as the 5-digit number in the sequence.

The programme listing for this procedure is shown in Appendix 2 [5]. Using this procedure, the series of automorphic numbers up to 20,000 digits in length was generated in a run time of 54 minutes. Repetition of the procedure using an AST 486DX running at 50Mhz generated automorphic numbers of up to 32,000 digits in length in a run time of 75 minutes. As a point of interest it may be noted that the leading ten digits and the trailing ten digits of the two 32,000-digit automorphic numbers are as follows:
6351634399..............................................................................8212890625
3648365600..............................................................................1787109376


Appendix 3 lists all the n-automorphic numbers to base b where b=2 to 10 and n=1 to b-1 [6]. The following points may be noted:
1. No base 2 automorphic numbers are apparent.
2. It is conjectured that an (n+1)-automorphic number to the base (n+2) is of the form:
.......nnn(n+1). For the cases n=5, b=6 and n=9, b=10 there are two accompanying numbers while single numbers only occur for all the other cases.

[1] http://www.google.com/patents/US4877732
      http://www.google.com/patents/US3636037
      http://www.google.com/patents/US4249015
      http://www.google.com/patents/US3701779
      and others................... 
[2] Note the timings given in this paper were from the initial work carried out approximately 20 years ago, and obviously would be very different if repeated these days.
[3] Unfortunately this appendix has been lost, if I find it I will add it here later for the sake of completeness.
[4] I have just run a very simple python script and using a brute force method it generated the first 16 in 128.222 seconds!
[5] Again this programme listing was not found, sparing people from seeing my lack of coding skills from 20 years ago!!
[6] The loss of this appendix is a great shame as this gives some interesting information. I will try to recreate this data at some time.

KwaMoja version 14.02 is released

 KwaMoja version 14.02

This is a brand new version of KwaMoja with many additional features, and many enhancements from webERP.

There is a completely rewritten installer giving an option of 27 different charts of account donated by contributors from around the world. Users have the choice to upload some demo data, or to go through the entire hand holding procedure to set up a new blank company.

Internal stock requests can now be edited or cancelled on a per line or per request basis.

When making a payment to suppliers, the invoices can be chosen from within the payments screen, and all allocations are performed automatically.

Inventory can now be analysed on an ABC basis, to identify fast/slow moving items. This analysis can be done using different bases, and multiple analyses kept.

KwaMoja has a dashboard that enables multiple views of the status of orders/inventory/banks etc. to be shown on one screen. This is configurable on a per user basis.

There is a new and more intuitive user interface for those using it for whom English is not the first language.

Shipments can now be entered with a start date before today's date thus enabling a more sensible ETA date to be entered.

The code has been simplified and smartened up in line with the coding guidelines.

Numerous bug fixes have been applied.

Form as are now verified at client side, and better error dialogs are shown.

The full change log can be viewed here: https://github.com/timschofield/KwaMoja/blob/release_1402/doc/Change.log

The state of resource planning in African Industry

A proper history of ERP would be beyond the scope of this article so what below is a radical précis of the facts, simplifying occasionally for the sake of brevity.

In the nineteen seventies a new approach to manufacturing systems started to spread outwards from Japan. Generally credited as starting at Toyota where it had evolved over a period of years. This approach had several names JIT (Just In Time), stockless production, and Material requirements planning (MRP).

What was happening was that the capabilities of computers was being utilised to plan the resources being used in manufacturing to dramatically reduce the cost of holding and handling these resources. It became possible to plan exactly what resources were going to be needed and when. Then correct management of the supply chain meant that these resources could be in the right place at exactly the right time. Better planning and efficient use of resources produced better quality finished goods.

This revolutionary approach began to move through western businesses during the eighties with such companies as Hewlett Packard leading the way. Through the eighties and into the nineties most western companies adopted at least some of this new manufacturing philosophy, the most successful at implementing this became the most competitive, and survived the recessions of those years.

Computer software to help this approach was developed, at first in house, and then by ISV's. This was called MRP, then MRP II also CRP (Capacity Requirements Planning) eventually evolving into one integrated solution ERP (Enterprise Resource Planning).

Like most new market places there was an initial explosion in the eighties of many vendors supplying this software, followed up as the market matured in the nineties by a consolidation into a small number of vendors.

Then came the open source revolution of the new century, when there was again an explosion of new products onto the market place.

So, first Asian businesses, then American and European businesses adopted this new philosophy their products became highly competitive in the world market. Where did this leave Africa?

I first began to get involved with African businesses in the second half of the last decade and was horrified at just how few companies had adopted this approach to manufacturing. Too often the approach was "Labour is cheap, if we have a problem we throw more cheap labour at it". This approach comes with many problems. Most obviously quality falls when you employ cheap temporary labour, but there is also the social aspect of this. The small amount of planning that seemed to be done was done by hand or spreadsheet. The resource planning revolution had not reached Africa.

Poor control of resources also meant that businesses were losing a great amount of stock through theft. This had a double affect on the business, there was the loss of money that had to be used to replenish the stock, but also the failure to meet customer orders was costing them dearly.

This meant that African goods just couldn't compete with western companies that used sophisticated tools to keep quality high, and costs low.

It would be nice to say that African business owners took to ERP very quickly, but as it was in the early days in the west it was a struggle, but more and more businesses are now seeing the benefits of good planning.

The only software that has been available to African businesses has been produced in the west. This was one of our motivations in producing KwaMoja. We wanted to produce some thing that would benefit African businesses, and something that was produced in Africa, and something that African consultants can sell services around.

We are happy to announce that a new version of KwaMoja is ready and hitting the mirrors already. This is version 14.02 and you can download this version from here.

Comments on "ICT Aid projects in Africa - Why so many failures?"

I got a lot of comments on this article, but the article was printed in many places, and so the comments were dotted around. I thought it might be useful to bring them together in one place.

On the Human Resources Africa Group Steve Oloo said:
"May be its because the Projects lacked good visibility study. another thing that happens in Africa and in my case I can speak of Kenya. you find that the Government can change policies and tax in a day thus making the equipments outsourced to be expensive than initially planned hence going for cheaper options that are generally expensive... another thing that happens is that the level of poverty in Africa is too much that the creativity is diverted in the line of vandalism of ICT projects...one example is the fiber-optics which is the best invention and thought to be useful to ICT only but people in Africa vandalize the just to make illuminating flowers structures to sell to the public thus hindering its usefulness...
the right personnel is also a problem since Africa , Kenya in particular see papers rather than what you can do.... Lastly the level of corruption in Africa is so deep that even a good project for all humanity must be bribed so as to be implemented..making the initial cost be peanuts compared to the cost of implementation...."

On Africa - All Things Business Phil Johnny said:
"ICT projects failure in Africa is largely due to [ LACK of will power, dedication, commitment & passion] to ensure that people in Africa benefit from Information & Communication technology which they rightly deserve. Conflict & Corruption have been plaging the continent for years. There is no doubt tons of investment opportunities in Africa but without the right people (Authorities) in the corridors of power, things could easily get out of control and no one will be seen to account for the mess. Moreover, when the willingness and readiness to make needed sacrifices is not in the hearts of the leaders, all else fails. Therefore, a COMPLETE & GENUINE CHANGE OF ATTITUDE is absolutely necessary."

 On Accra Business Club - Africa | Ghana | Networking Andrew Brookes said:
"Tim great piece - very astute.
One obvious resource for ICT in Africa and other developing countries (India)is LInux and other free source software; but because the general ethos is that because people (e.g Ricard Stallman and GNU) don't charge there is next to no money to support projects. Microsoft on the other hand has a better business model ,so what it decides to get behind usually doesn't fail
Secondly it seems to me there is no thought or co-ordination by say the Ghana Government to take the data it has on official registered NGO's concerned with ICT and link activities together.
As you say some projects are maybe vague. What about this project i've been working on- You take the school wiki download a quality E-encyclodpedia of 6000 articles, 26 million words and 50,000 images which has been checked and based on the UK curriculum( http://schools-wikipedia.org) you enhance it with a search function and work out how say 10 or more children would be able to use it with a set up of server/client.
see http://www.youtube.com/watch?v=HkCjzlVQ6_g&feature=youtu.be
There would be potential to "personalize" the system if scholars and historians contributed since the E-Encyclopedia is basically a bunch of web pages that can easily be edited. Since the set up involves a web server there is the capacity to use it to teach children construction of web pages, CSS style sheets and computer languages such as PHP.
I have had a previous meeting with the ICT co-ordinator of the Ministry of Education in Accra, and I bet if I was sitting opposite him now and put the above to him I wouldn't be surprised if he could even comprehend the possible value of such a project.
Microsoft on the other hand has just appointed Otema Yirenkyi in Ghana; what I can imagine is if Microsoft comes and says "we have the money, the ideas etc so you don't have to do much " then its easy for those with lack of imagination, vision and leadership to just go along with it.
Personally I am not against Microsoft and admire their business model ; also there is potential for joint projects such as LInux servers and Windows clients "  
I replied:
"I agree fully with you Andrew. I wrote an article here http://weberpafrica.blogspot.co.uk/2013/10/africa-and-open-source-software.html on the subject of why African governments should look to open source as a way of building a local IT industry.
I do believe that if these governments invested the money they spent on foreign IT products and services in a local open sourced based IT industry everybody except the multinationals would gain,
I have set out in that article how I envisioned this working.
Very much like your wikipedia for schools. Have you tried the Ministry for Education? I am sure you are correct in what you would expect from them. I have previously come across the "if it's not American and expensive how can it be any good" philosophy in Govt departments. There are potentially donor organisations that could help. "
Andrew Brookes commented:
"cheers Tim
from the perspective of an Educational resource which could be extended , I can not at the moment imagine a better one than the school wiki with search facility.When you say there are potentially donor organisations that could help, could you elaborate a little on who they may be and how I can contact them?
One problem I have is that I went through quite a few hoops to get an NGO registered in Ghana but don't have anything registered in the UK. I did try to get support in the U.K but the feedback is " we don't help organizations or charities unless they are UK registered"!
I am not keen to bang my head against a brick dealing with UK possible EU bureaucracy to be honest"
And I replied: 
"Getting money for an African NGO or other charitable organisation directly from western countries is very hard. Too much money vanished down that hole in the past. Going through a UK/EU based organisation provides any donor with some legal recourse if funds go missing.
However there are UK based organisations that already have this link between UK and Africa in place. One such that immediately springs to mind for your project is http://www.africaeducationaltrust.org which is UK based but works in Africa. There are others than could possibly help.
I have some other contacts that could possibly help. Contact me on tim.schofield1960@gmail.com if you would like us to try and work together to get this moving" 

On Windhoek Business Club - Namibia Ashraf Bharmal said:
"Wrong projects for wrong reasons. There are cases of spectacular successes too but few and far apart."
and Salehe Khatibu replied: 
"poor management of them "
and I said:
"@Ashraf Agreed. I feel that many donor organisations get this balance wrong because of a lack of local knowledge. A person or group is sent to Africa to evaluate the project. They stay in a luxury tourist hotel, are entertained by local people eager to say whatever they think is needed to be said to get the money flowing. None of this is wrong, but means that they don't get a clear view of what is needed and the people locally will not always tell them for fear that the project will not go ahead. 
@Salehe Very true. Project management skills are some of the hardest to learn, rarest, but least appreciated skills going. Bad leadership will cause failure whatever else happens"

On Dar es Salaam Business Club - Tanzania Catherine Mkude said:
"Dear all, My name is Catherine G. Mkude and I am a PhD researcher at the University of Koblenz-Landau in Germany working on a framework for e-government systems design for developing countries. In my research, I am investigating e-government strategies, programmes and projects (applications, infrastructures, comprehensive solutions, etc.) in developed and in developing countries. In doing so, I want to determine how developing countries can leverage from the more successful e-government endeavours in developed countries.
I am currently in a stage of collecting information on experiences, practices and solutions in 5 domains of e-government implementation in developed and developing countries. These domains are (1) electronic public services, (2) electronic participation, (3) application of information and communication technologies (ICT) in policy making processes, (4) e-government infrastructure and, (5) evaluation and sustainability of e-government.
Therefore I would like to kindly ask you to participate in a survey, which investigates these domains through separate questionnaires. I would highly appreciate if you could fill in one (or even more) of the below questionnaires. The responses for the questionnaires are entirely confidential and anonymous.
The following links direct you to the respective questionnaire per domain. The approximated time to fill in a questionnaire is also indicated below. Please choose the link(s) of the domain(s) you feel most comfortable to answer.

1. Domain electronic public services: http://cmkude.limequery.com/index.php/983413/lang-en. Approximate time is 40 minutes.
2. Domain electronic participation: http://cmkude.limequery.com/index.php/388819/lang-en. Approximate time is 40 minutes.
3.  Domain ICT in policy making: http://cmkude.limequery.com/index.php/776413/lang-en. Approximate time is 35 minutes.
4. Domain e-government infrastructure: http://cmkude.limequery.com/index.php/375388/lang-en. Approximate time is 30 minutes.
5. Domain e-government evaluation and sustainability: http://cmkude.limequery.com/index.php/582399/lang-en. Approximate time is 30 minutes.
   

In advance I appreciate and thank you for your time and contributions. If you are aware of someone who I can ask to fill in either of the questionnaires, please let me know by email and I will invite them. Thank you and kind regards,  Catherine G. Mkude. "
Ashraf Bharmal said:
"Hope you paper will produce some positive results. Best wishes and Good luck"
Leticia Slame said:
"Hello Tim, it quiet interesting that has been my question why ICT Project fail to successed and if they successed it wont last long and most of the people have negative response, I will be glad if I get the reasons. "
and Ashraf Bharmal said:
"My Take:
1. Politically expeditious projects
2 Poor planning
3 FEEDS and Feasibilities , Colorfully printed, beautifully bound and presented, full of sound and fury in which affected sectors, people have no say.
4. Foreign contractors, not involving local entities in the project from the beginning who would gain hand on experience of the project, instead of six week orientation seminars at the end of the completed projects
5. Lack of post project planning of operating, maintaining."

On KwaMoja - Open Source ERP for Africa Nicholas Mmasi said:
"-Too many unfair side deals...people want to spend money and write a good report
- Demotivated staff ,less communication and unclear benefit of the system to the operating staff.
- No plan for sustainability right from the beginning,so once the donor pulls out the things end up there.
-Unrealistic requirements and system rationale... "
and I replied
"Hi Nicholas,
"-Too many unfair side deals...people want to spend money and write a good report "
I agree, I have seen too many "stage managed" visits by donors to sites where people at the sites have been given money to back up a false report.
"- Demotivated staff ,less communication and unclear benefit of the system to the operating staff. "
This is what I meant by lack of good project management. It is the job of the project management to motivate and communicate with staff.
"- No plan for sustainability right from the beginning,so once the donor pulls out the things end up there. "
Excellent point. Sustainability is some thing I should have gone into greater length about in the article. Who maintains once the donor leaves. Where does the financing of that support come from? "
Nicholas said:
"Hi Tim, Donors also have bad policies that are not applicable in Africa.I have been going around trying to see why so many projects fails eve before donors pulls out.
Almost all project are in pilot mode/Nursery and never get out of the lab.Similar scenarios are readily available and visible in areas of agriculture(farming technology and techniques), small scale industries, bio-gas,ICT, healthy ,and many more....
I normally find them in exhibitions only.... "
and I replied:
"Hi Nicholas, sadly you are right, despite most involved having the best intentions. I don't believe that it is necessary though, with some changes in policy and outlook a much higher percentage will succeed. There will always be failures but the failure rate shouldn't be this low. Tim "

On Information and Technology Lisa Schnellinger said:
"Excellent points. From my experience, I think they are often true of all types of development projects, in all regions. "

On Monrovia Business Club - Africa | Liberia | Networking Deodatus Shayo said:
 "Lack of ownership "

On Harare Business Club - Zimbabwe | Southern Africa Viola Marufu said:
"Tim, you have an interesting article. Interesting that you list your perspective as statements made from observations of certain African projects which does not necessarily implying that all projects are run like this. However, you should note that the major reason why some donors want local community members to staff and manage projects, rather than outsiders is because the locals know their community better and thats another way of empowering the community. Furthermore, it does not justify the expense of getting an outsider, so to speak, than getting an equally qualified local staff member.
You also say that ICT projects are a newer idea in Africa than in the west and there is limited number of qualified local project managers available. Thats not necessarily true. ICT projects are welcome and expanding in Africa. The current development is the spread of ICT effectively in rural communities and schools. In most areas the major setback is electrification. They are more and more qualified business people, educationists, economists and ordinary people who have well advanced ICT skills. So it is not necessarily an issue of skill but they are other factors influencing this. You are mixing points here.Furthermore if jobs are advertised, the right candidates apply for the job.
Then you say project employees are more interested in perpetuating the project than completing it, they prolong the project for personal interest etc. That is true where the project itself is not well managed. There is always need for an independent Monitoring and Evaluation exercise. They are also independent auditors.
A project that is really interested in benefiting the country in which its operating in will not wait to get a report on their desk. They will also put in measures to ensure all is well. This would be true no matter where the project runs. Whether its in Africa or the West, there is always need for accountability. "
I replied:
"Hi Viola, Thanks for your interesting comments. Firstly I should make clear that I am not nor have I ever been part of a donor organisation. I write from the perspective of someone who has either worked in, or observed many projects.
"Interesting that you list your perspective as statements made from observations of certain African projects which does not necessarily implying that all projects are run like this" - I agree, I tried to make the point I was writing from personal experience only, and was trying to answer why it appeared to me the failure rate was higher than normal in donor funded ICT projects. There is a high failure rate in all ICT projects.The UK NHS IT project is one of the most high profile failures.
"However, you should note that the major reason why some donors want local community members to staff and manage projects, rather than outsiders is because the locals know their community better and thats another way of empowering the community. Furthermore, it does not justify the expense of getting an outsider, so to speak, than getting an equally qualified local staff member. " - obviously it makes sense to employ local staff, my company always has, it keeps money within the local community. However my experience of projects where only local staff work has not been good, for reasons I said. It requires a balance that few projects actually have.
"You also say that ICT projects are a newer idea in Africa than in the west and there is limited number of qualified local project managers available. Thats not necessarily true. ICT projects are welcome and expanding in Africa. The current development is the spread of ICT effectively in rural communities and schools. In most areas the major setback is electrification. They are more and more qualified business people, educationists, economists and ordinary people who have well advanced ICT skills. So it is not necessarily an issue of skill but they are other factors influencing this. You are mixing points here.Furthermore if jobs are advertised, the right candidates apply for the job. " - Well again I can only comment from my own experience. Recruiting qualified local staff has always been a problem. I have regularly trawled the universities, and advertised extensively. I am not saying that there are not capable African staff, just that either they are either in private industry, or moved to the west. I have also seen many projects run by project managers with little or no training in project management. I tried in the article to understand why this is. Project management skills are very different from ICT skills.
"Then you say project employees are more interested in perpetuating the project than completing it, they prolong the project for personal interest etc. That is true where the project itself is not well managed. There is always need for an independent Monitoring and Evaluation exercise. They are also independent auditors. " - That is the point I was trying to make. It is human nature to make the projects last when you are earning money from it. The fault lies in the agencies not managing and monitoring the projects.
"A project that is really interested in benefiting the country in which its operating in will not wait to get a report on their desk. They will also put in measures to ensure all is well. This would be true no matter where the project runs. Whether its in Africa or the West, there is always need for accountability. " - Agreed, as I said at the start the only reason I wrote about Africa was that was where my experience was. "

As you can see, lots of very interesting comments came from this discussion on top of the comments on the article itself.

Sustainability and Corruption in donor funded projects.

I wrote this article a couple of days ago and it attracted a lot of comments. Many of the comments focused on these two issues which I didn't go into in much detail, but they are very important to donor funded ICT projects.

These are somewhat controversial subjects so again I will keep from naming specifics.

Any donor funded project should be sustainable. That is it should continue to function when the donor leaves. Sounds obvious I know, but most people would be amazed at just how few do carry on working. Anybody who has like me, worked and traveled extensively in Africa will be able to recount stories of when this has failed. Here are just a few of mine:

• Water pumps that cannot be maintained when they break down because there are no spare parts, no money or means to get them, nobody trained to fit them if they were available. 
• Fields full of farm machinery (Tractors, Canadian sized combine harvesters etc) rotting away. Why? No spare parts, and nobody trained to maintain them.
• I once visited a large hospital in East Africa which had a modern but non-functioning CT scanner. Again the reason given for its lack of functionality was that it had broken down and nobody could repair it. The hospital was losing considerable income from its not working. This income could easily have paid for a maintenance contract but nobody had arranged it. Lives were being lost in that area of East Africa because the only hospital with a CT scanner had no plan to maintain the scanner once it broke down. The hospital director told me that eventually somebody would donate a new one and the old one would be thrown away.

I am not finger pointing here, this is a story you will hear throughout Africa. In order for projects to be sustainable they have to generate some income, and that income has to be put back into the project in order to provide for the maintenance. For instance I saw a very good scheme in rural Tanzania where the donors had paid for a water pipeline bringing fresh water from a mountain spring many miles away. The local towns people were charged a few shillings (one shilling equals 0.00037 British pounds at current exchange rate) for the water. This money was used to pay local towns people to maintain the pipeline. The money stayed within the local community, and the water continues to flow to this day. Why can't a similar model be used for the above mentioned pumps?

I have seen projects providing hospitals with software. The hospitals were led to believe that the software was free, so no provision was made to support the system once it was installed. When bugs were found in the system there was nobody to fix them, and the software fell into misuse. However this software made the hospitals more efficient, improved their income, that income should have been used to fund local support for that software.

This is one of the reasons why billions of dollars in aid money floods into Africa but things never get better for its citizens.

The other reason is the corruption that follows these projects. I have over the years had conversations with people who have been found to have taken money from projects.  The common theme is always that they do not see it as stealing, or as something wrong. The best analogy I have is that aid money is seen like a river flowing down the mountain, and if you divert a little to irrigate your own field, then the water doesn't stop flowing, and you get a better harvest. The flaw with this argument is that the supply of money is finite and the river does stop flowing.

The best solution I have for this is closer and more rigorous scrutiny of the project by onsite managers who are appointed by the project donors to supervise the use of the money. Just the same as would be done with any commercial company when a budget is allocated to a project.

International aid is not working, but it can. It needs a change of attitude from both the donors and the receivers of the aid.

Updated Supplier Payments in KwaMoja

One frequently asked questions we get on the KwaMoja project is why you cannot just select the supplier items you want to pay, when you are making a payment to a supplier.

Well now you can:

As can be seen in the above screenshot, all open items are shown for the supplier. Checking those items adds it to the amount to be paid. If it is a credit or old payment, then the amounts will be deducted instead of added.

If the item is unchecked then the amount is deducted.

Once you hit the "Accept and Process Payment" button then the payment is posted and the items are allocated against this payment.

ICT Aid projects in Africa - Why so many failures?

Before I start this article let me make a couple of statements:

Firstly my experience of donor funded ICT projects is limited to Africa, so by necessity any anecdotes in this article refer to projects in Africa. This isn't meant to indicate that any of the points I make are special to the continent of Africa, and are quite probably true of similar aid projects throughout the rest of the world.

Secondly I will mention no names of people, or institutions. This is an article about what I perceive as issues in many of the projects I have witnessed, either as an observer or as a participant, and is not intended as an indictment of any person, or institution.

Failure of ICT projects is not an uncommon thing. Most statistics seem to show a failure rate of between 50% and 70%. So Africa is not on its own in having these failures. However from my observations I have noticed specific areas in donor funded projects that seem to make these projects more liable to failure:

• "We are a donor funded organisation so we shouldn't use for-profit companies". I have heard this a lot from the donor organisations. This means that they use charitable or religious organisations in order to do the ICT work. This means that local skilled people who happen to work in the commercial sector will not be able to participate in the project. For-profit companies tend to have a better understanding of the importance of meeting deadlines, and they have a reputation to keep up, which means that a successful completion of the project is to their advantage. Non-profit organisations tend to react more slowly and worry less about deadlines. This is a curious decision from the donor organisations as they are happy to hand over money to Toyota for their vehicles, Microsoft/Apple/Dell etc for IT products etc. but when it comes to the most important aspect of the project they limit themselves to the non-profits.
• "The project should be staffed and managed by local people, and not by outsiders". This is a laudable intention, but does it make sense in this sort of project? As pointed out in the above point many of the quality project manager staff will be in the private industry. Also the fact that ICT projects are a newer idea in Africa than in the west, there is a limited number of qualified local project managers available.
• Project employees are more interested in perpetuating the project than completing it. Donor funded projects generally pay much better in local terms than other employers. As the project is run by a local project manager, with local staff, then the major interest of these people is to make sure that the money continues to flow, rather than in getting the project completed. In fact, completing the project often goes against their personal interests. I know of several projects where the donors are taken on periodic "stage managed" tours to show that the work is really being done.
• Projects encourage "cronyism". Too often have I seen projects staffed by the family and relations of the senior members of the non-profit institution charged with the running of the project. I even know of one project that is supposed to be writing software that doesn't employ a programmer as part of it's large staff.

• Project aims are often too vague. I know of projects where the aim is to do something vague, such as "design and implement software for schools". Project aims should be specific, and the time scale should be set down at the start. 

My experience shows that projects should:

1. Be managed by an external person employed by the donor organisation charged with meeting targets.
2. Use the best resources available to them regardless of whether they are non-profit or for-profit.
3. Set definite targets at the start, both in timescale and project goals. The project manager should be the person held accountable.
4. Donor organisations should be firmer in their dealings on the ground. Too often I see donor organisations that take a far too "charitable" view of bad work. The project should be run as a commercial project. The original donors of the money deserve nothing less.

These thoughts are based on many years of watching the failings of such projects in Africa. Donor organisations need a radical change in how they view such projects.

Not all projects fail, there have been some outstanding successes but the failure rate is way too high.