[IAEP] C�dula de Identidad Uruguaya - D�gito de Control / Uruguayan ID Card - Control Digit

[Carlos Rabassa]

thank you Tony for following up with all the details of a solution!

I didn´t tryi it when I made the suggestion.

I was thinking of Pippy / Python.

Carlos


On Nov 9, 2011, at 2:22 AM, forster at ozonline.com.au wrote:

> Carlos
> 
> The checksum calculated in TurtleArt
> 
> http://tonyforster.blogspot.com/2011/11/turtle-checksums.html
> 
> 
> Tony
> 
> 
>> English Text Follows Spanish Text
>> 
>> Pensamos este podrï¿∏a ser un tema interesante para un proyecto usando algunas de las aplicaciones en las computadoras del Plan Ceibal.
>> 
>> Todos los que vivimos en Uruguay debemos tener,  desde la edad de 45 dï¿∏as,  nuestra cï¿∏dula de identidad que contiene nuestro nombre, foto, firma, impresiï¿∏n digital, fecha de nacimiento y un nï¿∏mero que nos identifica por el resto de nuestras vidas:
>> 
>> 
>> 
>> Estos son algunos de los muchos usos de la cï¿∏dula:
>> 
>> - Poder recibir la computadora del Plan Ceibal.  El plan mantiene una base de datos donde cada computadora entregada estï¿∏ asociada a un estudiante o educador.
>> 
>> - Tener una cuenta personal en el BPS, Banco de Previsiï¿∏n Social.  Presentando la cï¿∏dula todos los que trabajan en Uruguay pueden verificar que el BPS les estï¿∏ acreditando correctamente los beneficios sociales,  que tienen derecho a recibir.
>> 
>> - Como identificaciï¿∏n para viajar a paï¿∏ses en nuestra regiï¿∏n,  en lugar de pasaporte.
>> 
>> Muy frecuentemente,  en la escuela,  en el lugar de trabajo,  en comercios,  en oficinas del gobierno y privadas,  nos piden nuestro nï¿∏mero de cï¿∏dula para anotarlo en algï¿∏n formulario.  Es muy fï¿∏cil que se cometa un error al anotarlo.
>> 
>> El dï¿∏gito de control,  que es el octavo dï¿∏gito,  que aparece a la derecha del guiï¿∏n como en este ejemplo:
>> 
>> 5.555.555-5
>> 
>> puede ser que no corresponda al que se puede calcular usando los siete primeros dï¿∏gitos.  Eso es una indicaciï¿∏n de que muy probablemente hubo un error al anotar este nï¿∏mero de cï¿∏dula.
>> 
>> Para los que les interese cï¿∏mo se calcula el dï¿∏gito de control,  hemos preparado esta planilla de cï¿∏lculo:
>> 
>> 
>> 
>> Este archivo pueden abrirlo con Excel, Open Office o Google Docs.
>> 
>> El primer proyecto que sugerimos serï¿∏a simplemente repetir el cï¿∏lculo que mostramos,  usando una o mï¿∏s de las aplicaciones que ofrecen las ceibalitas.
>> 
>> Luego, podrï¿∏a ser resolver otros problemas:
>> 
>> - Dados siete de los ocho dï¿∏gitos en una cï¿∏dula,  calcular el faltante.
>> 
>> - Siempre que haya un error,  ï¿∏nos darï¿∏ mal el cï¿∏lculo del dï¿∏gito de control? Justificar la respuesta.
>> 
>> - Si transponemos dos dï¿∏gitos consecutivos,  un error muy frecuente, ï¿∏cambiarï¿∏ el dï¿∏gito de control calculado?  ï¿∏Podremos darnos cuenta en ese caso,  cuï¿∏l fue el error y corregirlo?
>> 
>> - ï¿∏Hay otras aplicaciones de los dï¿∏gitos de control en el mundo real,  ademï¿∏s de la cï¿∏dula de identidad?
>> 
>> Para los que quieran profundizar en el tema y hacer otros ejercicios,  con gusto les enviaremos el trabajo de Omar Gil y Ricardo Vilarï¿∏,  que mencionamos en la tabla de cï¿∏lculo adjunta.
>> 
>> English Text:
>> 
>> We believe this could be an interesting subject for a project using some of the applications in the Plan Ceibal computers.
>> 
>> All of us who live in Uruguay must have, from the age of 45 days,  our ID Card containing our name, picture, signature, finger print, date of birth and a number that identifies us for the rest of our lives.
>> 
>> These are some of the many uses for the ID card:
>> 
>> - To be able to receive Plan Ceibalï¿∏s computer.  The plan maintains a database where each computer they have delivered is associated to a student or an educator.
>> 
>> - To have a personal account with BPS, Banco de Previsiï¿∏n Social.  Anyone working in Uruguay may present the ID card and check that BPS is properly crediting the social benefits that person is entitled to receive. 
>> 
>> - As ID to travel to countries in our region,  instead of a passport.
>> 
>> Quite frequently we are asked for our ID card number to fill-in a form,  This happens at school, at the work place, at shops, at government and private offices. It is very easy for errors to occur.
>> 
>> The control digit,  this is the eighth digit,  shown to the right of the dash as in this example:
>> 
>> 5.555.555-5
>> 
>> might not be the same that may be calculated using the first seven digits.  This is an indication that most probably there was an error when writing down this ID card number.
>> 
>> We have prepared this spreadsheet for those interested in learning how this control digit is calculated:
>> 
>> 
>> 
>> This file may be opened with Excel, Open Office or Google Docs.
>> 
>> The first project we would like to suggest is to just repeat the calculation we show,  using one or more of the applications in Plan Ceibalï¿∏ computers.
>> 
>> Then,  it could be resolving other problems:
>> 
>> - Given seven of the eight digits in an ID card,  calculate the missing digit.
>> 
>> -  Whenever there is an error,  is the calculation going to return the wrong control digit?  Justify the answer.
>> 
>> - If we transpose two consecutive digits,  a very frequent error, will the calculation result change? Are we going to be able,  in such case,  to find out what the error was and correct it?
>> 
>> - Are there other applications in the real world for control digits,  besides the ID card?
>> 
>> We will be glad to send the paper by Omar Gil and Ricardo Vilarï¿∏,  mentioned in the attached spreadsheet, to anyone who might wish to further study the subject and do other exercises.
>> 
>> 
>> Carlos Rabassa
>> Volunteer
>> Plan Ceibal Support Network
>> Montevideo, Uruguay
>> www.tiny.cc/AprendoILearn
>> 
>> 
>> <html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><span class="Apple-style-span" style="font-size: 18px;"><b><font class="Apple-style-span" color="#ff1314">English Text Follows Spanish Text</font></b></span></div><div><span class="Apple-style-span" style="font-size: 18px;"><b><font class="Apple-style-span" color="#ff1314"><br></font></b></span></div><div><span class="Apple-style-span" style="font-size: 18px;">Pensamos este podrï¿∏a ser un tema interesante para un proyecto usando algunas de las aplicaciones en las computadoras del Plan Ceibal.<br><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "></span><br><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">Todos
>> los que vivimos en Uruguay debemos tener,  desde la edad de 45 dï¿∏as, 
>>  nuestra cï¿∏dula de identidad que contiene nuestro nombre, foto, firma, impresiï¿∏n digital, fecha de nacimiento y 
>> un nï¿∏mero que nos identifica por el resto de nuestras vidas:</span></span></div><div><span class="Apple-style-span" style="font-size: 18px;"><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "><br></span></span></div><div><span class="Apple-style-span" style="font-size: 18px;"></span></div></body></html>
>> [ Cedula-4.jpg ]
>> <html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><head></head><div><br><div><span class="Apple-style-span" style="font-size: 18px;"></span></div><div><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "></span></span><div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">Estos son algunos de los muchos usos de la cï¿∏dula:</span><br><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "></span><br></span></div><blockquote class="webkit-indent-blockquote" style="font-size: medium; margin-top: 0px; margin-right: 0px; mar!
> gin-bottom: 0px; margin-left: 40px; border-top-style: none; border-right-style: none; border-bottom-style: none; border-left-style: none; border-width: initial; border-color: initial; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; "><div><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">- Poder recibir la computadora del Plan Ceibal.  El plan mantiene una base de datos donde cada computadora entregada estï¿∏ asociada a un estudiante o educador.</span></span></div><div><span class="Apple-style-span" style="font-size: 18px; "><br></span></div><div><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">- Tener una cuenta personal en el BPS, Banco de Previsiï¿∏n Soci!
> al.  Presentando la cï¿∏dula todos los que trabajan en Uruguay pueden
> verificar que el BPS les estï¿∏ acreditando correctamente los beneficios sociales,  que tienen derecho a recibir.</span></span></div><div><span class="Apple-style-span" style="font-size: 18px; "><br></span></div><div><span class="Apple-style-span" style="font-size: 18px; ">- Como identificaciï¿∏n para viajar a paï¿∏ses en nuestra regiï¿∏n,  en lugar de pasaporte.</span></div></blockquote><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "></span><br><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">Muy frecuentemente,  en la escuela,  en el lugar de trabajo,  en comercios,  en oficinas del gobierno y privadas,  nos piden nuestro nï¿∏mero de cï¿∏dula para anotarlo en algï¿∏n formulario.  Es muy fï¿∏cil que s!
> e cometa un error al anotarlo.</span><br><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "></span><br><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">El dï¿∏gito de control,  que es el octavo dï¿∏gito,  que aparece a la derecha del guiï¿∏n como en este ejemplo:</span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><br></span></div></div></div></div><blockquote class="webkit-indent-blockquote" style="margin: 0 0 0 40px; border: none; padding: 0px;"><div><div><div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">5.555.555-5</span></span></div></div></div></div></blockqu!
> ote><div><div><div><div style="font-size: medium; "><span class="Apple
> -style-span" style="font-size: 18px; "><br><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">puede ser que no corresponda al que se puede calcular usando los siete primeros dï¿∏gitos.  Eso es una indicaciï¿∏n de que muy probablemente hubo un error al anotar este nï¿∏mero de cï¿∏dula.</span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "></span><br><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">Para los que les interese cï¿∏mo se calcula el dï¿∏gito de control,  hemos preparado esta planilla de cï¿∏lculo:</span></span></div><div><span class="Apple-style-span" style="font-size: 18px;"><br></span></div></div><d!
> iv><span class="Apple-style-span" style="font-size: 18px;"></span></div></div></div></body></html><html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><head></head><div><div><div><span class="Apple-style-span" style="font-size: 18px;"></span></div><div style="font-size: medium; "><div></div><div><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "><br></span></span></div><div><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">Este archivo pueden abrirlo con Excel, Open Office o Google Docs.</span></span></div></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); b!
> ackground-color: transparent; font-variant: normal; text-decoration: n
> one; vertical-align: baseline; "><br></span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">El primer proyecto que sugerimos serï¿∏a simplemente repetir el cï¿∏lculo que mostramos,  usando una o mï¿∏s de las aplicaciones que ofrecen las ceibalitas.</span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "><br></span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">Luego, podrï¿∏a ser resolver otros problemas:</!
> span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "><br></span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">- Dados siete de los ocho dï¿∏gitos en una cï¿∏dula,  calcular el faltante.</span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "><br></span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: !
> transparent; font-variant: normal; text-decoration: none; vertical-ali
> gn: baseline; ">- Siempre que haya un error,  ï¿∏nos darï¿∏ mal el cï¿∏lculo del dï¿∏gito de control? Justificar la respuesta.</span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "><br></span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; ">- Si transponemos dos dï¿∏gitos consecutivos,  un error muy frecuente, ï¿∏cambiarï¿∏ el dï¿∏gito de control calculado?  ï¿∏Podremos darnos cuenta en ese caso,  cuï¿∏l fue el error y corregirlo?</span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><br></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; ">- ï¿∏Hay otras aplicaciones de los dï¿∏gitos de control en el mundo real,  ademï¿∏s de la cï¿!
> ∏dula de identidad?</span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><br></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; ">Para los que quieran profundizar en el tema y hacer otros ejercicios,  con gusto les enviaremos el trabajo de Omar Gil y Ricardo Vilarï¿∏,  que mencionamos en la tabla de cï¿∏lculo adjunta.</span></div><div style="font-size: 18px; "><span class="Apple-style-span" style="font-size: 18px; "><br></span></div></div><div><div><span class="Apple-style-span" style="font-size: 18px; "><b><font class="Apple-style-span" color="#ff1314">English Text:</font></b></span></div></div><div><font class="Apple-style-span" color="#ff1314"><span class="Apple-style-span" style="font-size: 18px;"><b><br></b></span></font></div><div><div><span class="Apple-style-span" style="font-size: 18px; ">We believe this could be an interesting subject for a project using some of th!
> e applications in the Plan Ceibal computers.<br></span></div><div><spa
> n class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "><br></span></span></div><div><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">All of us who live in Uruguay must have, from the age of 45 days, Â our ID Card containing our name, picture, signature, finger print, date of birth and a number that identifies us for the rest of our lives.</span></span></div><div><div><div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><br></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; ">These are some of the many uses for the ID card:<br><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: norm!
> al; text-decoration: none; vertical-align: baseline; "></span><br></span></div><blockquote class="webkit-indent-blockquote" style="font-size: medium; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 40px; border-top-style: none; border-right-style: none; border-bottom-style: none; border-left-style: none; border-width: initial; border-color: initial; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; "><div><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">- To be able to receive Plan Ceibalï¿∏s computer.  The plan maintains a database where each computer they have delivered is associated to a student or an educator.</span></span></div><div><span class="Apple-style-span" style="font-size: 18px; "><br></span></div><div><span class="Apple-style-span" style="font-size: 18px; "><span styl!
> e="color: rgb(0, 0, 0); background-color: transparent; font-variant: n
> ormal; text-decoration: none; vertical-align: baseline; ">- To have a personal account with BPS, Banco de Previsiï¿∏n Social.  Anyone working in Uruguay may present the ID card and check that BPS is properly crediting the social benefits that person is entitled to receive. </span></span></div><div><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "><br></span></span></div><div><span class="Apple-style-span" style="font-size: 18px; ">- As ID to travel to countries in our region,  instead of a passport.</span></div></blockquote><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><br></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; ">Quite frequently we are asked for our ID card number to fill-in a form,  This happens at school, at the work plac!
> e, at shops, at government and private offices. It is very easy for errors to occur.</span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "><br></span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">The control digit, Â this is the eighth digit, Â shown to the right of the dash as in this example:</span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><br></span></div></div></div></div></div></div><blockquote class="webkit-indent-blockquote" style="margin: 0 0 0 40px; border: none; padding: 0px;"><div><div><div><div><div><div style="font-size: medium!
> ; "><span class="Apple-style-span" style="font-size: 18px; "><span sty
> le="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">5.555.555-5</span></span></div></div></div></div></div></div></blockquote><div><div><div><div><div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><br><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">might not be the same that may be calculated using the first seven digits. Â This is an indication that most probably there was an error when writing down this ID card number.</span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "><br></span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: !
> 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">We have prepared this spreadsheet for those interested in learning how this control digit is calculated</span></span><span class="Apple-style-span" style="font-size: 18px; ">:</span></div><div><span class="Apple-style-span" style="font-size: 18px; "><br></span></div></div><div><span class="Apple-style-span" style="font-size: 18px;"></span></div></div></div></div></div></body></html><html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><div><div><div><div><span class="Apple-style-span" style="font-size: 18px;"></span></div><div style="font-size: medium; "><div><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "><br></sp!
> an></span></div><div><span class="Apple-style-span" style="font-size: 
> 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">This file may be opened with </span></span><span class="Apple-style-span" style="font-size: 18px; ">Excel, Open Office or Google Docs.</span></div></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "><br></span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">The first project we would like to suggest is to just repeat the calculation we show,  using one or more of the applications in Plan Ceibalï¿∏ computers.</span></span></div><div style="font-size: medium; "><s!
> pan class="Apple-style-span" style="font-size: 18px; "><br></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; ">Then, Â it could be resolving other problems:</span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; "><br></span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">- Given seven of the eight digits in an ID card, Â calculate the missing digit.</span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decorat!
> ion: none; vertical-align: baseline; "><br></span></span></div><div st
> yle="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><span style="color: rgb(0, 0, 0); background-color: transparent; font-variant: normal; text-decoration: none; vertical-align: baseline; ">- Â Whenever there is an error, Â is the calculation going to return the wrong control digit? Â Justify the answer.</span></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><br></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; ">- If we transpose two consecutive digits, Â a very frequent error, will the calculation result change? Are we going to be able, Â in such case, Â to find out what the error was and correct it?</span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><br></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; ">- Are there other applications in !
> the real world for control digits,  besides the ID card?</span></div></div></div></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; "><br></span></div><div style="font-size: medium; "><span class="Apple-style-span" style="font-size: 18px; ">We will be glad to send the paper by Omar Gil and Ricardo Vilarï¿∏,  mentioned in the attached spreadsheet, to anyone who might wish to further study the subject and do other exercises.</span></div><div><span class="Apple-style-span" style="font-size: 18px; "><b><font class="Apple-style-span" color="#ff1314"><br></font></b></span></div><div><span class="Apple-style-span" style="font-size: 18px; "><b><font class="Apple-style-span" color="#ff1314"><br></font></b></span></div><div>
>> <span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Arial; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><div>Carlos Rabassa</div><div>Volunteer</div><div>Plan Ceibal Support Network</div><div>Montevideo, Uruguay</div><div><a href="http://www.tiny.cc/AprendoILearn">www.tiny.cc/AprendoILearn</a></div></span><br class="Apple-interchange-newline">
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