Spam Automatic Machine – Blogs

Eu sei que esse post, com este título – Spam Automatic Machine – vai atrair gente errada, querendo uma máquina pra fazer spam automático em blogs, mas eu estou escrevendo só pra reclamar destas mensagens automáticas (geralmente SPAM em inglês, mas tenho recebido em francês e, recentemente, uma em português).

De vez em quando um idiota mal preparado esquece de configurar corretamente seu programa automático de SPAM e eu recebo o arquivo inteiro de sentenças, o que é útil para detectar outros (futuros) golpes de “vou elogiar ou comentar e ele vai aprovar miinha mensagem sem saber que é um spam descarado”.

Spam Automatic Machine não existe, de verdade, mas scripts para postar comentários em blogs e fazer propaganda de graça tem aos montes por aí….

Ta aí o arquivo, para quem quer estudar a coisa:

 

{
{I have|I’ve} been {surfing|browsing} online more than {three|3|2|4} hours today, yet I
never found any interesting article like yours.

{It’s|It is} pretty worth enough for me. {In my opinion|Personally|In my view}, if all {webmasters|site owners|website owners|web owners} and bloggers made good content as you
did, the {internet|net|web} will be {much more|a lot more}
useful than ever before.|
I {couldn’t|could not} {resist|refrain from} commenting.
{Very well|Perfectly|Well|Exceptionally well} written!|
{I will|I’ll} {right away|immediately} {take hold
of|grab|clutch|grasp|seize|snatch} your {rss|rss feed} as I {can not|can’t} {in finding|find|to
find} your {email|e-mail} subscription {link|hyperlink} or {newsletter|e-newsletter}
service. Do {you have|you’ve} any? {Please|Kindly} {allow|permit|let} me {realize|recognize|understand|recognise|know}
{so that|in order that} I {may just|may|could} subscribe.
Thanks.|
{It is|It’s} {appropriate|perfect|the best} time to make some plans for the
future and {it is|it’s} time to be happy. {I have|I’ve} read this post and if I could I {want
to|wish to|desire to} suggest you {few|some} interesting things or {advice|suggestions|tips}.
{Perhaps|Maybe} you {could|can} write next articles
referring to this article. I {want to|wish to|desire to} read {more|even more} things about it!|
{It is|It’s} {appropriate|perfect|the best} time to make {a few|some} plans
for {the future|the longer term|the long run} and {it is|it’s} time
to be happy. {I have|I’ve} {read|learn} this {post|submit|publish|put up} and if I {may just|may|could} I {want to|wish
to|desire to} {suggest|recommend|counsel} you {few|some} {interesting|fascinating|attention-grabbing} {things|issues} or {advice|suggestions|tips}.

{Perhaps|Maybe} you {could|can} write {next|subsequent} articles {relating to|referring to|regarding} this article.
I {want to|wish to|desire to} {read|learn} {more|even more} {things|issues} {approximately|about} it!|
{I have|I’ve} been {surfing|browsing} {online|on-line} {more than|greater than} {three|3} hours {these days|nowadays|today|lately|as of late},
{yet|but} I {never|by no means} {found|discovered} any {interesting|fascinating|attention-grabbing} article like yours.
{It’s|It is} {lovely|pretty|beautiful} {worth|value|price}
{enough|sufficient} for me. {In my opinion|Personally|In
my view}, if all {webmasters|site owners|website owners|web owners} and bloggers made {just right|good|excellent} {content|content material} as {you did|you probably
did}, the {internet|net|web} {will be|shall be|might be|will probably be|can be|will likely be}
{much more|a lot more} {useful|helpful} than ever before.|
Ahaa, its {nice|pleasant|good|fastidious} {discussion|conversation|dialogue} {regarding|concerning|about|on the topic of} this
{article|post|piece of writing|paragraph} {here|at this
place} at this {blog|weblog|webpage|website|web site}, I have read
all that, so {now|at this time} me also commenting {here|at this place}.|
I am sure this {article|post|piece of writing|paragraph} has touched all the internet {users|people|viewers|visitors}, its really really {nice|pleasant|good|fastidious} {article|post|piece of writing|paragraph} on building up
new {blog|weblog|webpage|website|web site}.|
Wow, this {article|post|piece of writing|paragraph} is {nice|pleasant|good|fastidious}, my {sister|younger sister} is analyzing {such|these|these kinds of} things, {so|thus|therefore} I am going to {tell|inform|let know|convey} her.|
{Saved as a favorite|bookmarked!!}, {I really like|I like|I love} {your
blog|your site|your web site|your website}!|
Way cool! Some {very|extremely} valid points! I appreciate
you {writing this|penning this} {article|post|write-up} {and the|and also the|plus the} rest of the {site is|website
is} {also very|extremely|very|also really|really}
good.|
Hi, {I do believe|I do think} {this is an excellent|this is a great}
{blog|website|web site|site}. I stumbledupon it ;) {I will|I am going to|I’m going to|I
may} {come back|return|revisit} {once again|yet again} {since I|since i have}
{bookmarked|book marked|book-marked|saved as
a favorite} it. Money and freedom {is the best|is the greatest} way to change, may you be rich and continue to {help|guide} {other people|others}.|
Woah! I’m really {loving|enjoying|digging} the template/theme of this {site|website|blog}.
It’s simple, yet effective. A lot of times it’s {very hard|very difficult|challenging|tough|difficult|hard}
to get that “perfect balance” between {superb usability|user friendliness|usability}
and {visual appearance|visual appeal|appearance}.
I must say {that you’ve|you have|you’ve} done a {awesome|amazing|very good|superb|fantastic|excellent|great} job with this.
{In addition|Additionally|Also}, the blog loads {very|extremely|super}
{fast|quick} for me on {Safari|Internet explorer|Chrome|Opera|Firefox}.
{Superb|Exceptional|Outstanding|Excellent} Blog!|
These are {really|actually|in fact|truly|genuinely} {great|enormous|impressive|wonderful|fantastic} ideas in {regarding|concerning|about|on the
topic of} blogging. You have touched some {nice|pleasant|good|fastidious} {points|factors|things} here.
Any way keep up wrinting.|
{I love|I really like|I enjoy|I like|Everyone loves} what you guys {are|are usually|tend to be} up
too. {This sort of|This type of|Such|This kind of} clever
work and {exposure|coverage|reporting}! Keep up the {superb|terrific|very good|great|good|awesome|fantastic|excellent|amazing|wonderful}
works guys I’ve {incorporated||added|included} you guys to {|my|our||my
personal|my own} blogroll.|
{Howdy|Hi there|Hey there|Hi|Hello|Hey}! Someone in my {Myspace|Facebook} group shared this
{site|website} with us so I came to {give it a look|look it over|take a look|check
it out}. I’m definitely {enjoying|loving} the information.
I’m {book-marking|bookmarking} and will be tweeting this to my followers!
{Terrific|Wonderful|Great|Fantastic|Outstanding|Exceptional|Superb|Excellent}
blog and {wonderful|terrific|brilliant|amazing|great|excellent|fantastic|outstanding|superb} {style and design|design and style|design}.|
{I love|I really like|I enjoy|I like|Everyone loves} what you guys {are|are
usually|tend to be} up too. {This sort of|This type of|Such|This kind of} clever work and {exposure|coverage|reporting}!
Keep up the {superb|terrific|very good|great|good|awesome|fantastic|excellent|amazing|wonderful} works guys I’ve {incorporated|added|included} you guys to {|my|our|my
personal|my own} blogroll.|
{Howdy|Hi there|Hey there|Hi|Hello|Hey} would you mind {stating|sharing} which blog platform you’re {working with|using}?
I’m {looking|planning|going} to start my own blog {in the near future|soon} but I’m having a {tough|difficult|hard} time
{making a decision|selecting|choosing|deciding} between BlogEngine/Wordpress/B2evolution
and Drupal. The reason I ask is because your {design and style|design|layout} seems different then most blogs and I’m looking for something
{completely unique|unique}. P.S {My apologies|Apologies|Sorry} for {getting|being} off-topic but I
had to ask!|
{Howdy|Hi there|Hi|Hey there|Hello|Hey} would you mind letting me know which {webhost|hosting company|web
host} you’re {utilizing|working with|using}?

I’ve loaded your blog in 3 {completely different|different} {internet browsers|web
browsers|browsers} and I must say this blog loads a
lot {quicker|faster} then most. Can you {suggest|recommend} a good {internet hosting|web hosting|hosting} provider at a
{honest|reasonable|fair} price? {Thanks a lot|Kudos|Cheers|Thank you|Many thanks|Thanks}, I appreciate it!|
{I love|I really like|I like|Everyone loves} it
{when people|when individuals|when folks|whenever people} {come together|get together} and share
{opinions|thoughts|views|ideas}. Great {blog|website|site}, {keep
it up|continue the good work|stick with it}!|
Thank you for the {auspicious|good} writeup. It in fact was a amusement account it.
Look advanced to {far|more} added agreeable from
you! {By the way|However}, how {can|could} we communicate?|
{Howdy|Hi there|Hey there|Hello|Hey} just wanted to give you a quick heads up.
The {text|words} in your {content|post|article} seem to be running off the screen in {Ie|Internet
explorer|Chrome|Firefox|Safari|Opera}. I’m not sure if this is a {format|formatting} issue or
something to do with {web browser|internet browser|browser} compatibility but I {thought|figured} I’d
post to let you know. The {style and design|design and
style|layout|design} look great though! Hope
you get the {problem|issue} {solved|resolved|fixed} soon.
{Kudos|Cheers|Many thanks|Thanks}|
This is a topic {that is|that’s|which is} {close to|near to} my heart…
{Cheers|Many thanks|Best wishes|Take care|Thank you}!

{Where|Exactly where} are your contact details though?|
It’s very {easy|simple|trouble-free|straightforward|effortless} to
find out any {topic|matter} on {net|web} as compared to {books|textbooks}, as I found
this {article|post|piece of writing|paragraph} at this {website|web site|site|web page}.|
Does your {site|website|blog} have a contact
page? I’m having {a tough time|problems|trouble} locating it but, I’d
like to {send|shoot} you an {e-mail|email}.
I’ve got some {creative ideas|recommendations|suggestions|ideas} for your blog you might be interested in hearing.
Either way, great {site|website|blog} and I look forward to seeing it {develop|improve|expand|grow} over
time.|
{Hola|Hey there|Hi|Hello|Greetings}! I’ve been {following|reading} your {site|web site|website|weblog|blog} for {a long time|a while|some time} now and finally
got the {bravery|courage} to go ahead and give you a
shout out from {New Caney|Kingwood|Huffman|Porter|Houston|Dallas|Austin|Lubbock|Humble|Atascocita}
{Tx|Texas}! Just wanted to {tell you|mention|say} keep up the {fantastic|excellent|great|good} {job|work}!|
Greetings from {Idaho|Carolina|Ohio|Colorado|Florida|Los angeles|California}!

I’m {bored to tears|bored to death|bored} at work so I decided to {check out|browse} your
{site|website|blog} on my iphone during lunch break.
I {enjoy|really like|love} the {knowledge|info|information} you {present|provide} here and can’t wait to
take a look when I get home. I’m {shocked|amazed|surprised} at how {quick|fast} your
blog loaded on my {mobile|cell phone|phone} .. I’m not even using WIFI, just 3G ..
{Anyhow|Anyways}, {awesome|amazing|very good|superb|good|wonderful|fantastic|excellent|great} {site|blog}!|
Its {like you|such as you} {read|learn} my {mind|thoughts}!
You {seem|appear} {to understand|to know|to grasp} {so much|a lot}
{approximately|about} this, {like you|such as you} wrote the
{book|e-book|guide|ebook|e book} in it or something.

{I think|I feel|I believe} {that you|that you simply|that
you just} {could|can} do with {some|a few} {%|p.c.|percent} to {force|pressure|drive|power} the message {house|home} {a bit|a little bit}, {however|but} {other than|instead
of} that, {this is|that is} {great|wonderful|fantastic|magnificent|excellent} blog.
{A great|An excellent|A fantastic} read. {I’ll|I will} {definitely|certainly}
be back.|
I visited {multiple|many|several|various} {websites|sites|web sites|web pages|blogs} {but|except|however} the audio {quality|feature} for audio songs {current|present|existing} at this
{website|web site|site|web page} is {really|actually|in fact|truly|genuinely} {marvelous|wonderful|excellent|fabulous|superb}.|
{Howdy|Hi there|Hi|Hello}, i read your blog {occasionally|from time to time} and i own a similar one and i was just {wondering|curious}
if you get a lot of spam {comments|responses|feedback|remarks}?
If so how do you {prevent|reduce|stop|protect against}
it, any plugin or anything you can {advise|suggest|recommend}?
I get so much lately it’s driving me {mad|insane|crazy} so any {assistance|help|support} is very much
appreciated.|
Greetings! {Very helpful|Very useful} advice {within this|in this particular} {article|post}!
{It is the|It’s the} little changes {that make|which
will make|that produce|that will make} {the biggest|the
largest|the greatest|the most important|the most significant} changes.
{Thanks a lot|Thanks|Many thanks} for sharing!|
{I really|I truly|I seriously|I absolutely} love {your blog|your site|your website}..
{Very nice|Excellent|Pleasant|Great} colors &
theme. Did you {create|develop|make|build} {this website|this site|this web site|this amazing site} yourself?

Please reply back as I’m {looking to|trying to|planning to|wanting to|hoping to|attempting to} create {my own|my very
own|my own personal} {blog|website|site} and {would like to|want to|would love to}
{know|learn|find out} where you got this from or {what the|exactly what the|just what the}
theme {is called|is named}. {Thanks|Many thanks|Thank you|Cheers|Appreciate it|Kudos}!|
{Hi there|Hello there|Howdy}! This {post|article|blog post} {couldn’t|could not} be
written {any better|much better}! {Reading through|Looking at|Going through|Looking through} this {post|article} reminds me of my previous roommate!
He {always|constantly|continually} kept {talking about|preaching about} this.
{I will|I’ll|I am going to|I most certainly will} {forward|send} {this article|this information|this post} to him.
{Pretty sure|Fairly certain} {he will|he’ll|he’s going to} {have a good|have a very good|have a great} read.
{Thank you for|Thanks for|Many thanks for|I appreciate
you for} sharing!|
{Wow|Whoa|Incredible|Amazing}! This blog looks {exactly|just} like my old
one! It’s on a {completely|entirely|totally} different {topic|subject} but it has pretty much the same {layout|page
layout} and design. {Excellent|Wonderful|Great|Outstanding|Superb} choice
of colors!|
{There is|There’s} {definately|certainly} {a lot to|a great
deal to} {know about|learn about|find out about} this
{subject|topic|issue}. {I like|I love|I really like} {all the|all of the} points {you made|you’ve made|you have made}.|
{You made|You’ve made|You have made} some {decent|good|really good}
points there. I {looked|checked} {on the internet|on the web|on
the net} {for more info|for more information|to find
out more|to learn more|for additional information} about the issue and found {most individuals|most people} will go along with your views on {this website|this site|this web site}.|
{Hi|Hello|Hi there|What’s up}, I {log on to|check|read} your {new stuff|blogs|blog} {regularly|like every week|daily|on a regular basis}.

Your {story-telling|writing|humoristic} style is {awesome|witty},
keep {doing what you’re doing|up the good work|it up}!|
I {simply|just} {could not|couldn’t} {leave|depart|go away} your {site|web site|website} {prior to|before} suggesting that I {really|extremely|actually}
{enjoyed|loved} {the standard|the usual} {information|info} {a person|an individual} {supply|provide} {for your|on your|in your|to your} {visitors|guests}?

Is {going to|gonna} be {back|again} {frequently|regularly|incessantly|steadily|ceaselessly|often|continuously} {in order to|to} {check up on|check out|inspect|investigate cross-check} new posts|
{I wanted|I needed|I want to|I need to} to thank you for this {great|excellent|fantastic|wonderful|good|very good} read!!
I {definitely|certainly|absolutely} {enjoyed|loved} every {little
bit of|bit of} it. {I have|I’ve got|I have got} you {bookmarked|book marked|book-marked|saved as a favorite} {to check out|to look at} new {stuff you|things you} post…|
{Hi|Hello|Hi there|What’s up}, just wanted to {mention|say|tell you}, I {enjoyed|liked|loved}
this {article|post|blog post}. It was {inspiring|funny|practical|helpful}.
Keep on posting!|
I {{leave|drop|{write|create}} a {comment|leave a response}|drop
a {comment|leave a response}|{comment|leave a response}} {each time|when|whenever} I {appreciate|like|especially enjoy} a {post|article} on a {site|{blog|website}|site|website} or {I have|if I have} something to
{add|contribute|valuable to contribute} {to the discussion|to the conversation}.

{It is|Usually it is|Usually it’s|It’s} {a result of|triggered by|caused by} the {passion|fire|sincerness} {communicated|displayed} in the {post|article} I
{read|looked at|browsed}. And {on|after} this {post|article} Como ocultar números de algumas páginas no
Word 2003 | xek.mexek.me. I {{was|was actually} moved|{was|was actually} excited} enough to {drop|{leave|drop|{write|create}}|post} a
{thought|{comment|{comment|leave a response}a response}} {:
-P|:)|;)|;-)|:-)} I {do have|actually do have} {{some|a few} questions|a couple of questions|2 questions}
for you {if you {don’t|do not|usually do not|tend
not to} mind|if it’s {allright|okay}}. {Is it|Could
it be} {just|only|simply} me or {do|does it {seem|appear|give
the impression|look|look as if|look like} like} {some|a few} of {the|these} {comments|responses|remarks}
{look|appear|come across} {like they are|as if they are|like}
{coming from|written by|left by} brain dead {people|visitors|folks|individuals}?
:-P And, if you are {posting|writing} {on|at}
{other|additional} {sites|social sites|online sites|online social sites|places}, {I’d|I would} like to
{follow|keep up with} {you|{anything|everything} {new|fresh} you have
to post}. {Could|Would} you {list|make a list} {all|every
one|the complete urls} of {your|all your} {social|communal|community|public|shared} {pages|sites} like your {twitter feed, Facebook page or linkedin profile|linkedin
profile, Facebook page or twitter feed|Facebook page, twitter feed, or
linkedin profile}?|
{Hi there|Hello}, I enjoy reading {all of|through} your
{article|post|article post}. I {like|wanted} to write a little comment to support you.|
I {always|constantly|every time} spent my half an hour
to read this {blog|weblog|webpage|website|web site}’s {articles|posts|articles or reviews|content} {everyday|daily|every day|all the time} along with a {cup|mug} of coffee.|
I {always|for all time|all the time|constantly|every time} emailed this {blog|weblog|webpage|website|web site} post page to all my {friends|associates|contacts}, {because|since|as|for the reason that} if like to read
it {then|after that|next|afterward} my {friends|links|contacts} will too.|
My {coder|programmer|developer} is trying to {persuade|convince} me to
move to .net from PHP. I have always disliked the idea because of the {expenses|costs}.
But he’s tryiong none the less. I’ve been using {Movable-type|WordPress} on {a number of|a variety of|numerous|several|various} websites
for about a year and am {nervous|anxious|worried|concerned} about
switching to another platform. I have heard {fantastic|very good|excellent|great|good}
things about blogengine.net. Is there a way I can {transfer|import} all my wordpress {content|posts} into it?
{Any kind of|Any} help would be {really|greatly} appreciated!|
{Hello|Hi|Hello there|Hi there|Howdy|Good day}! I could have sworn I’ve {been
to|visited} {this blog|this web site|this website|this site|your
blog} before but after {browsing through|going through|looking at} {some of the|a few of the|many of the} {posts|articles} I realized it’s new to me.
{Anyways|Anyhow|Nonetheless|Regardless}, I’m {definitely|certainly} {happy|pleased|delighted} {I found|I discovered|I came across|I stumbled upon} it and I’ll be {bookmarking|book-marking} it and
checking back {frequently|regularly|often}!|
{Terrific|Great|Wonderful} {article|work}!

{This is|That is} {the type of|the kind of} {information|info} {that are meant to|that are supposed to|that should} be shared {around the|across the} {web|internet|net}.
{Disgrace|Shame} on {the {seek|search} engines|Google} for {now not|not|no longer} positioning this {post|submit|publish|put up}
{upper|higher}! Come on over and {talk over with|discuss with|seek advice
from|visit|consult with} my {site|web site|website} .
{Thank you|Thanks} =)|
Heya {i’m|i am} for the first time here. I {came across|found} this
board and I find It {truly|really} useful & it helped me out {a lot|much}.
I hope to give something back and {help|aid} others like you {helped|aided} me.|
{Hi|Hello|Hi there|Hello there|Howdy|Greetings}, {I think|I believe|I
do believe|I do think|There’s no doubt that} {your site|your website|your web site|your blog}
{might be|may be|could be|could possibly be} having {browser|internet browser|web browser} compatibility {issues|problems}.
{When I|Whenever I} {look at your|take a look at your} {website|web site|site|blog} in Safari, it looks fine {but when|however when|however, if|however,
when} opening in {Internet Explorer|IE|I.E.}, {it has|it’s got} some
overlapping issues. {I just|I simply|I merely} wanted to {give you a|provide you with a} quick heads up!
{Other than that|Apart from that|Besides that|Aside from that},
{fantastic|wonderful|great|excellent} {blog|website|site}!|
{A person|Someone|Somebody} {necessarily|essentially} {lend a hand|help|assist}
to make {seriously|critically|significantly|severely} {articles|posts}
{I would|I might|I’d} state. {This is|That is} the {first|very first} time I frequented your {web page|website page} and {to
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with the {research|analysis} you made to {create|make} {this actual|this particular} {post|submit|publish|put up} {incredible|amazing|extraordinary}.
{Great|Wonderful|Fantastic|Magnificent|Excellent} {task|process|activity|job}!|
Heya {i’m|i am} for {the primary|the first} time here.
I {came across|found} this board and I {in finding|find|to
find} It {truly|really} {useful|helpful} & it helped me
out {a lot|much}. {I am hoping|I hope|I’m hoping} {to give|to offer|to
provide|to present} {something|one thing} {back|again} and
{help|aid} others {like you|such as you} {helped|aided} me.|
{Hello|Hi|Hello there|Hi there|Howdy|Good day|Hey there}!
{I just|I simply} {would like to|want to|wish to} {give you a|offer you a} {huge|big} thumbs
up {for the|for your} {great|excellent} {info|information} {you have|you’ve got|you
have got} {here|right here} on this post. {I will
be|I’ll be|I am} {coming back to|returning to} {your blog|your site|your website|your web site} for more soon.|
I {always|all the time|every time} used to {read|study} {article|post|piece of writing|paragraph} in
news papers but now as I am a user of {internet|web|net} {so|thus|therefore} from now I am using net for {articles|posts|articles or
reviews|content}, thanks to web.|
Your {way|method|means|mode} of {describing|explaining|telling} {everything|all|the whole thing} in this {article|post|piece of writing|paragraph}
is {really|actually|in fact|truly|genuinely} {nice|pleasant|good|fastidious}, {all|every one} {can|be able
to|be capable of} {easily|without difficulty|effortlessly|simply} {understand|know|be aware of} it,
Thanks a lot.|
{Hi|Hello} there, {I found|I discovered} your {blog|website|web site|site} {by means of|via|by the use of|by way
of} Google {at the same time as|whilst|even as|while} {searching for|looking for}
a {similar|comparable|related} {topic|matter|subject},
your {site|web site|website} {got here|came} up, it {looks|appears|seems|seems
to be|appears to be like} {good|great}. {I have|I’ve} bookmarked it in my google
bookmarks.
{Hello|Hi} there, {simply|just} {turned into|became|was|become|changed
into} {aware of|alert to} your {blog|weblog} {thru|through|via} Google, {and found|and located} that {it is|it’s} {really|truly} informative.

{I’m|I am} {gonna|going to} {watch out|be careful} for brussels.

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you|in case you|for those who|if you happen to} {continue|proceed} this
{in future}. {A lot of|Lots of|Many|Numerous} {other folks|folks|other people|people} {will be|shall be|might be|will probably be|can be|will likely be} benefited {from your|out of your} writing.
Cheers!|
{I am|I’m} curious to find out what blog {system|platform} {you have
been|you happen to be|you are|you’re} {working with|utilizing|using}?
I’m {experiencing|having} some {minor|small} security
{problems|issues} with my latest {site|website|blog} and {I would|I’d} like to find something more {safe|risk-free|safeguarded|secure}.
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well as} with the layout on your {blog|weblog}. Is this a paid theme or
did you {customize|modify} it yourself? {Either way|Anyway} keep up
the {nice|excellent} quality writing, {it’s|it
is} rare to see a {nice|great} blog like this one {these days|nowadays|today}.|
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your|together with your|along with your} {site|web site|website} in {internet|web} explorer, {may|might|could|would} {check|test} this?
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of|a few of} your ideas!!\

 

Triste, né? :-(

Como resolver o problema “quantos triângulos há nesta figura?”

Tenho visto coisas…

triâng

Quantos triângulos há nesta imagem?

Gente maluca que não sabe contar direito! Explico: nesses quebra-cabeças do tipo “quantos triângulos há na figura” que abundam nas redes sociais, as pessoas aparecem com as respostas mais estapafúrdias possíveis, pois têm dificuldade de:
(a) identificar triângulos (ou outra figura geométrica) quando formado por outros triângulos,
(b) visualizar o que já foi contado antes, contabilizando o mesmo triângulo mais de uma vez e
(c) conseguir explicar como chegou ao número de triângulos que diz ter certeza ser o certo.
Bom, então como estas questões às vezes aparecem em concursos, na seção denominada (ridiculamente) de “raciocínio lógico”, resolvi elaborar um método, um sistema que permita não só as pessoas contarem corretamente o número de triângulos (ou quadrados ou retângulos, etc.) corretamente como, também, mostrar e convencer outras pessoas de que sua resposta é a única e certa possível (se você ganhar alguma aposta após usar o meu sistema, por favor, envie 20% dos ganhos pra mim).
Vamos começar com um bem simples: quantos triângulos você vê na figura 01, abaixo?

Figura 01

Figura 01

Por favor, não me decepcione… Só há um triângulo!
Por que eu sei isso? Por que a definição de um triângulo é algo do tipo “figura geométrica com três lados” (onde lado quer dizer uma linha reta, ou seja: não é um triângulo a imagem da figura 02)

Figura 02

Figura 02 – isto não é um triângulo

(Foi apenas uma sobra da pizza que comi outro dia, não é um triângulo)

Vamos começar com algumas definições, pra ajudar: três retas (segmentos de reta, pra ser mais preciso) formam um triângulo (exceto se forem paralelas ou coincidentes), a interseção de 3 retas num plano determinam três pontos, que na figura 03 eu dei os nomes de A, B e C e que chamam-se “vértices”.

triângulo02

Figura 03

 

Segmentos de retas unindo estes três pontos, formam o triângulo da figura 04.
Agora algo MUITO IMPORTANTE: se eu contar 3 vértices em ordem diferente, isto não forma um novo triângulo. Os vértices A, B e C, nesta ordem, formam um único triângulo, independente de eu começar a relacionar os vértices em ordem contrária (A, depois C e depois B) ou se eu começar a contar a partir de outros vértices. ABC, ACB, BAC, BCA, CAB e CBA são as 6 possíveis combinações de vértices, mas todos formam um mesmo triângulo, portanto não devem ser contados como triângulos extras! Para evitar isso, quando tivermos muitos triângulos, usaremos a ordem alfabética das letras que dão nome aos pontos para evitar que contemos duas ou mais vezes o mesmo triângulo.

Figura 04

Figura 04

Outro ponto importante, é que três pontos numa linha reta não formam um triângulo, pois ele teria área de tamanho zero.
Bom, voltemos aos testes: se eu colocar um ponto D no meio do meu primeiro triângulo e traçar retas dos pontos B ao D e do ponto C ao D, ficarei com dois triângulos, certo? Olhe a figura 5.
Observe que se eu combinar, em ordem alfabética, duas das letras (A, B, C ou D), eu só precisarei verificar se as outras letras, em ordem, formam um triângulo. Segundo a matemática, a combinação de 4 elementos 3 a 3 dá 4. Para saber quantas combinações são possíveis a partir de certo número de vértices, veja a postagem http://xek.me/?p=1049.

doistriângulo02

Figura 05

As combinações possíveis para n=4 e p=3 seriam: ABC, ABD, ACD e BCD.
Nesta figura, Começando com A e B, só posso ter as combinações ABC ou ABD, mas somente ABC forma um triângulo, já que não há uma reta entre os pontos A e D. Depois tenho a combinação ACD, que também não forma um triângulo. Eliminando as combinações que agora começam com B, sempre em ordem alfabética, só posso ter BCD como combinação (e este é o nosso segundo triângulo).

Figura 06

Figura 06 – Quantos triângulos você vê?

Vamos tentar o método para um caso mais difícil, veja a figura com 6 pontos, a figura 6. São possíveis um total de 20 combinações, n=6, p=3 e =COMBIN(6,3) dá 20 no sábio Excel.
Tente descobrir quantos triângulos há antes de ver a resposta na figura 7.

respostas

Figura 07

Por fim, o grande problema, o que já caiu em alguns concursos, a pilha de triângulos da figura 8. Quantos triângulos há?
Tente resolver sozinho e depois veja se confere…

quebra-cabeça com triângulos

Figura 08 – Tá difícil?

Então resumindo o método:
1) Crie todas as combinações possíveis de três letras de cada um dos vértices da imagem;
2) Vá descartando as combinações que não formam triângulos por não terem ligações ou por formarem um linha reta.
Ajuda: a resposta do problema da figura 8 passa por verificar as seguintes 455 combinações… Quais delas geram triângulos?

Eis a lista para verificação:
ABC, ABD, ABE, ABF, ABG, ABH, ABI, ABJ, ABK, ABL, ABM, ABN, ABO, ACD, ACE, ACF, ACG, ACH, ACI, ACJ, ACK, ACL, ACM, ACN, ACO, ADE, ADF, ADG, ADH, ADI, ADJ, ADK, ADL, ADM, ADN, ADO, AEF, AEG, AEH, AEI, AEJ, AEK, AEL, AEM, AEN, AEO, AFG, AFH, AFI, AFJ, AFK, AFL, AFM, AFN, AFO, AGH, AGI, AGJ, AGK, AGL, AGM, AGN, AGO, AHI, AHJ, AHK, AHL, AHM, AHN, AHO, AIJ, AIK, AIL, AIM, AIN, AIO, AJK, AJL, AJM, AJN, AJO, AKL, AKM, AKN, AKO, ALM, ALN, ALO, AMN, AMO, ANO, BCD, BCE, BCF, BCG, BCH, BCI, BCJ, BCK, BCL, BCM, BCN, BCO, BDE, BDF, BDG, BDH, BDI, BDJ, BDK, BDL, BDM, BDN, BDO, BEF, BEG, BEH, BEI, BEJ, BEK, BEL, BEM, BEN, BEO, BFG, BFH, BFI, BFJ, BFK, BFL, BFM, BFN, BFO, BGH, BGI, BGJ, BGK, BGL, BGM, BGN, BGO, BHI, BHJ, BHK, BHL, BHM, BHN, BHO, BIJ, BIK, BIL, BIM, BIN, BIO, BJK, BJL, BJM, BJN, BJO, BKL, BKM, BKN, BKO, BLM, BLN, BLO, BMN, BMO, BNO, CDE, CDF, CDG, CDH, CDI, CDJ, CDK, CDL, CDM, CDN, CDO, CEF, CEG, CEH, CEI, CEJ, CEK, CEL, CEM, CEN, CEO, CFG, CFH, CFI, CFJ, CFK, CFL, CFM, CFN, CFO, CGH, CGI, CGJ, CGK, CGL, CGM, CGN, CGO, CHI, CHJ, CHK, CHL, CHM, CHN, CHO, CIJ, CIK, CIL, CIM, CIN, CIO, CJK, CJL, CJM, CJN, CJO, CKL, CKM, CKN, CKO, CLM, CLN, CLO, CMN, CMO, CNO, DEF, DEG, DEH, DEI, DEJ, DEK, DEL, DEM, DEN, DEO, DFG, DFH, DFI, DFJ, DFK, DFL, DFM, DFN, DFO, DGH, DGI, DGJ, DGK, DGL, DGM, DGN, DGO, DHI, DHJ, DHK, DHL, DHM, DHN, DHO, DIJ, DIK, DIL, DIM, DIN, DIO, DJK, DJL, DJM, DJN, DJO, DKL, DKM, DKN, DKO, DLM, DLN, DLO, DMN, DMO, DNO, EFG, EFH, EFI, EFJ, EFK, EFL, EFM, EFN, EFO, EGH, EGI, EGJ, EGK, EGL, EGM, EGN, EGO, EHI, EHJ, EHK, EHL, EHM, EHN, EHO, EIJ, EIK, EIL, EIM, EIN, EIO, EJK, EJL, EJM, EJN, EJO, EKL, EKM, EKN, EKO, ELM, ELN, ELO, EMN, EMO, ENO, FGH, FGI, FGJ, FGK, FGL, FGM, FGN, FGO, FHI, FHJ, FHK, FHL, FHM, FHN, FHO, FIJ, FIK, FIL, FIM, FIN, FIO, FJK, FJL, FJM, FJN, FJO, FKL, FKM, FKN, FKO, FLM, FLN, FLO, FMN, FMO, FNO, GHI, GHJ, GHK, GHL, GHM, GHN, GHO, GIJ, GIK, GIL, GIM, GIN, GIO, GJK, GJL, GJM, GJN, GJO, GKL, GKM, GKN, GKO, GLM, GLN, GLO, GMN, GMO, GNO, HIJ, HIK, HIL, HIM, HIN, HIO, HJK, HJL, HJM, HJN, HJO, HKL, HKM, HKN, HKO, HLM, HLN, HLO, HMN, HMO, HNO, IJK, IJL, IJM, IJN, IJO, IKL, IKM, IKN, IKO, ILM, ILN, ILO, IMN, IMO, INO, JKL, JKM, JKN, JKO, JLM, JLN, JLO, JMN, JMO, JNO, KLM, KLN, KLO, KMN, KMO, KNO, LMN, LMO, LNO, MNO.

Ok, esse método não se mostrou prático para grande número de triângulos, mas podia ser pior, com retângulos ficaria muito mais doido! Pelo menos o sujeito que disser que viu 51 triângulos (que não é a resposta certa) vai poder enumerar os vértices pelo nosso método antes de tentar nos convencer que sabe mais do que a gente…

Resposta:

ABC, ABD, ABE, ABF, ABG, ABH, ABI, ABJ, ABK, ABL, ABM, ABN, ABO, ACD, ACE, ACF, ACG, ACH, ACI, ACJ, ACK, ACL, ACM, ACN, ACO, ADE, ADF, ADG, ADH, ADI, ADJ, ADK, ADL, ADM, ADN, ADO, AEF, AEG, AEH, AEI, AEJ, AEK, AEL, AEM, AEN, AEO, AFG, AFH, AFI, AFJ, AFK, AFL, AFM, AFN, AFO, AGH, AGI, AGJ, AGK, AGL, AGM, AGN, AGO, AHI, AHJ, AHK, AHL, AHM, AHN, AHO, AIJ, AIK, AIL, AIM, AIN, AIO, AJK, AJL, AJM, AJN, AJO, AKL, AKM, AKN, AKO, ALM, ALN, ALO, AMN, AMO, ANO, BCD, BCE, BCF, BCG, BCH, BCI, BCJ, BCK, BCL, BCM, BCN, BCO, BDE, BDF, BDG, BDH, BDI, BDJ, BDK, BDL, BDM, BDN, BDO, BEF, BEG, BEH, BEI, BEJ, BEK, BEL, BEM, BEN, BEO, BFG, BFH, BFI, BFJ, BFK, BFL, BFM, BFN, BFO, BGH, BGI, BGJ, BGK, BGL, BGM, BGN, BGO, BHI, BHJ, BHK, BHL, BHM, BHN, BHO, BIJ, BIK, BIL, BIM, BIN, BIO, BJK, BJL, BJM, BJN, BJO, BKL, BKM, BKN, BKO, BLM, BLN, BLO, BMN, BMO, BNO, CDE, CDF, CDG, CDH, CDI, CDJ, CDK, CDL, CDM, CDN, CDO, CEF, CEG, CEH, CEI, CEJ, CEK, CEL, CEM, CEN, CEO, CFG, CFH, CFI, CFJ, CFK, CFL, CFM, CFN, CFO, CGH, CGI, CGJ, CGK, CGL, CGM, CGN, CGO, CHI, CHJ, CHK, CHL, CHM, CHN, CHO, CIJ, CIK, CIL, CIM, CIN, CIO, CJK, CJL, CJM, CJN, CJO, CKL, CKM, CKN, CKO, CLM, CLN, CLO, CMN, CMO, CNO, DEF, DEG, DEH, DEI, DEJ, DEK, DEL, DEM, DEN, DEO, DFG, DFH, DFI, DFJ, DFK, DFL, DFM, DFN, DFO, DGH, DGI, DGJ, DGK, DGL, DGM, DGN, DGO, DHI, DHJ, DHK, DHL, DHM, DHN, DHO, DIJ, DIK, DIL, DIM, DIN, DIO, DJK, DJL, DJM, DJN, DJO, DKL, DKM, DKN, DKO, DLM, DLN, DLO, DMN, DMO, DNO, EFG, EFH, EFI, EFJ, EFK, EFL, EFM, EFN, EFO, EGH, EGI, EGJ, EGK, EGL, EGM, EGN, EGO, EHI, EHJ, EHK, EHL, EHM, EHN, EHO, EIJ, EIK, EIL, EIM, EIN, EIO, EJK, EJL, EJM, EJN, EJO, EKL, EKM, EKN, EKO, ELM, ELN, ELO, EMN, EMO, ENO, FGH, FGI, FGJ, FGK, FGL, FGM, FGN, FGO, FHI, FHJ, FHK, FHL, FHM, FHN, FHO, FIJ, FIK, FIL, FIM, FIN, FIO, FJK, FJL, FJM, FJN, FJO, FKL, FKM, FKN, FKO, FLM, FLN, FLO, FMN, FMO, FNO, GHI, GHJ, GHK, GHL, GHM, GHN, GHO, GIJ, GIK, GIL, GIM, GIN, GIO, GJK, GJL, GJM, GJN, GJO, GKL, GKM, GKN, GKO, GLM, GLN, GLO, GMN, GMO, GNO, HIJ, HIK, HIL, HIM, HIN, HIO, HJK, HJL, HJM, HJN, HJO, HKL, HKM, HKN, HKO, HLM, HLN, HLO, HMN, HMO, HNO, IJK, IJL, IJM, IJN, IJO, IKL, IKM, IKN, IKO, ILM, ILN, ILO, IMN, IMO, INO, JKL, JKM, JKN, JKO, JLM, JLN, JLO, JMN, JMO, JNO, KLM, KLN, KLO, KMN, KMO, KNO, LMN, LMO, LNO, MNO.

Testes para Concurso – Legislação

Que tal um teste rápido para determinar se você tem hábitos de gênio ou de louco?

Gênio, Normal ou Insano? http://xek.me/tst/eq/quiz.php?quiz=2

Ok, foi só um pouco de humor para relaxar… Agora um teste sério:

Testes para Concurso – Legislação I

Caso esteja procurando um teste mais sério, eis minha página de testes para concurso (estou fazendo elas aos poucos):

http://xek.me/tst/xlq/

Boa sorte!