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This post has been updated. It was originally published on 8/18/2024.

One of the most common problems in all of chemistry and materials science: stain removal. From a scientific perspective, oil on the garage floor, red wine on a white rug, and chewing gum on your pants seat all present different cleaning challenges (at least until self-cleaning clothes hit the market). Let’s look at how stains work, and how we can use chemistry to remove them.

Ground rules

A stain depends on two factors: the contaminant and how it interacts with the material it hits. Most household stains are surface ones, where the contaminating substance flows into the gaps of a material, such as the fibers of a cloth or the pores in a concrete floor, and become trapped there.

Another type of stain is due to a molecular reaction. For example, those notorious yellow marks appear on the armpits of your white shirt because your sweat reacts with the aluminum chloride in your antiperspirant. (If you’re actually sweating yellow liquid, you have more than stains to worry about.) In other cases, a dye can form covalent bonds with a material to create visible marks, as when you tie-dye clothing. Fortunately, those stains are extremely rare, and usually deliberate.

In all cases, your first step should be to pretreat the stain as quickly as possible. This means wiping up any excess spillage and then putting down something that will start to draw out the stain. For example, you could dab—never rub—at an untreated stain with a paper towel or other absorbent item, allowing capillary action to draw up the liquid. Then dampen the mark with cold water, which generally helps keep stains from setting.

At this point, once you’ve pretreated the stain, you can apply a stain remover (and, depending on the substance, even rub the mark with it). But you need to choose your cleanser wisely.

Cleaning toolkit

After you’ve pretreated the stain, you need to look at the specific substance you’re dealing with. That’s because different types of contaminants respond to different cleansers. Here are a few you should know.

The most common stain removers are surfactants. Examples include dish soap, laundry detergent, and many industrial suds. Surfactant molecules have two polar ends, one hydrophilic (or water-friendly) and one hydrophobic. These cleaners work a bit like velcro: One end attaches to a water molecule, one end attaches to a molecule of the stain, and off they swirl. However, the same reaction allows surfactants to remove dyes as well as stains from your clothes, so read the label before using this type of stain remover.

[Related: Master odor removal with a little help from science]

Also popular, especially for organic stains, are enzymatic cleaners. These use sets of enzymes to break down the molecules of the staining substance. Lipases, for example, break down lipids like olive oil. Many of these are more environmentally friendly than their harsher brethren. But these cleaners can vary widely in concentration and the type of enzymes used. In some, the labels won’t disclose which enzymes are in the mix; instead, they list an “enzymatic blend” as an ingredient. Unlike surfactants, you might have a harder time finding these stain removers in a pinch, such as when you’re traveling or away from home. To purchase this type of cleaner, check the label of a commercial stain remover for terms such as “enzymatic action,” and look closely at which types of stains it promises to treat.

Finally, for the toughest of the tough stains, you’ll need solvents like rubbing alcohol and acids like white vinegar. These harsher cleansers let you dissolve, grind off, or corrode away the tenacious color. When you do use vinegar, you’ll want to dilute its concentration with water, such as adding one part vinegar to two parts water.

So now that you have the tools, let’s get rid of those stains!

Red wine stain

This is really your fault for owning a white carpet in the first place.

How to remove red wine stains

You may not think of your red wine as a dye, but it’s full of anthocyanins, which are common natural dyes for textiles. Even worse, when you find them in wine, they’re dissolved in alcohol and water, making your glass’s contents the perfect cocktail to ruin any cloth they touch.

When possible, use a surfactant to remove the stain on the surface. That may not be enough, so also apply an oxidizer to knock out the chromophores. For example, you might start with dish soap and follow it up with hydrogen peroxide.

How to remove honey and syrup stains How to remove coffee stains

Just as coffee left to cool will change in taste and consistency, so will a coffee stain. If you get a drop of coffee on your shirt, then blot it up, turn the cloth around, and run cold water through the back of the stain. This turns your clothes into a sort of reverse filter, pulling the coffee out of the material.

If the stain has dried, at this point, all you’re really dealing with is the chromophores. So do what the coffee professionals do: Grab some sodium percarbonate. At high concentrations, this substance cleans out industrial-grade coffee machines, so a solution of ¼ cup sodium percarbonate to 2 cups water should easily destroy your stain.

How to remove chocolate stains

Chocolate is a one-two punch. It’s both oily, so you’ll need a surfactant, and organic, since the sweet treat includes vegetable oil (such as cocoa butter) and various cocoa solids.

That means for best results, start with soap and then follow up with an enzymatic cleaner. Use plenty of cold water. Once you’ve pretreated a chocolate stain, this is one of the rare occasions where you should rub the mark to loosen it.

Ketchup stain

You knew this would happen when you wore a white shirt while eating ketchup.

How to remove tomato sauce and ketchup stains

With tomato stains, time is of the essence. Ripe tomatoes get their red color from tannins, which are also used as dyes. They have enough sticking power to stain plastic. So the second the sauce hits the linen, rug, or other material, apply cold water. If you didn’t notice that stray ketchup squirt right away, older stains can still benefit from treatment with warm water and an enzymatic cleaner.

How to remove stain sweats

Fortunately for your laundry bill, you can tackle sweat stains with multiple approaches. We recommend tailoring your approach with the item itself. Dyed delicates, for example, should respond well to surfactants. But with light-colored, sturdy items, save yourself some energy: Make a paste of baking soda and warm water and rub it into the stain. Let it dry for up to two hours and then wash it out.

By the way, the latter technique will also work with any mineral stains (including depleted uranium!).

How to removes blood stains and other biological materials

Anybody who lives with a baby animal (including baby humans) quickly becomes familiar with the many fluids and semi-solids that escape our bodies—and the seemingly-permanent marks they leave on everything. The good news is, if the stain is fresh, water will likely erase most of it, once you clear away the offending matter. Any leftover traces should quickly yield to enzymes.

You may want to use the enzymes a few times, and then use a solvent like rubbing alcohol to clean whatever’s left. If you’re concerned about applying a solvent to a delicate item, use a weaker solution available at drugstores, or dilute your rubbing alcohol with one part water to one part alcohol.

How to remove grass stains

Grass is a bit tougher than other biological stains, because, much like red wine, it’s a fairly effective dye—especially on light-colored clothing. Start with an enzymatic cleaner, preferably one specifically designed to tackle these kinds of stains. If there’s some stain left over, or enzymatic cleaners don’t meet the bill, try an acid, such as diluted vinegar, to pull the stain out of the fabric.

However, before you apply any vinegar to dyed cloth, put a small amount on a clean area of the garment that people won’t see, wait for a few minutes, and then wash it out. This will tell you whether the vinegar reacts with the dyed clothing. If it damages the material, then you may want to consult with a dry cleaner instead of tackling the stain on your own.

How to remove grease and oil stains

[Related: This is the one power cleaner you need for your kitchen]

For really tough grease stains, look for industrial soaps. They use the same action, but have stronger pull. However, for delicate garments that aren’t colorfast—that is, where the dye hasn’t fully permeated the fibers—industrial soap may strip dye as well as grease out of your clothing.

How to remove ink stains

Since ink is supposed to be permanent, you need to resort to solvents for this type of stain. (This is why your parents run for the hairspray; it used to be loaded with alcohol, although you won’t find that solvent in most modern formulas.) To lift it out, you need to bust out a rag and some alcohol. Soak a sturdy cloth rag that you won’t mind ruining in the solvent; as the ink dissolves, it’ll transfer to the rag. After you’ve dabbed the stain a few times, try applying an oxidizer to take the color out of what’s left.

You’ll definitely have to clean up some mud stains when you get home. Depositphotos

How to remove mud stains

Mud will require everything in your toolkit, because dirt contains a mix of everything. First, dry out the mud completely and brush off as much as you can. Then hit it with a surfactant and some cold water. After that, if the fabric can take vinegar, apply some of the acid to eat away at other parts of the mud. Anything left will succumb to enzymes. We also recommend using psychology: Make whoever is responsible for the mud stains do all this; it’s a superb way to stop those stains before they start.

These are just the most common stains, of course, but what’s most important is the toolkit. Once you understand both how the stain works, and how different cleaners clear it away, the battle against contaminants is (almost) won.

You're reading How To Remove Stains Of Any Kind

What Kind Of Content Goes Where?

Orientate content around people at different stages of purchase intent

Since I’m always pushing the importance of content marketing and creating infographics about how to use content marketing, it’s interesting to see the questions marketers ask about them. This week a client asked me a great and simple question this week…

“I understand creating content, but where do I put all this content… what kind of content goes where”?

That’s a fair question that I think many will have.

Information that sells your expertise and builds trust

The core aim that we all have is to ultimately sell something, so let’s start here. By definition this content is going to be on your website in the most-part. So you’re going to need a place to place content in a way that can be related to what you want to sell – important!

Categorise great content in a content hub such as a blog, online resource centre, customer magazine or resource centre so that you can easily relate it to product/service information – you need a home for it, we say this all of the time of course but not just any home. Making the “next step” obvious is absolutely crucial, even if this is just some form of data capture. Often blogs or social media outposts are disconnected from the place to purchase. Make the customer journeys seamless

Make the content valuable, we hear this a lot and it sounds vague? Simple, solve problems that people have at the related stage in purchasing your kinda stuff! If you don’t know, go find out. Content that “talks to me”, that empathises, is what matters. Great sales is solving problems not selling for selling’s sake

Use a range of content types otherwise it gets boring, this also allows you to put a different spin on very similar topics – doing an infographic one week and then a SlideShare or video the next engages much more and encourages people to come back, in the very least it has the potential to hook different types of people. See our content marketing matrix infographic for ideas and think how they relate to the buying process

Design in a reason for me to give you my data, this way you earn the right to follow up. Placing your content into interactive tools such as quizzes might also be a smart move

The goal is to help! Of course we hope that content in a blog is information that gets indexed by Google, content that in turn is good enough to warrant sharing by you.

Content that engages and nurtures a fan-base

You need content that is built to nurture a community or fan-base. That community is most-often virtual, spread everywhere, but you’re on their radar because you create valuable stuff. Smart Insights do this via our blog, but in most commercial cases you still see this done well in emails, especially in the B2B space. It’s not that you can’t sell to the community, an effort to be valuable is sales in it’s softest sense, but the intent is to be valuable first and foremost, which is what makes it different. So forget about the money off banners here 🙂

So as not to lose that privilege of having a strong fan base – here are a few tips for managing your content marketing:

Create great stories that are interesting on the topic of choice, since the goal is entertainment and/or education content curation works really well here

Keep on topic and on-trend 80% of the time, be useful – and 20% of the time try being entertaining (I’ve wondered if we should try this on Smart Insights too!?)

Combing email and social media is pretty key now, these are the key customer communications channels, Dave’s written good stuff on this before

Consider content that’s easy to digest in short periods of time and that content is similarly dead easy to re-share on your behalf

I’m a big fan of ebooks and guides in this area, they’re great to demonstrate a credibility and thought leadership, if you plan ahead they also break down easily into multiple blog posts and webinars too, as an example

Content that’s placed to hooks new fans

Here we’re talking about outposts, something we’ve covered before in infographic form. What should you create for those places? The key again is in recognising that your audience are already present in multiple locations, this “new business” (if we’re thinking B2B as example) maybe don’t know you exist or even care so much at the moment. Putting content in their lap therefore makes great sense.

How might you get a regular gig, guest blogging or sharing content to an important outpost for your industry?

From a B2C perspective you might be doing anything from game creation and video virals to running fun quizzes and contents in Facebook (though keep it valuable – we’re primarily hooking fans, earning the permission, not trying to coupon our way to more sales)

Don’t forget to invest your time where the questions are being asked, demonstrate your value. Whether LinkedIn Groups (B2B) or sites like Lonely Planet’s Thorntree (if you were B2C travel, for example) – it’s not just Facebook and Twitter, though of course they matter

Image courtesy of Kevin Thom photography

Dna And A New Kind Of Racial Profiling

by Courtesy DNAPrint

DECEMBER 2002: Serial-murder investigators initially seek a white man. MAY 2003: The man charged is black, confirming what DNA evidence had suggested.

Nothing in American police work is more controversial than racial profiling. Minorities are targeted for small offenses in the hope of uncovering bigger crimes, and the practice has generated successful lawsuits by the ACLU and pledges from state governments and law enforcement agencies to clean up their discriminatory acts.

Add to this charged atmosphere the prospect of a DNA-race angle. By now most Americans know that when criminals leave traces of themselves–blood, semen, hair, a scrape of skin under a victim’s fingernails–at crime scenes, they leave a unique genetic fingerprint that can establish their presence at the scene with great certainty. Less known but more controversial is that DNA traces also leave clues about ancestry and appearance, clues that, as genetic science matures, might be used to generate a sort of police sketch.

Racial differences constitute small notes within the great opus of the human genetic code, but the very fact that genetic markers linked to ethnic origin are, in a sense, cosmetic–that is, they affect outward appearance–makes them potentially useful in the hunt for criminals. Is a suspect of fair Celtic stock or of darker African origin? His or her DNA may tell. Such information could prove far more useful to street-pounding cops than notoriously unreliable eyewitness reports. But unless the science proves reliable, there is risk here: The use of DNA markers could confer authority on police searches–isn’t genetic information more reliable than even fingerprints?–that, in the area of racial markers and appearance, it may not deserve.

In 1997, when members of the national DNA Advisory Board officially selected the gene markers for DNA evidence matching, they could have included a few markers associated with ancestral geographic origins (European, East Asian, sub-Saharan African)–which are a good indication of race and ethnicity. “We deliberately chose not to do so,” says Ranajit Chakraborty, director of the University of Cincinnati’s Center for Genome Information. Chakraborty says the board skirted the racial-marker issue in part because of the political minefield it represented. Thus today’s standard American DNA fingerprint, with its battery of 15 gene markers (two were recently added to the standard 13), is a sort of bar code identifier that is fine for matching two DNA samples but offers no hints about the human package from which a crime-scene DNA sample is derived.

Not that DNA hasn’t already been quietly used for ethnic identification. Following the 9/11 terrorist attacks, Chakraborty acceded to the request of a family whose son had been a passenger on United Flight 93 (the thwarted terrorist mission brought down in Pennsylvania). “We had a specimen that consisted of at least two individuals’ remains, one of which was their son’s,” he explains. “The family was reluctant to bury it with his other body parts if it contained any remains that might belong to a hijacker.” Chakraborty determined, with 95 percent certainty, that the unidentified tissue did not belong to anyone of Middle Eastern ancestry.

“We may not be able to tell German from French,” says Chakraborty, “but we can place individuals in major continental groups.” In turn, within each of these groups, certain types of hair texture, eye and skin color, and other facial features predominate. Such information could prove useful in an investigation, admits Chakraborty. “But (it) should not be interpreted that you can say with 100 percent accuracy that a person will have, say, brown eyes.”

Because geneticists have largely kept mum about ethnic markers, it proved something of a shock when DNAPrint Genomics concluded last March that a Louisiana serial killer’s “biogeographical ancestry” was 85 percent sub-Saharan African and 15 percent Native American. At the time, the police were on an altogether different track: They had been seeking a white man who had been seen lurking in the neighborhood of one of the crime scenes.

silent,” says Tony Frudakis, research director at DNAPrint, describing the conference call in which he revealed the lab’s results to police investigators. They were dubious, Frudakis says, and asked to see DNAPrint’s analyses of 20 other DNA samples of known individuals they’d sent along with the killer’s sample to test the lab’s reliability. “We got them all right,” Frudakis says.

The investigators were convinced enough to expand their search to include African-Americans, then had a break in the case due to an unrelated incident. Derrick Todd Lee, called in for questioning about two unrelated killings, voluntarily gave a DNA sample, which police say matched DNA from the serial murders. Arrested on May 27 and now awaiting trial, Lee is African-American.

A basic ancestry profile may be just the beginning for the DNA-based police sketch, boosters say. “To be honest, most of us are mongrels,” says Frudakis. “We reside somewhere along a continuum rather than as members of physically distinct groups.” He says DNAPrint is developing genomic tests to detect more specific physical traits, and it hopes to have the first such test–Retinome, for eye color–ready for market by the end of 2003. “After that, give us another year for hair color,” he says. The latter is a particularly bold boast, since not much is known about hair color markers beyond one associated with red hair.

DNAPrint is not the first to claim progress toward a gene-based police sketch. In the late 1990s, Britain’s Forensic Science Service trumpeted the development of something called a DNA photofit. Emboldened by the identification of the gene marker for the “Celtic look” (fair skin and red hair), it poured money into an ambitious project at University College London. Scientists scanned the faces of hundreds of volunteers in an attempt to correlate digitized facial geometry with genetic markers.

as nose height and width, eye shape and the distance across the broadest part of the face.

The Forensic Science Service had faith that the University College team could deliver in a couple of years, says team member Alf Linney, a medical imaging expert at University College London. But the connection between genes and facial appearance proved too complex for the London scientists, and the project was suspended in 2000.

symmetry.” As every high school biology student learns, genotype plus environment equals phenotype–the physical expression of our genes. All of which Frudakis concedes. Still, he argues that the sophistication of new “high-throughput” computer analysis of genetic information greatly expands the layers of genetic clues that can go into a DNA-based best guess about a person’s physical appearance.

a treasure hunt in which we systematically determine, OK, the treasure isn’t here, let’s search the next grid.” This contrasts, he says, with gene searches of just a few years ago, which were much more hit-and-miss.

Critics fear that the DNA sketch concept opens the door to biased, unscientific racial profiling based on unproven gene markers for behavior, including criminal behavior. “The temptation will be to run DNA data through computers to conclude, for example, that you can identify markers for, say, sexual offenders,” warns sociologist Troy Duster, author of Backdoor to Eugenics and a consultant to the National Human Genome Research Institute. Imagine such a data crunch based on the DNA of convicted criminals, given the preponderance of black and Hispanic men in American prisons. “It would be like going to the NFL and concluding that the DNA marker for sickle-cell anemia (associated with African ancestry) makes you a good football player.”

Despite such objections, forensic biologists like Benecke predict that the accuracy of DNA-based descriptions will edge past that of eyewitness accounts within 15 years, barring legal roadblocks. Germany currently outlaws the disclosure of DNA-gleaned information, except in medical situations with a patient’s consent. “Technically, we’re not even supposed to notice if there’s a Y (male) chromosome,” says Benecke. “But how can it be an invasion of privacy if we’re only looking at things that can be seen from the outside?”

of the crime.”

How To Remove Some Last Elements Of A Vector In R?

A vector in R can have infinite number of elements but we might want to remove some of them. To remove the last elements of a vector, we can use head function with negative sign of the number of values we do not want. For example, if we have a vector of length 200 but we don’t want last fifty elements then we can use head(vector_name,-50).

Examples x1<-rnorm(100) x1 Output [1] 0.19166338 1.55254427 0.91424229 0.35862537 0.17509564 -0.84726777 [7] 0.97823166 1.80586826 0.12291480 -0.12977203 -0.21642866 1.44647817 [13] 0.40970980 0.91091657 1.43035817 -0.38129196 0.20230718 -0.80619919 [19] 0.29463418 1.40488308 1.02376685 0.47612606 -0.67033033 0.15923432 [25] -0.38271538 0.93576259 -0.63153227 -0.09830608 1.03198498 0.38780843 [31] -1.25612931 -0.78695273 0.42981155 -0.37641622 -1.21622907 1.02927851 [37] 0.43039700 -1.24557402 -0.60272849 0.66006939 2.05074953 0.49080818 [43] -1.73147942 0.71088366 0.01382291 -1.40104160 1.25912367 -0.12747752 [49] -0.72938651 -1.21136136 0.59961974 -1.16032953 0.43909343 0.20485374 [55] -0.69918134 -0.92662568 -1.01348238 0.60498706 1.73440013 -0.34985053 [61] 1.19918551 1.02390100 -0.04627515 1.38650843 -2.19527272 -0.12755691 [67] -1.31699684 -1.42693514 0.87944163 0.39399158 0.68892548 2.35371650 [73] -1.01509767 0.29097752 1.56532608 -0.84711837 1.32766016 0.47704633 [79] 0.18525094 0.25329489 2.59222735 1.07434699 -1.59690189 -0.08758860 [85] 0.36076759 -0.87995998 -3.32333496 -0.46751545 0.43154027 -0.60398945 [91] 0.67444669 0.63592054 -0.61297039 0.41489135 0.87734337 0.02115758 [97] 1.81038329 -0.45209570 -0.12512399 0.76680042 Example head(x1,-50) Output [1] 0.19166338 1.55254427 0.91424229 0.35862537 0.17509564 -0.84726777 [7] 0.97823166 1.80586826 0.12291480 -0.12977203 -0.21642866 1.44647817 [13] 0.40970980 0.91091657 1.43035817 -0.38129196 0.20230718 -0.80619919 [19] 0.29463418 1.40488308 1.02376685 0.47612606 -0.67033033 0.15923432 [25] -0.38271538 0.93576259 -0.63153227 -0.09830608 1.03198498 0.38780843 [31] -1.25612931 -0.78695273 0.42981155 -0.37641622 -1.21622907 1.02927851 [37] 0.43039700 -1.24557402 -0.60272849 0.66006939 2.05074953 0.49080818 [43] -1.73147942 0.71088366 0.01382291 -1.40104160 1.25912367 -0.12747752 [49] -0.72938651 -1.21136136 Example head(x1,-10) Output [1] 0.19166338 1.55254427 0.91424229 0.35862537 0.17509564 -0.84726777 [7] 0.97823166 1.80586826 0.12291480 -0.12977203 -0.21642866 1.44647817 [13] 0.40970980 0.91091657 1.43035817 -0.38129196 0.20230718 -0.80619919 [19] 0.29463418 1.40488308 1.02376685 0.47612606 -0.67033033 0.15923432 [25] -0.38271538 0.93576259 -0.63153227 -0.09830608 1.03198498 0.38780843 [31] -1.25612931 -0.78695273 0.42981155 -0.37641622 -1.21622907 1.02927851 [37] 0.43039700 -1.24557402 -0.60272849 0.66006939 2.05074953 0.49080818 [43] -1.73147942 0.71088366 0.01382291 -1.40104160 1.25912367 -0.12747752 [49] -0.72938651 -1.21136136 0.59961974 -1.16032953 0.43909343 0.20485374 [55] -0.69918134 -0.92662568 -1.01348238 0.60498706 1.73440013 -0.34985053 [61] 1.19918551 1.02390100 -0.04627515 1.38650843 -2.19527272 -0.12755691 [67] -1.31699684 -1.42693514 0.87944163 0.39399158 0.68892548 2.35371650 [73] -1.01509767 0.29097752 1.56532608 -0.84711837 1.32766016 0.47704633 [79] 0.18525094 0.25329489 2.59222735 1.07434699 -1.59690189 -0.08758860 [85] 0.36076759 -0.87995998 -3.32333496 -0.46751545 0.43154027 -0.60398945 Example head(x1,-90) Output [1] 0.1916634 1.5525443 0.9142423 0.3586254 0.1750956 -0.8472678 [7] 0.9782317 1.8058683 0.1229148 -0.1297720 Example head(x1,-30) Output [1] 0.19166338 1.55254427 0.91424229 0.35862537 0.17509564 -0.84726777 [7] 0.97823166 1.80586826 0.12291480 -0.12977203 -0.21642866 1.44647817 [13] 0.40970980 0.91091657 1.43035817 -0.38129196 0.20230718 -0.80619919 [19] 0.29463418 1.40488308 1.02376685 0.47612606 -0.67033033 0.15923432 [25] -0.38271538 0.93576259 -0.63153227 -0.09830608 1.03198498 0.38780843 [31] -1.25612931 -0.78695273 0.42981155 -0.37641622 -1.21622907 1.02927851 [37] 0.43039700 -1.24557402 -0.60272849 0.66006939 2.05074953 0.49080818 [43] -1.73147942 0.71088366 0.01382291 -1.40104160 1.25912367 -0.12747752 [49] -0.72938651 -1.21136136 0.59961974 -1.16032953 0.43909343 0.20485374 [55] -0.69918134 -0.92662568 -1.01348238 0.60498706 1.73440013 -0.34985053 [61] 1.19918551 1.02390100 -0.04627515 1.38650843 -2.19527272 -0.12755691 [67] -1.31699684 -1.42693514 0.87944163 0.39399158 Example head(x1,-20) Output [1] 0.19166338 1.55254427 0.91424229 0.35862537 0.17509564 -0.84726777 [7] 0.97823166 1.80586826 0.12291480 -0.12977203 -0.21642866 1.44647817 [13] 0.40970980 0.91091657 1.43035817 -0.38129196 0.20230718 -0.80619919 [19] 0.29463418 1.40488308 1.02376685 0.47612606 -0.67033033 0.15923432 [25] -0.38271538 0.93576259 -0.63153227 -0.09830608 1.03198498 0.38780843 [31] -1.25612931 -0.78695273 0.42981155 -0.37641622 -1.21622907 1.02927851 [37] 0.43039700 -1.24557402 -0.60272849 0.66006939 2.05074953 0.49080818 [43] -1.73147942 0.71088366 0.01382291 -1.40104160 1.25912367 -0.12747752 [49] -0.72938651 -1.21136136 0.59961974 -1.16032953 0.43909343 0.20485374 [55] -0.69918134 -0.92662568 -1.01348238 0.60498706 1.73440013 -0.34985053 [61] 1.19918551 1.02390100 -0.04627515 1.38650843 -2.19527272 -0.12755691 [67] -1.31699684 -1.42693514 0.87944163 0.39399158 0.68892548 2.35371650 [73] -1.01509767 0.29097752 1.56532608 -0.84711837 1.32766016 0.47704633 [79] 0.18525094 0.25329489 Example head(x1,-80) Output [1] 0.1916634 1.5525443 0.9142423 0.3586254 0.1750956 -0.8472678 [7] 0.9782317 1.8058683 0.1229148 -0.1297720 -0.2164287 1.4464782 [13] 0.4097098 0.9109166 1.4303582 -0.3812920 0.2023072 -0.8061992 [19] 0.2946342 1.4048831 Example head(x1,-95) Output [1] 0.1916634 1.5525443 0.9142423 0.3586254 0.1750956 Example head(x1,-99) Output [1] 0.1916634 Example head(x1,-45) Output [1] 0.19166338 1.55254427 0.91424229 0.35862537 0.17509564 -0.84726777 [7] 0.97823166 1.80586826 0.12291480 -0.12977203 -0.21642866 1.44647817 [13] 0.40970980 0.91091657 1.43035817 -0.38129196 0.20230718 -0.80619919 [19] 0.29463418 1.40488308 1.02376685 0.47612606 -0.67033033 0.15923432 [25] -0.38271538 0.93576259 -0.63153227 -0.09830608 1.03198498 0.38780843 [31] -1.25612931 -0.78695273 0.42981155 -0.37641622 -1.21622907 1.02927851 [37] 0.43039700 -1.24557402 -0.60272849 0.66006939 2.05074953 0.49080818 [43] -1.73147942 0.71088366 0.01382291 -1.40104160 1.25912367 -0.12747752 [49] -0.72938651 -1.21136136 0.59961974 -1.16032953 0.43909343 0.20485374 [55] -0.69918134 Example x2 <-LETTERS[1:26] x2 Output [1] "A" "B" "C" "D" "E" "F" "G" "H" "I" "J" "K" "L" "M" "N" "O" "P" "Q" "R" "S" [20] "T" "U" "V" "W" "X" "Y" "Z" Example head(x2,-6) Output [1] "A" "B" "C" "D" "E" "F" "G" "H" "I" "J" "K" "L" "M" "N" "O" "P" "Q" "R" "S" [20] "T" Example head(x2,-20) Output [1] "A" "B" "C" "D" "E" "F"

What Is Imei Number And How To Find Imei Of Any Device

You might have heard of the term “IMEI number” numerous times and chances are, you have heard of it while buying a new phone, selling your older phone or when you are reporting a case of your phone being lost. Well, if you have wondered about what exactly is this IMEI number, we are here to tell you all about it. So, let’s begin, shall we?

What is IMEI number?

IMEI number aka International Mobile Station Equipment Identity number is a unique 15 or 16-digit identity number assigned to mobile phones with a GSM, UMTS or LTE modem. The number includes information on the origin, model number and the unique serial number of the device. The initial 8 digits comprise of details around the origin and model number while the rest of the digits are decided by the device manufacturer.

IMEI is attached to the modem in the device, so if a mobile phone features dual SIM functionality, it will feature two unique IMEI numbers for the dual modems used. Along with IMEI numbers, there are other identity standards for mobile devices like ESN and MEID, so let’s take a look at how they are different:

IMEI vs MEID vs ESN: What’s the difference?

The common ground between IMEI, MEID (Mobile Equipment Identifier) and ESN (Electronic Serial Number) is the fact that they are all device identifiers. Chances are, you haven’t heard of ESN and that’s because it has been phased out a long time ago, with its last assignment being back in 2010. ESNs were previously used with AMPS and TDMA devices along with the occasional use on CDMA devices.

Different ways to find IMEI

There are various different ways to find your device’s IMEI number. The method remains the same on different smartphone platforms (Android, iOS, Windows, BlackBerry etc.) and feature phones, except for a few exceptions. So, here are the different ways:

Through USSD code

Dialing *#06# brings up the IMEI number on all feature phones and smartphones. Just go to the dialer, enter the USSD code and the IMEI number should pop up. However, this method does not work on Windows Phone devices.

In Phone Settings

On the Phone’s back or Battery

If your device has a removable battery, you can be sure of finding your device’s IMEI number printed on the battery. Also, some smartphones like the iPhone come with the IMEI number engraved on the back while most other devices come with a sticker on the back, which has IMEI info printed. Moreover, some devices like the iPhone also have the IMEI number printed on the SIM tray, so you can check out there too.

Retail box or Bill

You can be assured to have your device’s IMEI number printed on its retail box and the bill as well. So, if for some reason, you are not able to find your device’s IMEI number, looking at the bill or the retail box should be a good idea.

Using Google Dashboard (Android only)

If you have an Android smartphone, you can check your device’s IMEI number online over at the Google Dashboard page. Simply login with the Google account you use on your smartphone and tap on the Android section, which will list all devices connected to your account along with details like IMEI number.

Using iTunes (iOS only)

Using Microsoft account (Windows Phone only)

How is IMEI useful?

The IMEI number of a your smartphone or feature phone is unique for a reason. It can be used to identify your device as uniquely yours.. Here are some ways IMEI numbers come to good use:


Buying an older device

When you are planning to buy an older smartphone, the first thing you should do is check the device’s IMEI number. If the IMEI description on the phone says “Bad IMEI”, then the GSM modem of the phone is most probably broken and the device won’t be able to connect to a network. So, the IMEI number comes handy when buying an older phone, as it also represents if a device’s cellular services are fine or not.

Tracking a lost/stolen phone

The first thing cops ask when you file a report of your lost/stolen phone is the IMEI number. That’s because a device’s IMEI number is the only way to track a device remotely. Once you file an FIR with the cops, your device will be blacklisted, which will block it from connecting to a network. So, it’s important that you know the IMEI number at all times.


When you first start up your new mobile phone, that’s when the device’s IMEI number gets activated along with the date. So, even if you lose the bill, your date of purchase will be attached with your device’s IMEI number. That means your phone’s IMEI number can help you with your warranty claim.

SEE ALSO: How To Find A Lost or Stolen Android Device

IMEI numbers are important and now you know them

How To Install Kodi On Any Device

Kodi is a massively popular media application for organizing and maintaining local libraries of content. It’s available on almost all the major platforms including Windows, macOS, Android, iOS, Amazon Fire TV Stick, etc. Having such a wide platform availability, it has got a massive user base across various platforms and hardware devices. In addition, users can now stream endless list of content through third-party add-ons and repositories. In a nutshell, Kodi is now a complete package with a wide reach and enticing features. So if you are tempted with Kodi’s offering and want to try it out then you have come to the perfect place. In this article, we have brought the Kodi installation process for all major platforms in one place. So go ahead and learn how to install Kodi for your particular device.

Install Kodi on Any Device in 2023

In this section, we will go through all the platforms on which Kodi is available and show you how to install Kodi on your device easily. Along with that, we will also share some articles with detailed instructions in case you want to have a better idea about the installation process. Having said that, let’s start with Windows OS first.

How to Install Kodi on Windows

There are two ways to install Kodi on Windows and here we are going to share both the methods. You can choose either of the methods based on what you find convenient.

Install Kodi From the Microsoft Store

The best way to install Kodi on Windows is through the Microsoft Store. You can install Kodi just by making a quick search on Microsoft Store and installing it then and there. No need to download an offline installer and manually installing it. The best part is that you can update Kodi through the Microsoft Store seamlessly without losing your favorite add-ons and repository. But do keep in mind, you must be using Windows 10 or 8.1 to have Microsoft Store. And in case you are unable to find Kodi on the Microsoft Store, follow the link provided below.

Install Kodi from the Microsoft Store (Free)

Install Kodi Using an Offline Installer

In case, your device is running Windows 7 or lower, you can download the offline installer from the Kodi’s official website. Just choose the architecture of your device and you can install it just like any other application.

How to Install Kodi on Android

To install Kodi on Android, the process is fairly simple and straightforward. Just open the Google Play Store and search for “Kodi”. After that, tap on the “Install” button and there you have it. You can also find Kodi on Play Store through the link provided below.

Install Kodi from the Google Play Store (Free)

How to Install Kodi on macOS

How to Install Kodi on iOS

How to Install Kodi on Amazon Fire TV Stick How to Install Kodi on Chromebook

You can install Kodi on Chromebook very similar to Android phones if your Chromebook has Play Store support. Just search for “Kodi” in the Play Store and install it. That’s it.

However, if your Chromebook doesn’t have support for Play Store then it’s a bit tedious process. You will have to use a development tool, ARC Welder to convert Android apps to compatible Chrome OS apps. To make things easier for you, we have made a complete guide to install Kodi on Chromebooks for both Play Store supported and unsupported devices. Just open the mentioned link above and go through the steps. You will be able to install and run Kodi on unsupported Chromebooks fairly well.

How to Install Kodi on Linux sudo apt-get install software-properties-common sudo add-apt-repository ppa:team-xbmc/ppa sudo apt-get update sudo apt-get install kodi

After the installation is complete, just type kodi in the Terminal to open it. You can also access Kodi from the Software Center.

How to Install Kodi on Xbox One

There is also another way to install Kodi on Xbox One. The gaming console has its own Xbox App Store. So go ahead and search for “Kodi” in the app store and install it right away.

SEE ALSO: How to Use Kodi – A Beginner’s Guide (2024)

Install Kodi on Your Device and Discover a New World of Entertainment

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