3/27/2023 0 Comments Best app screenshot maker![]() ![]() Really, if not for Snappy’s great interface, Cloud App would have surely snapped #1 on our list.Ĭheck out these features and tell me that you’re not impressed with what Cloud App can offer: It’s a screencasting, gif-making, screenshot-taking powerhouse. That being said, Cloud App is next-level though. No other app even comes close to the usability, quality, and convenience while maintaining powerful features and annotation.Ĭloud App might be the best screenshot tool available in terms of quality, but the price and UX of Snappy banished this app to #2 on our list this year. The overall UX and price give it the top spot easily. Snappy takes screenshots (“Snaps”) in a single click from your browser, then lets you share, annotate, password protect, and even resize your snap all from the same window (So you don’t have to have so many tabs open).įrom there, Snappy makes sharing your screenshots with colleagues, friends or family a breeze: It’s so feature rich that we can’t believe it’s 100% FREE. It’s already used on 2 million smartphones, and by big names like Microsoft (Ever heard of them?). Snappy is hands down the best screenshot app for Mac in 2019, and in our opinion the best overall on the market now. Coolest Features: Sharing Features, UX, Price.Snappy – The Best Overall Screenshot App in 2019 (Best Features) Ready to start taking screenshots? We thought so! Screenshot apps for Mac (Free and paid)Īnd here’s a list of the best apps for taking screenshots in order of performance:. ![]() Screenshot apps for Andriod users (2019 update).Here’s a brief overview of what we cover: The Best Apps for Screenshots – At A Glance Don’t Just Screenshot Your PDFs, Modify Them!.The Best Apps for Screenshots – At A Glance. ![]()
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3/27/2023 0 Comments Blackmagic desktop video v10.4.2![]() The AW-UE50 also features a brand new web interface for professional operators working within darker environments to easily navigate the advanced GUI for operators. RTMP/RTMPS provides direct streaming to live broadcasting services such as YouTube Live and Facebook Live from the camera directly. NDI|HX version 2 is available via an optional paid-for upgrade and enables video transmission at low bitrates over a single LAN cable. SRT is supported out of the box to maintain stability while transmitting high-quality video, even in unstable network environments. The camera supports a wide variety of IP transmission protocols, including SRT, NDI|HX version 2, and RTMP/RTMPS. It supports up to 4K 25p/30p video at 3840 x 2160 to provide professional and high-quality shooting of moving images, as well as a wide variety of output interfaces such as 3G-SDI, HDMI, and IP. The AW-UE50 includes a new powerful chipset platform, making the PTZ incredibly responsive and capable of increased video processing tasks for higher image quality and lower latency. The camera also has optical image stabilization (OIS) to ensure smooth pan-tilt movement when in busier environments or moving or being placed onto a robotic system. The camera also introduces a new wide-angle lens with a 74.1° field of view and a 24x optical zoom, enabling a wide area to be shot from a limited installation space, in addition to maintaining high image quality at high zoom ratios. It features a new 1/2.5-type 4K MOS sensor that produces stunning UHD video with true 4K resolution of 1,500 TV lines in UHD. The AW-UE50 supports 3G SDI, HDMI, and IP, making it an ideal option for use within existing HD or 4K workflows. ![]() This opens up more opportunities for PTZ operation, including faster, precise movement and higher accuracy in preset positioning, making it Panasonic’s fastest, quietest, and most accurate PTZ yet. The camera features a direct drive system based on Panasonic’s own technology for quiet and smooth vertical and horizontal direction, with a reduced operating sound of NC25 or lower. It offers PoE+ support for camera power, control, and video transmission over a single cable, simplifying installation and reducing clutter. ![]() The AW-UE50 features a newly-designed and compact body with a weight of only 1.8kg, which makes it easy to handle and install in any kind of setting, especially when positioning the camera on trusses or ceilings. The AW-UE50 is a standard model perfect for people who want to utilize online video streaming more frequently or enhance the quality of online video streaming. The camera’s excellent system flexibility simplifies wiring and operation, and it can be linked with online conference software or online applications for easy online video streaming. It is designed for a variety of applications ranging from online classes to online seminars and offers high security and easy installation and operation for capturing stable images. ![]() The Panasonic AW-UE50 is a 4K 25/30p PTZ camera with 24x optical zoom that supports NDI|HX version 2 and SRT protocol. Panasonic AW-UE50(Black/White) 4K Integrated Ultra Quiet PTZ Camera ![]() 3/27/2023 0 Comments Ringphone booking software![]() ![]() Set by the GDPR Cookie Consent plugin, this cookie is used to record the user consent for the cookies in the "Advertisement" category. These cookies ensure basic functionalities and security features of the website, anonymously. Necessary cookies are absolutely essential for the website to function properly. With this feature you can expand your services very easily, and to make sure the appointment is valid, remember you are able to take online payments, either in full or partial. If you are a mobile business with an easy tweak, you can add in your booking form the address field for you to grab making it required to fill. ![]() Our appointment scheduler online is also suitable for automotive repair and service businesses, accountants, lawyers & notaries, pet groomers, photographers, coaches, consultants, and many more. Our appointment scheduler online software is mainly used by beauty & wellness, health & medical, professional services and many more including doctors who need to take online patients appointments, salons, including but not limited to hair salons & hairdressers, barbers, massage therapists & spa, fitness centres & personal trainers, nail salons, yoga classes, physical therapists, acupuncturists, chiropractors, naturopath clinics, nutritionists, podiatrists. BookOn appointment booking system, is very suitable for almost any businesses of all sizes. ![]() As a business owner, you will have your own dedicated reports page where you will be able to identify your profits, the most earning location, service, and staff.Īs mentioned earlier, you have full powers in customizing your booking form. Very easy to set up and even easier to make your customers happier. Staff scheduling has never been easier.Īnother of the several features you will have in your free (forever) plan, is gift cards and coupons. With our efficient appointment scheduler booking system you will be able to set breaks, days off, special days, holidays, etc. It is paramount to have your staff organized as well and we made it super easy for you. The same is valid for group appointments where you can choose and set the lower and upper limits of people you can take. Recurring appointments is another feature you will probably want to offer to your customers, and yes this is available for you to use. You can set to send a reminder 10-20-40-60 minutes or up to several hours or days and you can send reminders to your staff as well. Our reminder feature is precise within few minutes and this time can be chosen by you. Reduce no-shows by sending your customers reminders about their online scheduling because let’s be honest, sometimes they simply forget. Or if you are a therapist or doctor and need extra info before being able to confirm an appointment, you can make the field appear. You can also add contact fields, eg: if you are a mobile service provider and you need the customer’s address, you can make it appear during the booking process. You can fully customize the booking form appearance with different colors to match your brand, reorder the booking steps, rename the fields and tag them as you wish. Why is this appointment scheduler online suited for all service businesses? You will be able to charge your customers by using PayPal, Stripe, Mollie and Square or they can pay in-store in any currency and send them automatic PDF invoices to their email address. If you don’t feel to let your customer pay in full in advance, you can disable this feature or just ask for a deposit and reduce no-shows. You can set extra services within the booking process, list a good amount of services and take payments before an appointment is fully booked. With our unlimited booking feature, you don’t need to worry about reaching your limits and get stuck feeling forced to upgrade to a paid plan. BookOn provides to businesses from all around the world, an appointment scheduling system to help them organize clients’ bookings logically and efficiently. ![]() 3/27/2023 0 Comments Todoist pomo timer![]() Hey Guys, Love PomoDone! It made my time logging seamless and has changed my work life. I use it every day in conjunction with Trello and I couldn't be without it. PomoDone is easily the best Pomodoro ® Technique app I have ever used. Without it I would live a life like a monkey. The integration with other software product is definitely its strength point.Įasy and straightforward it helps to run my day in a positive way It has become an integral part of my work routine. Pricing: Free Pro: 2. Collaborate seamlessly by assigning tasks to your team members from within the app Sync your Todoist and Slack so that you have access to all the to-dos and messages in one place across devices. When a notification pops up, click Start and begin to focus right away. button at the bottom right corner of a task detail view > select Start. Your app works naturally and I love how it helps me tracking my focus time separately from planning what to do.Įasily one of the best Pomodoro ® apps on Windows and Mac. Use the simple /todoist command to create a task about anything within the app. button on the right side of a task name in the list view > select Start. I also really enjoy the fact that I can use todoist and PomoDone on all my devices OS, iOS, and Windows. Set the timer for 20 or 25 minutes and focus on one task until the alarm goes off. It’s really great being able to effortlessly link my pomodoro sessions with my tasks and also get a measurable sense of how much time I spend doing deep work everyday. Once you complete four pomodoros, take a longer break (15-30 min.) to refresh for your next session.I really love PomoDone App. PomoDoneApp enhances your task management system with timeboxing methodology (including Pomodoro technique and many others) to boost your efficiency. After finishing four focus sessions, the app tells you to take a longer break (between 15-30 minutes). Productivity Countdown timer to apply a timeboxing methodology for your Todoist, Trello, Wunderlist, Asana, Evernote, Slack, Microsoft To-Do and Microsoft Outlook Tasks, Google Calendar etc. Step 2: Pick one of the apps as a trigger, which will kick off. Step 1: Authenticate PomoDoneApp and Todoist. ![]() Let your eyes rest by looking away from the screen, or get up, stretch, and walk around. How PomoDoneApp + Todoist Integrations Work. Integrated Pomodoro Timer help you to work and learn efficiently. After completing each pomodoro, mark it as done and take a short break (3-5 min.). Stay focused until the timer rings, alerting you it’s time for a break. Focus To-Do, a time management application that combines the pomodoro technique and task list. When you start working on a Pomodoro, set a timer (traditionally to 25 min.).With additional features like pomodoro timer and idle detection, it's the ultimate tool to maximize your productivity and streamline time tracking into your workflow without needing to jump. If a task takes more than 30 minutes, break it up into smaller sub-tasks. Toggl Track's free browser extensions embed a Toggl Track timer into the interface of more than 100 apps, allowing you to track time within the app itself. Estimate how long each task would take to complete. ![]()
3/26/2023 0 Comments Minimalist backgrounds![]() Are you wondering how to form a new habit? Trey committing your life to a desired change for just the next 29 days. Does managing and maintaining your home cause you stress? If so, here are 15 easy ways to make caring for your your home less stressful.Ģ9 Days to a Better You | YouTube by Joshua Becker. Recently Released Inspiring Videosġ5 Little Changes You Can Make in Your Home to Help It Serve You Better | YouTube by Joshua Becker. When you embrace simple living, you can be content with what you have. If you care about restoring an old car or creating a setup for model trains, you can still do either of those things as a minimalist.ħ Secrets to Simple Living: The Ultimate Guide for 2023 | Heart’s Content Farmhouse by Katie Shaw. Abstract minimal geometric circle background for business annual report book cover brochure flyer poster Adobe Stock. Minimalism is about removing the things you don’t need or want in order to make time and space for the things you value. Why Minimalism Might Make You Happy Even If You’re Skeptical | No Sidebar by Karen Trefzger. Being a minimalist doesn’t have to mean always going without. An excess of items in your environment can result in increased anxiety, frustration, and the hormone cortisol, which is produced in our bodies when we feel stressed.Ĭan You Treat Yourself While Living Minimally? | The Simplicity Habit by Cora Gold. Why Having A Minimalist Living Style May Be Good For Your Health | Glam by Amanda Vining. Polling in America has demonstrated a marked decline in all spheres of social life, including close friendships, intimate relationships, trust, labor participation and community involvement. Is America Suffering a ‘Social Recession’? | The Guardian by Anton Cebalo. values that reflect unique backgrounds and understandings of any given group. For maximum effect, find a quiet moment this weekend and enjoy them with a fresh cup of coffee or tea. 1491, 1540 (2002), has noted that it is odd that judicial minimalism. To that end, I hope you will find motivation in these articles below.Įach post was intentionally chosen to inspire simplicity in your life. Overcoming the pull of consumerism is a difficult challenge regardless of our stage in life. Beige Minimalist Wallpaper Free PNGs, stickers, photos, aesthetic backgrounds and wallpapers, vector illustrations and art. And it begs us to work diligently with optimism and promise. It invites us to dream dreams of significance for our lives. Never underestimate the importance of removing stuff you don’t need.Įncouragement provides us with motivation to persevere. ![]() 3/26/2023 0 Comments Photo emulsion screen printing![]() ![]() Google Patents US4789621A - Screen emulsions comprised of diacetone acrylamide You can find all of our promotional products available for screen-printing with the emulsion method on the Quality Logo Products website.US4789621A - Screen emulsions comprised of diacetone acrylamide Emulsion is great for tote bags, but it also works for round products such as tumblers or pens. However, the emulsion process is still one of the most effective ways to imprint logos onto promotional products. However, with the advent of digital photography, and those smartphone cameras that continue to improve exponentially with each new generation, the use of photographic emulsion to print pictures isn't as popular anymore. It was called the Kodak system!Įventually with the advancement of developers, you could have your film ready to go in under an hour. Eastman's company would take the camera, develop the film, and return the pictures back to the customer. George Eastman, who made the first camera in 1887, put an emulsion onto a plastic-like material eventually known as 'film' and enclosed it in a camera (which is why you aren't supposed to expose film to light before developing it – remember, silver halide crystals are sensitive to light!). The emulsion process actually played a role in how the camera company Kodak was formed. See emulsion in action with our video here! All that's left after that is to spread ink onto the screen, which is then pressed through the logo and onto the promotional product. This makes it easy to wash away, leaving a negative imprint of your logo. The emulsion gel is still soft in the area that was protected from the UV light. ![]() When the emulsion is exposed to UV light, it hardens, except for where your logo is printed. Acetate is a thin film sheet that is used in a variety of different ways – including in baking!īoth of these methods block UV waves, which is important because after your logo is applied to the screen, it goes under a UV light. This is done either with a super special UV-blocking ink, or with clear acetate. ![]() Prior to the emulsion drying, your logo is printed onto the emulsion-covered mesh screen. The emulsion gel is spread over both sides of a mesh screen that will be used to transfer the logo onto the promotional item. It's a slightly different process when it comes to promotional products. In photographs, the silver halide reacts to the chemicals used in the film developing stage, which produces the image from the film on the photograph paper. The silver halide crystals, which are light-sensitive, rest in the gelatinous material they can be incorporated onto a variety of mediums such as paper, plastic, fabric, or glass during the manufacturing process. It typically contains silver halide crystals, which disperses evenly throughout the gel. In other words, photographic emulsion is more of a gel-like substance rather than a substance that's totally liquid. In fact, it was used back in the day to develop photographs.īasically, photographic emulsion is a colloidal suspension of liquid within another liquid. The actual process is known as photographic emulsion, and it's been around for a long time. To put it simply, emulsion is a substance that's used in screen printing to get a logo on promotional products. Get ready to put your thinking caps on and dive into the world of emulsion! We'll break it down and explain what exactly emulsion involves and how it relates to the promo industry. ![]() Emulsion is an extremely fascinating printing process for branding promotional products. ![]() 3/26/2023 0 Comments Mumble peg![]() ![]() As long as it is “stuck” and no part of the handle is touching the ground, then it is “good.”) If it sticks (rules differ, but typically only the metal part of the knife can be touching the ground. He begins his routine choosing a place to hold the knife, typically against his body somewhere, then “flicks” it from his body to the ground. View the video below to see how this works. ![]() Similar to the basketball game HORSE” a boy chooses where to hold the knife.The boys cut a peg and carve a point on one end. There is a small peg, typically made at the time of the game.So getting a set of rules to pass on is not as simple as you might think! But here are the basics: Some group of boys would develop elaborate rules including the exact sequence of throws. Just like other boy games, the rules have evolved over the years. Want to watch the game in action? This 3 minute video will show how it is played: The name of the game comes from a forfeit required in the early days of the game: a small peg was driven into the ground by a prescribed number of knife blows, and the loser had to pull the peg out (“mumble the peg”) with his teeth. Although positions vary, the most common ones are (1) flipping from the palm, (2) flipping from the back of the hand, (3) flipping by a twist of the fist, (4) throwing by holding the blade tip between the thumb and forefinger, (5) flipping from between the teeth, (6) throwing from each shoulder or behind each ear, (7) tossing backward over the head, and (8) throwing around the head from the back.Įach player performs in turn until he misses, resuming after other players miss unless one wins by performing all positions. The object of the game is for each player to flip or toss the knife in a progression of moves such that, after each one, the knife sticks in the ground and stands erect. The game was played as early as the 17th century in the British Isles. Mumblety-peg , also spelled mumbledy-peg, or mumbly-peg, original name mumble the peg, game of skill played with a knife, usually a jackknife. Here is the description from Encyclopedia Britannica: Instead, I am talking about the game from the 17th century. And I certainly don’t mean the new game where a boy stabs the knife between his fingers, faster and faster until he stabs himself or chickens out or can’t go any faster. And I don’t mean the modern version which requires throwing a knife as close to his foot as possible, then stretching out his foot to touch the knife until one of the two contestants can’t stand anymore. The game Mumblety-peg has nearly been lost. ![]() For boys who have learned to be responsible there is nothing like a nice pen knife to spend hours fiddling, making small lashed items and playing Mumblety-peg. Moms, you want your son off video screens – right? One way is to give him something he can do with his hands. Boys playing ‘Mumble-the-Peg’ Peekskill NJ 192u Source of Photograph: Library of Congress. ![]() 3/26/2023 0 Comments Typewriter keyboard for pc![]() ![]() It has gained around 50000 installs so far, with an average rating of 4.0 out of 5 in the play store. Typewriter Keyboard is an Android Personalization app developed by B-P Theme Design Studio and published on the Google play store. Handwriting and slide (Swype input) input method will soon be available. Your phone is Samsung, Sony, Huawei, HTC, Millet, Microsoft or any other brand. The typewriter theme is designed to provide you with faster, smoother mobile operation experience. Thank you for choosing this cool typewriter 3D theme. Thank you!ĭownload and apply typewriter themes for free and stylized your Android phone. ★ If you like our application, please do not forget to write a review. The typewriter keyboard is a very cool visual effect. Want to enter the typewriter world? Quickly download typewriter theme input method! ✪ Custom fonts ✎: More font styles will be available soon on typewriter themes ✪ Animation Theme ✈: Let your cell phone have a unique variety of cool animations ✪ Supported languages: Typewriter keyboard themes support more than 80 languages The typewriter keyboard does not charge any personal or personal information, identity information and bank card information. You may receive an alert privacy (for example, the typewriter keyboard may collect your personal information), which is a security warning for all Android operating system standards when making third-party applications. There are more support topics waiting for you to explore the load. ✪ button to press the sound ♪: Personalized keyboard keypad tone with different themes. You can find all the topics you like in the theme center and enjoy the greatest typing experience!Ĭompatibility ✍: Applies to all applications, including many popular applications such as Facebook Messenger, microblogging, WhatsApp, microseconds, Google conversations, and more. ✪ Theme Center: Find all kinds of cute, colorful keyboard themes from different categories, including high tech, basic, cool, crystal, golden yellow, pink and so on. Send and easily share all kinds of expressions, emoticons, cute and smart emoticons!Īutomatic expression predictions allow you to search for keyboard and emoticons by simply typing simple words. ✪SmartEmoji ☺: 800+ pre-installed emoticons! In the expression symbol, all support for all Android devices and other mobile operating systems. Click the install button for free download! If you have already installed the main keyboard, click the Apply button and the typewriter theme will automatically install on your phone. Note: The typewriter theme is a plugin application, please download the main keyboard application to run the typewriter theme. How do I apply the typewriter keyboard theme? People who like this theme are welcome to use. ![]() The typewriters have been integrated into the lives of modern people. The great invention of the last century has been extended now. The typewriter is the product of civilization. The typewriter keyboard theme offers wonderful typing experience and personalized typewriter enjoyment. ![]() 3/26/2023 0 Comments Medium length hair![]() ![]() Allow this list to show you exactly how cool curly hair can be. But whether your hair is tightly coiled or more of a wave, there are a variety of cuts and styles that can bring out the natural texture and allow you to embrace your curls with confidence and panache. A good moisturizing conditioner and hair cream is all you need to define and enhance your curls while reducing frizz.Ĭurly hair is the signature style of so many guys in Hollywood, from Matthew McConaughey's relaxed waves to Bruno Mars' pompadour curls. Layering can be a tool to make fine, thin hair look thicker and have more volume. They’re especially great for fine hair, according to Mia Morris, a senior hairstylist from Fort Lauderdale, FL. One can only appreciate the beauty of their curls once they accept and embrace their natural hair texture instead of trying to control it. Medium-length layered haircuts are the best way to create movement, dimension, and versatility with your hair. ![]() When a guy grows out his curls, it suddenly transforms their look and becomes the thing they're known for. Guys with curly hair might be tempted to tame their curls by cutting their hair short in order to make it easier to style, but we're here to convince you otherwise. This means you can wash your hair less and spend less time getting ready in the morning. Unlike straight hair, which requires a handful of products and potentially professional intervention to style it in a way that doesn't fall limp after a few hours, curly hair also holds a style very well. Yes, it can be difficult to manage and knots easily, but it also has natural volume, movement and texture, making this hair type perfect for styling. It results in a smooth gradation between long and short where the back and sides blend into the hair on top. Layers, however, may be a better alternative, as they can get the most of your locks naturally.Curly hair has its kinks (pun intended), but it's one of the better hair textures to have simply because it's so versatile. The taper is a barbering technique most commonly used in medium-length hairstyles whereby two different lengths of hair are blended together using either clippers, scissors, or a combination of the two. In general, for thicker-looking hair, you should use products designed for thickening the hair texture or go for salon treatments. Q: Do layers make your hair look thicker?Ī: Layers can make your hair look fuller rather than thicker by providing movement and volume to the texture. As a result, your waves will look even more alive. You can also enhance the effect of wavy layers with a touch of highlights. And if you have thick locks, they will look best with bigger waves. For fine hair, little thin waves will be the best choice. Just look at these pics! As you can see, 2022 layers look ravishing when they're wavy! Waves can be different, and your task is to style them so that they fit your hair type. On top of that, these haircuts work great for all hair textures. In fact, by experimenting with the ways of trimming the ends and the number of layers, you can explore a surprisingly big number of stunning looks. Mid-length is also called shoulder-length hair, so if the ends of locks are longer than the chin line and cover the neck fully, they’re medium length. In case you don’t have a measurement tape at hand, you can define your length visually. Q: What is considered medium-length hair?Ī: Medium-length hair is the middle ground between long and short hair, and it’s basically 12 inches long. ![]() Simply spritz your locks with some sea salt spray to get the look! At the same time, choppy ends are what allow for everyone's favorite beach waves. It will lighten up the weight of your tips, thus making your hair more manageable. For the best results, we recommend you getting choppy ends. The best thing is, that a round brush is all you need for styling. A rounder silhouette is indeed the best choice for straight styles. Once you add a touch of layers, it will get a little bit twisty at the edges which will make it even more attractive. Perfectly straight hair always looks neat and tidy, especially when it voluminous and balanced enough. And that is why shoulder-length layered haircuts are so popular in 2023 – they are universal. So, besides being beautiful, we want our hairstyles to be practical, as well. All, in all we all wish to look well-groomed and elegant, no matter how old we are. ![]() Medium length layered hair is always a great choice, as it is flattering for any woman. Super Volume at The Crown for Medium Layered Curls.Wavy Shag Medium Haircut with Thick Bangs.Shoulder Hair with Short Layers and Fringe.Whom Do Layered Medium Haircuts Flatter?. ![]() 3/26/2023 0 Comments Simple math puzzle![]() ![]() It does so in some cases when there are more than four digits. As we shall see below, it could have ended in a repeating cycle where it bounced between two or three different numbers or even more. But even if 6174 were the only nontrivial solution to such subtractions, that does not mean that our procedure has to end in it. Not only that, we would also have to show that other four-digit numbers with two or three repeated digits do not have any solutions. So we would have to try 23 other cryptarithms such as SETA − ATES = TEAS or SEAT, etc., to show that they have no solution. For starters, there are 24 ways that four different digits can be ordered, all of which would yield the same Kaprekar subtraction. We have shown that at least one four-digit number maps to itself using the Kaprekar procedure, but there could conceivably have been others. This only partially answers our previous question about why this occurs. You can actually solve the cryptarithm using conventional methods ( Douglas Felix detailed one way of solving it) and confirm that 6174 is the only solution. Knowing that the only other four-digit string that yields itself is 0000, which is ruled out in this case, we expect there to be a single solution, 6174. The order of the digits matches that of the number 6174, so we expect 6174 to be a solution. The number EAST will generate the subtraction SETA − ATES to yield EAST again. ![]() Observe that the above subtraction problem exactly reflects the procedure that we have been carrying out above. How many solutions do you expect it to have? Here is a cryptarithm (digit substitution) puzzle that may help (incidentally, all these words are acceptable in Scrabble). The maximum number of steps to reach 6174 is seven, which is required by several numbers (1040 is an example).ĭ. ![]() The other 9,990 numbers all result in 6174. As for exceptions, the only four-digit strings that do not end in 6174 with the Kaprekar procedure are the ones with identical digits: 0000, 1111, 2222, etc., for which the procedure ends with 0. Let’s save the first question for the end of this section. ![]() Explore further: Why does this occur? Can you find exceptions? Can you find numbers that require more steps than any of our examples? Keep generating numbers until something interesting happens: 6174 repeats forever.ī. Follow the same procedure to generate sequences starting with the following numbers. The next number in the series is obtained by subtracting the second number in parenthesis from the first. Find the next three numbers in the sequence: 5634 (6543, 3456), 3087 (8730, 0378), 8352 …įor each number in the series, the first number in the parentheses is obtained by arranging the digits in descending order, and the second by arranging them in ascending order. Let’s first learn more about Kaprekar’s constant in this four-minute video:Ī. Since you’ve already done the work of trying to discover these constants, let’s sit back and experience their magic. The first is an interesting curiosity in recreational number theory, while the second is a universal constant central to many chaotic phenomena in the real world. The second, ∂ = 4.6692016…, was discovered in 1975 by the mathematical physicist Mitchell Feigenbaum with the aid of an HP-65 programmable calculator.īoth of these constants remain somewhat mysterious. Kaprekar through pen-and-paper arithmetic explorations. The first constant, 6174, was discovered in 1946 by the Indian mathematician D.R. Readers found that the procedures ended in a repeating cycle - either in a single number (a “cycle” of one) or in a cycle of two or more numbers. In the April Insights puzzle, I tried to guide readers down a path that might be best described as “experimental mathematics.” The goal was to rediscover two constants by iterating simple arithmetic procedures. ![]() |
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