| How to Solve Hard Sudoku Puzzles Posted: 10 Nov 2021 04:00 PM PST Sudokus are phenomenal brain teasers, but if you find yourself solving easier puzzles in a jiffy, you may have moved on to harder puzzles only to discover that they feel impossible! The neat thing about sudoku is that there's always another thing to try if you get stuck, and if you work carefully, you should be able to solve the puzzle through deductive thinking and logic alone. If you're looking for some extra help on your next puzzle or you've come here out of a looming sense of despair that your most recent guess has ruined your current game, we've got your back! [Edit]Use a pencil. - This may seem obvious to you, but some folks don't do this! It's possible for adept players to solve easier sudokus with pen, but for harder puzzles it's going to help a lot if you use pencil. Harder puzzles require a lot of testing and note-taking, and being able to erase your marks will make it easier to visually process what you're doing.[1]
- You can also write in the margins outside of the cells (the individual boxes of 9 squares inside of larger puzzle). Feel free to take notes or jot down reminders to yourself.
- Using pencil also allows you to draw on the puzzle. If you use any patterns or uniqueness tests, you may want to visually track what you're doing by circling or drawing around given cells.
[Edit]Note potential candidates in open squares. - Taking notes is mandatory if you're solving complex puzzles. Write potential candidates down lightly in open boxes. Most people use the corners, but you can use whatever method makes the most sense to you. This will help you narrow down choices, identify patterns, and avoid deadly patterns. If you're a veteran, you probably already do this, but on the off-chance you don't, it's an essential way to play.[2]
- Candidates refer to the potential solutions for a given square. If you know that square has to be a 6, 4, or 8, then 6, 4, and 8 are all candidates.
- It may feel like you're making things harder by writing down every candidate, but the more information you have, the easier it will be to identify patterns and rule out incorrect answers.
- Some sudoku enthusiasts will "rank" their potential solutions by putting numbers they're fairly confident in at the top corners, and numbers they're less confident in at the bottom.
[Edit]Scan the board to process the puzzle. - Take a minute to look over the board and take it all in. You're probably not on a timer here, so don't rush anything. Scan each cell to mentally map out and internalize the given numbers. This will get you comfortable with this specific puzzle, and keep you from making an early move that accidentally throws off the entire course of the puzzle.[3]
- There are two popular scanning techniques: one direction and two directions. Scanning in one direction involves viewing the cells from left-to-right and up-to down. Scanning in two directions involves looking at perpendicular rows and columns together to process early combinations.
- If anything stands out to you as exceptionally obvious once you're done scanning the given numbers, go ahead and fill in the squares you're 100% confident in.
[Edit]Start with the obvious singles. - Naked and hidden singles are the easiest squares to solve. A naked single is when a number can only go in one possible cell. A hidden single is when there is only cell for a given candidate. These singles are easy to identify, so spend a few minutes scanning each row, column, and cell for any squares with only one possible solution.[4]
- Cells refer to the collection of 9 squares that are inside of each sudoku puzzle.
- For example, if there's a 6 in the middle square of the center cell and a 6 in the righthand column of the top-center cell, but there is only one available square in the left-hand column of the bottom-center cell, then a 6 has to go there!
[Edit]Revisit your candidates after you solve singles. - After you fill a square in, use the rule of one to find additional singles. Whenever you solve a square, double-check the other candidates in the number's row, column, and cell. Erase any notes you made that would violate the rule of one (there can only be one instance of a number in every row, column, and cell). This may give you even more hidden and naked singles.[5]
- Keep doing this over and over again until you've exhausted all of the potential singles on the board.
[Edit]Identify naked or hidden pairs. - After hidden and naked singles, pairs are the most helpful. If you have two squares inside of a cell that could only be one of two numbers, you have a naked pair. This may seem unsolvable right now (since there's no way to know which square takes which candidate), but they're helpful for the cell you're in. Use the pair to deduce which potential candidates exist for the other squares in that cell. By eliminating the pair, you may end up with a hidden single![6]
- For example, let's say you've got two 3s written down in the top two rows of squares in the top right cell. This is a naked pair. On the top left cell, a 3 may be able to go in any square right now. Since your pair rules out the bottom row in the top left, you can cross those candidates out. If this reveals a single, you've got a new square to fill in![7]
[Edit]Move on to triples and quads. - Exhausting pairs and singles should reveal naked triples and quads. Whenever you reveal 3 potential candidates across 2 or more squares in a given row, column, or cell, you've got a triple. You can use triples to reveal hidden singles the same way you used naked and hidden pairs. Once you've exhausted all of your pairs, take a look at the triples and quads you spot. At this point, with a large number of candidates crossed off of potential squares, you may be able to fill in additional squares.[8]
- Quads are much rarer, and they're less helpful in a way since they don't let you narrow down a large number of candidates all at once, but if you spot one, it's worth investigating. Solving single squares can also turn quads into triples or pairs, so don't forget about these!
[Edit]Identify patterns in the remaining numbers. - There are a handful of patterns most players look for at this point. Patterns refer to configurations of solved squares that help players regularly solve a sequence of candidates. There are a bunch of different patterns out there, but if you can spot one, they'll typically help you solve some element of the puzzle that you're struggling with.[9] A few common patterns include:
- Corners (a collection of 4 solved squares in any of the 4 corners). Corner patterns help eliminate a ton of potential candidates in the rows and columns connected to it. Revisit these regularly to make sure you don't provide a false solution.[10]
- Skyscrapers (two rows or columns of a given candidate that are unequal in length). This pattern can help you isolate rows and columns to solve entire rows or columns of the puzzle.[11]
- Right angles (any 3 given numbers in an L-shape inside of a cell). Right angles give you a lot of information regarding the empty columns and rows in the cell they're in, which can help you cancel out incorrect candidates in the adjacent cells.[12]
[Edit]Scan for x-wings to eliminate false candidates. - The x-wing technique can be used to remove a ton of potential answers. If you identify a set of 4 identical candidates that form a rectangle across multiple cells, you can use the x-wing technique. Since 2 identical numbers cannot be placed in the same row or column, you know that one "wing" has to be correct, and the other cannot be. Once you identify the x-wing, scan the cells, columns, and rows of the two wings and eliminate any candidates that would invalidate one of your wings.[13]
- Remember, this only works if the candidates are located in different cells. You cannot use an x-wing if one of the wing pairs are in the same cell.
- This is easiest to visualize when the candidates are really close together, but the rectangular pattern required to use this technique could theoretically involve the 4 outermost corners of the puzzle.
[Edit]Identify swordfish patterns to solve tough parallels. - This is a variation of the x-wing that can get you out of tough locks. A swordfish occurs when 3 rows or columns contain 2 (or 3) cells that hold matching and locked candidates. If the candidates repeat, they cannot overlap and there must be one combination where the rule of one is not violated.[14]
- Finding swordfishes can be kind of challenging since it requires a closed chain of 6 candidates with a redundant candidate in each row and column.[15]
[Edit]Use uniqueness tests to avoid deadly patterns. - These tests help you avoid impossible candidate compositions. Deadly patterns refer to potential points in a puzzle where more than one solution can be equally viable based on the remaining candidates. These patterns stop a puzzle in their tracks, but uniqueness tests can help you avoid these gaps. At junctures where you risk a potential deadly pattern, use uniqueness tests to rule out false solutions.[16] Variations include:
- If only one square in a given cell contains multiple candidates, you can eliminate the other candidates from that cell. This is the simplest version of a uniqueness test.
- If you have two triples in a cell, but one of the candidates appears a third time in a different square in that cell, you can eliminate it from the triples to reveal a naked pair.
- If you have two cells in a rectangle with one extra candidate, you can eliminate that candidate from any rows or columns in the adjacent cells.
[Edit]Skip a square or cell if you get stuck. - If you're caught up on a square or cell, take a break from that area. If a sudoku is valid and solvable, it will (usually) require zero guesswork. There should always be an area somewhere on the board where you can methodically deduce an answer. If you find yourself totally stuck on a row, column, or set of candidates, take a break and look elsewhere. You may solve some other area of the puzzle and find the answer you were digging for suddenly revealed.[17]
- It can also just help to return to an area with a fresh eye. If you get stuck, you're going to get frustrated. Taking a break and moving on will allow you to return with a new attitude that may help you find a solution.
[Edit]Double-check solved sections with the 45 rule. - If you solve a row, column, or cell, use the 45 rule to confirm the solution. If you solve a part of the puzzle but you simply can't find an answer to another part of the puzzle and it seems impossible, check your work. Any solved row, column, or cell should add up to 45. If you made a mistake and doubled-up your answers somewhere, it will keep you from solving other portions of the puzzle, so check your work![18]
- If you did make a mistake somewhere, it can create a snowball effect where you suddenly have incorrect answers everywhere. If it's a super difficult sudoku, calculate each row, column, or cell as soon as you solve it to make sure you haven't made an obvious mistake.
[Edit]References |
| How to Access Blocked Sites Without a Vpn Posted: 10 Nov 2021 08:00 AM PST This wikiHow will teach you how to access blocked sites without a VPN. You can use short links, like TinyURL or Bitly, to see these sites. Alternatively, you can use a restricted website's IP address instead of their URL. Finally, you can use a proxy website, like ProxFree; however, some proxy sites may be blocked by your network, so you may have to use another one. [Edit]Using Short Links - Go to a link shortening site like Bitly. You can use any web browser to get shortened links and use them to visit blocked sites.
- Paste your URL into the shortening service. Once you enter the URL for the blocked site, you'll get a shortened URL.
- Copy the shortened URL and paste it into your address bar. Once the URL is shortened, you should be able to access the blocked site.
- If that method doesn't work, try using the website's IP address.
[Edit]Using an IP Address - Open Command Prompt or PowerShell. Press Win + X and open the command line prompt.
- Enter the following command: . That line of code will give you the URL for the blocked website you need to enter next.
- Enter the blocked website's address and press . It'll look like this: and then you press Enter.
- Copy the IP address listed. After you press Enter, you should get a return that shows the IP address, which looks like 55.155.135.27.
- Paste the copied address into your web browser's address bar. Using the blocked website's URL should let you see the site differently than using the web address with letters.
- Since most secure websites use HTTPS, you might get a warning that your connection is not secure.
[Edit]Using a Proxy Site - Open the ProxFree site. Go to https://www.proxfree.com/ in your browser. A proxy acts like a middle man that may unblock sites for you.
- There are many websites that offer free proxy services like ProxFree; if this certain site is blocked by your network, you can use another one, like Whoer, which works similarly to ProxFree.
- Click the search bar. It's near the bottom of the page, to the right of the padlock icon.
- Enter your website's address. Type in the address of the website that you want to access.
- You can select a different country to use by clicking the "Server Location" drop-down box and then clicking a different country's name.
- Click . It's a blue button to the right of the search bar. Doing so will search for your website.
- If you selected a country significantly outside of your own for your IP address' location, the search results may take several seconds to a minute to display.
- Browse your site. Once the website loads, you should be able to use it like usual. Keep in mind, however, that your website's load times will likely be significantly slower than usual.
- You can also try using a translator service, like Google Translator or Microsoft Translator. Just go to one of them, input the blocked site, and it'll translate the site for you in any language you'd like.
[Edit]Quick Summary [Edit]Related wikiHows |
| How to Treat Someone Who Betrayed You Posted: 10 Nov 2021 12:00 AM PST When someone betrays you it can feel shocking or even sickening. After all, you thought you knew the person and they destroyed your trust. You probably have no idea how to proceed or whether or not to rebuild your relationship. While there are no easy solutions, we've got suggestions for how to move on and interact with the person in the future. [Edit]Take time to sort through your feelings. - You may feel a lot of conflicting emotions. Instead of immediately reacting and confronting the person, you may feel better if you get some personal space. Write down your feelings or call a trusted friend and talk with them about what happened. Working through your own emotions is a good guide for how you'll interact with the person who betrayed you.
- For instance, if a close family member went back on their word about an agreement you had, you might feel intensely angry. Give yourself time to calm down and come up with a plan for approaching them about your arrangement.[1]
[Edit]Listen to what the person has to say. - Give them the opportunity to explain themselves. This is really important if you want to mend the relationship and move on. Maybe the betrayal was actually a miscommunication and you can clear things up, or perhaps listening to their explanation can help you decide whether or not you want to repair the relationship.[2]
- For instance, if you're feeling hurt because you feel like a friend has disappeared—not taking your calls, ignoring your texts, etc—and you learn they're dealing with depression, you'll realize they weren't betraying your friendship.
- You may listen to a co-worker explain why they talked about you behind your back and realize that the person feels totally justified and doesn't realize what they did was wrong. You may decide to be more cautious around them in the future.
[Edit]Put yourself in their shoes. - Imagine the situation from the other person's perspective. You're not trying to excuse what they did but to understand it so you can move on. For instance, if your partner cheated on you, you'll obviously be upset and hurt. Upon reflection, you might realize that they did it because you were emotionally unavailable. Seeing this from their perspective helps you understand the betrayal.[3]
- Viewing the betrayal from their perspective can remind you that they're human. You may feel more forgiving toward them or, at the very least, understand why they did what they did.
[Edit]Express your concern so they know you feel hurt. - Share how you feel, especially if they don't think they've betrayed you. This can be tough to do—you probably feel vulnerable—but it's important. Tell them exactly how their actions made you feel. Talking about it can make you feel better and it lets the person know that what they did was harmful.[4]
- If you and your partner are dealing with the issue of betrayal, you might find that you talk about it all the time. Instead of letting it sneak into every conversation, plan a specific time to discuss it.
[Edit]Try to keep your cool. - Focus on staying calm so you communicate effectively. If you're trying to rebuild a relationship with a partner, friend, or colleague, lashing out will make it much harder. They may start to resent you or feel like you no longer want to be friends.[5]
- It's really easy to lash out in anger, but remind yourself that it won't necessarily make you feel better or repair the relationship.
[Edit]Express what you want going forward. - Tell them what you'd like them to do so you can both move on. It's completely natural to want an apology if they betrayed you, but you might need to make this clear to them. Maybe you'd rather that they just see your perspective and realize they've hurt you. You may also explain that you won't tolerate betrayal in the future.[6]
- Being really clear with what you want also lets the other person make a choice. They can either respect your wishes and boundaries or disagree and possibly end the relationship.
[Edit]Forgive the person if you want to rebuild the relationship. - You can tell the person or just acknowledge it to yourself. Forgiveness is really something you do yourself. It means you've come to terms with what happened and how you feel and you're ready to move forward. This means letting go of your hurt feelings. Give the person opportunities to prove that you can trust them again.[7]
- You might say to the person, "You know, it really hurt when you told my friends those secrets. I'm still really unhappy that you did that, but I want to stay friends if I know I can trust you."
[Edit]Build trust if you want to reconnect with the person. - Give them a chance to prove that you can stay friends or partners. Rebuilding trust doesn't happen overnight—it's more of a mindset that you cultivate. Continue to be open and honest with the person about your feelings. Sure, you both won't always be comfortable around each other, but let them know you're making the effort.[8]
- It's okay to tell the person that you're still struggling with trusting them, especially if it's a partner who betrayed you. Acknowledge these challenging feelings so they can try to support you.
[Edit]Try to make new positive experiences. - Betrayal hurts because someone you care about hurt you. If you're trying to move on with your relationship, set aside your painful feelings and work on making positive ones. You don't have to pretend as though nothing bad happened, but you should make a conscious effort to enjoy yourself around them.[9]
- If you're rebuilding trust with a partner, do something fun together. Go out for drinks, challenge each other at the arcade, paint pottery together—anything that gives you a mental break and a pleasant experience.
[Edit]Break off contact if you don't want a relationship. - Let the relationship go if you can't trust them at all. This isn't a decision to make lightly, but if you realize that the person doesn't care about your feelings or the fact that they hurt you, it may be time to develop other relationships.[10]
- You don't have to have a dramatic confrontation with them. You can be polite and still keep them at arms' length. This might be the best option for interacting with a co-worker who's betrayed you.
[Edit]Work with a therapist to address trauma. - A licensed counselor can help you move past debilitating trust issues. Unfortunately, betrayal can cause deep psychological trauma that can actually cause physical problems like headaches, nausea, insomnia, or muscle tension. If you feel like the betrayal and your interactions with the person are making it hard to function, don't hesitate to reach out for professional mental health services.[11]
- Your therapist may use cognitive behavioral therapy. This type of talk therapy helps you challenge your negative thinking to see things in a more positive light. This can help if you struggle to interact with the person who betrayed you.
[Edit]References |
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