Unforgivable

It started around a similar time last year, when I first posted about people having the freedom of choice (It's My Life). It was parents respecting the passions and wishes of their sons and daughters. It was the sons and daughters following their heart and doing whatever they desired, so long as they became aware of the attached consequences. None of this has changed. But there is one significant thing about choices that I feel the need to address with greater focus. That being the type of choices or to be more specific, the wrong ones. It doesn't matter whether they are big or small, because bad decisions are exactly what they are; bad decisions. And given the harm many of them can do, I see the need to share my stance. There's a reason for punishment, and I will always support it whenever it makes sense. Intentionally make a wrong move, then expect to pay a hefty price. There are even some things I do not believe one can ever come back from.

What classifies as a bad choice? Well there is one straightforward answer. A bad choice is any taken option by one that has negative impact on both themselves and other people. They come in a few different forms including risks, passions and inclinations. But all lead to one or more undesirable results. These results can be anything from financial struggles to life-threatening situations. Hence why punishment exists. We all know how the saying goes. It's better to be safe than sorry. They are unpleasant and nobody wishes to be on the end of them, but punishment is every bit necessary. It is a type of guidance. It teaches everybody to avoid mistakes and learn from those already made. It helps with further distinguishing the right from the wrong. And it encourages the rise of remorse. All have copped this harsh treatment at least once in their life. Punishment hurts very much, but it is there wanting for our best selves to always show.

I myself, have made many horrible decisions and have taken countless missteps throughout my childhood and teenage years. I was selfish. I picked on people. I made a mockery of things I shouldn't have. Plenty of my actions were performed without much thought put into them. Most times I was rightfully told off. The mistakes were pointed out. I took in whatever consequence that came my way (no matter how much I did not enjoy them). Looking back on my overall behaviour, I now often find myself full of shame. I can't execrate the kid I was any more than I do at the moment. I know not to take it back, as it has all built me up to be the better man I am today. However, these indelible memories keep returning to remind me of how foolish I used to be. Sure there are people who have done worse and do not regret anything. I'm just the sort to take a lot of things to heart. If you want to know a little more about this side of me, click the following link: The Room For Improvement.

Back to the topic of choices, some bad decisions are not what they are until harm is seen. Meaning that many behaviours we naturally consider to be inappropriate, are not always that. The most common of them being the acts of keeping secrets and telling lies. There's no denying how wrong they look on the outside. Not to mention the latter further brings down the ability to trust our surroundings (read The Truth About Trust for more on this). But taking these routes at times can often be based on good reason. Hiding or fabricating the truth is a popular action made by good people. While much thought is disregarded, the intentions can be perfectly clear. Such risks as these are able to hint a sign of care. People can now and then sense the truth will doing more harm than good to others. They'll tend to the idea that secrecy is key and that what one doesn't know, won't hurt them. It is though, a misjudgement. One that can bottle up emotion and bring forward pressure. When the lid pops off in any way, the consequences are likely to be tougher to deal with. Liars and secret-keepers are still in general the least worrisome, as punishment isn't as significant for them (and reason more often than not determines the size of such).

Here is where I dig deeper into the topic. To a more specified argument and another step closer to the 'unforgivable'. It's a greater look into another set of wrongdoers, much bigger ones in fact. It should be no surprise to anyone who I consider these bigger offenders to be. A group which make certain bad choices while knowing full well of the already-existing laws telling them not to. We hear about them every day. They go by the common terms 'criminals' or 'law-breaking citizens'. We all know what they do. Speeding, drug-smuggling, vandalism, driving whilst under the influence of alcohol, driving whilst using a phone, running red lights and so on. It baffles me how these people just don't care. It's as if they are rolling in dough and/or simply don't give a toss. It's like they want to be punished or think that they can get away from it. Like they are above the law. They just don't consider the danger they put themselves in. More importantly, they don't consider the danger they put others in. They're completely apathetic. These people are like every other hazard in our lives. What's worse is that they don't bother to see it and some of them believe it or not, like it this way. Despite the normality of criminality, I still find it crazy to think such immoral behaviour coexists with us.

Finally, it comes to the highest point. The point of no return. What's best described by the title of this piece. It's when others do end up getting hurt by these hazardous malefactors. The innocent lives of everyday people, unjustly caught in the danger zone. The harmless and valuable souls that become nothing but collateral damage. Whether it be severe injuries or a lives lost, it remains a permanent mark. Things won't ever return to how they once were. Survivors are left traumatised. Families and friends are left with broken hearts, as the righteous and good-hearted are left cleaning up evil's mess. There are even greater victims, who are targets of danger and indefensible crime. Many women for example have over the years been sexually assaulted and then brutally killed by heartless, warped men. On the other side of the world from me, young children are metres away from school shootings with some not making it through. It's sad, it's sickening and it's hard to stomach. Many of us just couldn't imagine the pain these sufferers go through.

No criminal behaviour is tolerated, and rightly so. But there are certain crimes I feel aren't dealt with hard enough. The most serious one being murder. People treat it as just another offense, but don't truly understand what it is and what it creates. It's the loss of a life at the hands of another. I find it to be the cruelest thing one can do. Taking a life is taking everything away. It's permanent damage that spreads sorrow and depression onto loved ones and close acquaintances. Sending a victim into the unknown and leaving others to never see their face again. Ripping away the opportunity for new experiences and new memories that come with them. A severe crime such as this deserves severe punishment (perhaps a lighter one for the regretful and emotional). Most murderers are practically (and deservedly) lost causes. Once they have a taste of the action, there is no turning back. Especially those responsible for ending multiple lives.

Life is a gift. A chance to experience both beauty and wonder A chance to enjoy and to examine. We humans along with numerous other creatures, are filled with curiosity and eagerness. We want to see how things play out wherever we go. We want to go beyond limits and explore the world we live in. And we humans in particular want to fill our lives with happiness and live them to the fullest. The best of us even attempt to share such joy, curing the ill and unfortunate all while bringing a smile to their faces. Life is a complete package of everything given to us. But the most important thing about the ultimate gift, is that it's a chance for all to return the favour to the higher powers. To leave these powers knowing they've created and blessed the right souls. Of course life doesn't come without its dangers, with the biggest one coming in the form of itself. An inner battle between the children of Earth, sort of an everlasting friction. Humanity has shown itself to be its own worst enemy.

We see it on the news. The heartbreak and tears. The anger towards the criminals. The frustration and displeasure towards the occasionally unfair verdicts. It's a wide range of negative emotions all tied up into one large ball. Crime proves to be a major catalyst in depression. It sparks chain reactions, and leaves some people never feeling as good as they once were. But we can be thankful that the support is always offered to those affected. The masses even get involved with their moral say. They're hostile with the wicked and wholeheartedly agree on the need for proper justice. The most important action of them all however, is the condolences and sharing of sentiments. The key word is 'empathy'. To remind those hurting that they are not alone and that the world is on their side. It's about making sure the suffering, fight through the pain and see the light. It's proof that the virtuous are what they are. Deserving of all the love and respect that can be given. Total opposites to the sin-committers, who most agree deserve the worst. 

I firmly believe that criminals with intent are beyond redemption. Anything from arsonists and murderers to hackers and stalkers. Their recklessness and willingness to inflict angst, pain and death on anybody around them, makes them worthy of abhorrence. These cold, selfish and inhumane monsters never stop to think about what they do. It's all a matter of personal gain, feeding addictions and believing they will always get away with the trouble they cause. And the sad thing is, criminals do succeed more often than not. With law enforcement constantly chasing tails and good-quality security hard to come by, guiltless members of society are forever feeling unsettled. Day or night, there is no telling what happens when one sets foot out the door. People are not even safe in their own homes. So there is no blaming anyone who calls for greater action and true justice to be served. There's still a lot of work to be done, but the direction remains promising. Intentional bad choice makers are rightly punished and repeat offenders are never forgiven.

We all will make multiple bad decisions throughout the rest of our lives. We'll face the awful consequences for some. We'll learn from some and avoid making them again. We'll even regret a few. But there'll always be saving for the lesser offenders. Can't say the same for those with criminal records or those with no hesitation whatsoever in destroying lives for the sake of their own sick and twisted ways. The fiends and sadists of the world. They own no mind and they own no heart. Everything is fun and games. Possessions hold more value to them than the living and breathing. If they don't get their way, they'll destroy for it. Even if it happens to be the greatest gift of all. It's almost unreal, but we are left to accept that we share planet Earth with them. We are left to hope that us as the light shines forever brighter. We know we are already superior, but for some of us it's still not enough. We want to ensure the unforgivable remain unforgivable and they take what they've given.

Travis "TJ" James

The Truth About Trust

There exists connections between us all. Connections that are yet another vital ingredient in the recipe that is life, impossible for us to live without. No one can even imagine the thought of living without them, as they have long been unavoidable and continue to forever expand like our universe. Such connections come about naturally and often without notice, to aid us on our journeys as we grow. They provide the sources of inspiration and motivation that further propel us to seek the ultimate happiness we so desire. They guide us whenever uncertainty raises its head, and they facilitate each and every challenge we face to some degree. Being our four walls and the many supplies within, we always feel safer when these connections are in play. And the strongest or most cared for of connections, guarantee us a better understanding of life as well as the choices we make. What links us together is precious and ensures good times and smiles are many.

What exactly are these connections I speak about here? Primarily they are the cogs to the machine of human interaction and communication. It's not clear as to how many there are, but at least two stand out the most. The first of them being one we are all very familiar with: 'Love'. Both a word and practice which speaks for our hearts. It is everything from appreciation, friendship and respect, to adoration, lust and intimacy. Regardless of whether it's conditional or unconditional, love is all we live for and all which makes us happy. It is a form of escapism, providing the endless ease and comfort we forever crave. We are always happy to show it and happier whenever we get to share it with others. Because of these pleasurable qualities, love is often likened to a drug. It isn't wrong to see it this way, as people can let it get to their head and allow for it to make them do crazy things. But so long as it's used well, it never becomes a problem. And if a drug, love would be the absolute best of them. Natural, safe and forever filled with benefits.

The other notable wire which connects us to one another, is one I feel the need to go into more detail about here. This wire represents 'Trust', and it is something that forever requires more thought. When love and its beauty lifts us off the ground, trust always makes sure we come back down. It's an occasional reminder of reality along with the importance of building true, solid relationships. Moments we often experience without much focus, are those when we test the characters of people around us. We leave them with the added responsibility of being there whenever we require assistance. We ask for favours and we share confidential information. Our dependence on others may now and then leave us feeling a little unsettled, as we give away some control over our lives. It is a normal occurrence in us, as we have the natural tendency to believe we can be trusted whilst doubting to a certain extent whether others can be trusted. For every time we feel uneasy with our reliance on another person, we're to always know that it's a question of trust.

Both love and trust are fundamental components in every single relationship between two or more people or things. But what I find to be a major problem is how we as a society are failing to measure the significant gap which separates them. In a world that's becoming more dangerous by the day, we are required to dedicate more time to proper thought and analysis. However, every single one of us is instead coaxed into the opposite direction where we are encouraged to accept everything for what it is without ever asking why. Love and trust as a result, are left to be treated in the exact same way. It's because we love a particular person or thing, we're to also immediately consider them trustworthy. We're to straight away believe they return everything back to us. At no time is there any presence of doubt or any chance of reconsideration. All of what we bind ourselves to is of complete coherence, and any possibility regarding otherwise does not exist.

The issues we face today, are having a larger impact on the health of many relationships between us. Adding further confusion, are the countless new science practices and media outlets competing with each other for profits as well as the faith of the general public. Because of this combined with constrained time, individuals are left approaching everything in either a rushed or relatively lazier manner. They are applying less exertion in selling themselves to people. They are more often than not jumping to conclusions, effortlessly assuming that most of what they see and hear from anyone and everyone around them is true. The time for thinking is minimal and the idea of having second thoughts is fast becoming some sort of relic. The very fabric of trust is being abused as we falsely make it out through our actions that we have greater power in reading one another's mind. Somehow and in some way, we have gained the ability to always (and with great effectiveness) detect truth and honesty within any person outside of ourselves.

How are we to know where and when we are being fed truthful information? How do we conclude whether one is honest or not when it comes to what they say? What truly is it about the news and people we follow, that has us believing much of what they share? These are extremely important questions, albeit difficult to answer. They are too questions we're tending to ignore at a time when they are growing further in relevance. Trust is something that relies purely on our judgement. All of what we put our faith in, are merely sources we seem to gain most from personally. They are our ways of advancing to become better versions of ourselves. And because trust is a matter of judgement, it is only ever measurable. Here is where I believe the problem lies. Our inability and refusal to commit to a proper review of our trusted sources, is sparking more feuds between people as well as communities. We are simply not putting enough time and effort into our judgements. 

The truth is getting lost within our mess. That truth being trust and how it is never concrete. As mentioned earlier, we are sacrificing a little control of ourselves. Each time trust is shown for someone, we are handing over a bit of our lives to them. Most importantly, we do this without ever being able to completely know them. We cannot read minds. We cannot ever work out exactly what one is thinking at any given point in time. Irrespective of how well we believe to know somebody, there will always at least remain the tiniest decimal of incertitude. A decimal which not even the honest words from a close friend can completely eradicate. This decimal represents the fact that we are not those whom we are trusting. We have no clear idea of their mentality and no clear idea of their approaches. It's like a case of 'seeing is believing', where we have to really be in each other's shoes and share experiences as well as memories to achieve 100% trust.

Not even a polygraph can truly separate the truth tellers from liars. Such technology is often used to detect lies in people through measuring blood pressure, heart rate and breathing. However, it too relies on a certain atmosphere for greater effectiveness. The lie detector test is often used for small rooms where there is almost complete silence. Also influencing the results, is the use of stern authority. Either these ensure better results or they are just nuisance variables. Regardless, any person who undertakes a polygraph can easily render it unsuccessful. In other words, they have a way of lying many times and getting away with it. The key involves training the body to relieve itself from all tensions and allowing the mind to stick by any fib and firmly establish it to the point where it in a way becomes a new truth. As of now, there remains no technology that can properly determine the honesty of a person.

Of course we don't ever have to go this far with trusting one another. It is safe at anytime to assume that most of whom we associate with and get to know well are genuine, trustworthy people. But we shouldn't really fault anybody for taking precautions here if they believe that is what helps them out, especially with life now continuing to open itself to greater dangers. Much of the internet nowadays is a new breeding ground for human relationships, providing several social media platforms for personal and business matters. However, it too has become a massive hotspot for obscurity and suspicious activity. People are provided the opportunity to conceal their identities online and reveal less about themselves to others. Then there's high-class cyber criminals deceiving innocent web users into giving out personal details through phishing, scams and other fraudulent schemes. With a fast-growing reliance on internet and modern computer technologies, there is no doubt we are heading into more dangerous times. Thinking and other trust building exercises have never looked so critical than they do today.

I base much of my online activity on the idea that love is easy to express and trust is hard to come by. I step onto platforms such as Instagram and Twitter, not trusting many people and believing nobody trusts me. So a lot of what I do on social media is a means of earning such trust. Whilst ensuring some of my personal details remain private for the sake of my family's heath and well-being, I attempt to reveal as much as I possibly can about myself. I share my passions and find many ways to engage with my audience in a friendly manner. I too try my hardest in sharing stories as well as listening to those from my fellow users. I regularly honour and praise others for their publicly shared content. And above all, I allow people the choice in sharing their details. Never do I try forcing personal information out of them. Never do I sell them out unless they approve or say otherwise. All of this is me hoping people can feel safe and comfortable around me. I also do this with the hope of making true friends.

With more risks coming into play, I'm seeing a greater importance in us opening ourselves to all possibilities. There is a growing need to be better prepared for anything and everything. None of this however is necessarily me saying that the world is full of liars. Besides, I don't see much of an issue in the act of lying when compared to the showing of faith. In spite of it being a sinful behaviour and one I by no means condone, lying at times can be a normal thing to do. Everybody does this, or at least has done so once at some point during their lives. I'm not afraid to admit that I have frequently lied about certain things in the past, and perhaps I still do now. At no time am I proud of it though, and I usually allow for each lie to weigh me down a fair bit. But one thing I know for certain is that whenever I myself lie about something, I do so with good intentions. Most of the time, it is me not wanting to hurt others or have them stressing out. It is understandable for anybody to take this approach. But we are to know that lying is never right and it's a part of our characters which we have to work in fixing.

None of us like ever being fooled into believing something that isn't true. However, I see the problems surrounding this not ever being as severe when we are more careful and thorough in our trusting of others. The effective ways of building honest relationships are fairly simple, but are disregarded by our lack of endeavour and misuse of time. Trust for the most part, depends on our knowledge of certain people along with the respect we have for them. The more love we show and get in return, would guarantee any showing of trust being safer than previously. As for such things that are not people like where we receive news or other factual information, it becomes a matter of determining the accuracy and validity of the source. This involves comparing it with other sources and studying general consensus. It can help just as much to read what critics say and view all separate opinions. Although we are all different in our personal experiences and tastes, our views can indeed reshape one another's. Trust may never be concrete, but all of these strategies with some hard thinking will ensure our trusting of the world is as close to concrete as possible.

As our world advances and steps into more topical territories, the complexities surrounding trust are becoming more prominent. And because we as a collective are looking the other way, we are faced with an unprecedented hostility between us. Opinions today are not as well constructed and people in general are becoming more easily persuaded by information. The energy to stop and think is slowly disappearing. So I'm here reminding whoever I can that trust is not a toy. We have an obligation to keep our minds exercising and continue taking steps with great caution. We're to acknowledge the differences in everyone of us and occasionally use them to improve on our own differences. I remind all to distinguish the connections of love and trust, for the sake of their safety. We all need to educate each other about faith and put an end to any growing divide. We're to prove our intelligence and show the world we can be ready for anything that comes our way.

Travis "TJ" James

The Numbers Game

Some are probably wanting to know why I share my joy and efforts when it comes Sudoku and other number puzzles. Well when my thirteen years of mandatory education came to an end, I felt this insane pressure suddenly disappear from my mind. The stress and anxiety from my need to meet with the demands of the school curriculum began to ease away, allowing me the time and space to recollect myself and prepare for my next move. However, I also began to realise that my knowledge was fading away at the same time. Each and every moment I revisited my school work, I would see the things I've learnt but struggle to comprehend the process. I was asking why something was the case. I lost touch with the basis and couldn't seem to connect things together the way I used to. It was as if I was becoming more stupid every day. My brain wasn't getting active. There wasn't any motivation to think. So I looked to try and change that. It was then I found a growing inclination to Sudoku. Had a book and a deck of cards with puzzles on it, so decided I would get the practice in and put my brain to the test.

It was only early this year, when I was introduced to six other Japanese logic puzzles after opening up an entire book of them (a book I was given as a Christmas present after my parents were aware of my interest in Sudoku). Some of these puzzles were of unusual design to me and while others came to put my mathematical abilities to the test. My interest in them grew much to the point where I felt the need to introduce others to them with my results along with a few live tutorials. It's not so much an obsession. It's rather a hobby. An activity always there for me whenever I am in the mood. An activity there to get me thinking. Here I share with you about each of the seven puzzles including the main one in Sudoku. I even provide some tips and approaches on how to go about solving some of them and show some supporting pictures. But be wary of my explanations as they might not sound as clear. Hopefully you will get an idea of the terminology. If not, then feel free to ask questions in the comment section and I'll be sure to answer them as soon as possible. Let's get stuck into this shall we?

Sudoku

Sudoku can come in many shapes and sizes, but the most common is the classic 9 x 9 version. A large grid of 81 cells divided evenly into 9 squares. You basically start off with a small amount of numbers, which are often set out in a pattern. The objective is then to work out from these where the rest of the numbers go so that the solution has each number from 1 to 9 on every row, column and 3 x 3 square. There are known to be four difficulties of standard Sudoku puzzles: easy, medium, hard and diabolical. The difficulties primarily depend on the amount of numbers given to work with, the way they are set out and which numbers appear more frequently. Regardless of the difficulty there is usually no need for guesswork, as there will always be at least one certain answer in front of the solver. This is where Sudoku also tests vision out and whether or not one can see the answers (I myself struggle to most times). In terms of process and challenge, I find these puzzles to be wedged in-between the two common literal games of word searches and crosswords.

Below are a few techniques I tend to follow when it comes to solving Sudoku puzzles.
The first of these is the mini-rows and mini-columns technique, where I separate rows and columns based on the 3 x 3 squares. This I like to consider a two-step process. In the first step, I look at the numbers and see whether they are positioned in the top, middle or bottom row of the particular square. From there I work my way across, eliminating certain rows where the same number can't be placed. The second step is going down and doing the same thing with separated columns to see if any more cells can be crossed out for a particular number. This is my go-to method when starting off any Sudoku puzzle, and I always find myself starting off with either the most common number or going in ascending order from one. The next couple of techniques will often depend on this one, as they require more numbers to work with (unless they are puzzles of very easy difficulty). 

The second technique involves whole rows and columns. It's where I look at an entire row or column (irrespective of the 3 x 3 square) and focus on whichever numbers are missing. This method sees both rows and columns dependent of one another. If I were to pick one particular row, I'd then be focusing on a set of columns and vice versa. Take 4 for instance. If I were to find 4 missing in a selected row, I'd focus on the empty cells and seeing whether the columns they're in are already occupied by a 4. Sometimes different numbers can help determine where your focused number goes in this technique. Finally there's the single-cell technique. The attention is placed on just one cell and looks at each of the row, column and 3 x 3 square it sits in. It's another process of elimination, with any number inside these areas being ruled out. The technique only works when there is one option remaining for the empty cell, so the chances of success are very small.

Mini Rows & Mini Columns Technique (Step 1)

Take the small picture on the left for example. To start off with, I am given two fives in adjacent squares. I then look at which rows they occupy within their square. First one sees the 5 in the top row and the second sees the 5 in the bottom row. From this, I already know that the top right square will have the 5 somewhere in the middle row.

Sometimes I don't require the same digit to appear in two adjacent squares. In the picture on the right, we only have one 5 in the top left square. No other 5 is given, however there is a 4, 9 and 3 occupying the entire bottom row of the top centre square. This tells us that a 5 has to be in the middle row in this square and the bottom row of the top right square.

Mini Rows & Mini Columns Technique (Step 2)

After determining which row 5 goes in, you can check to see whether you can narrow it down further. This is when you look at the columns. In the following example on the left, we have a 5 in the middle column of the middle right square and a 5 in the right column of the bottom right square. This goes on to narrow it down to one cell (in green) where five can go in the top right square. Most times, we won't be as lucky as to have the same number given that many times. In the following example on the right, we don't have a 5 in the middle right square. However we have a 2 occupying the centre cell in the top right square and there is still the 5 in the bottom right square. This can still help determine where the 5 goes.

Whole Rows & Whole Columns Technique

This technique is one selecting any particular row or column (preferably one with most of the numbers filled) and figuring out which missing numbers go where. This is mainly determined by looking at the empty cells and going the opposite way to see if a missing number of the row appears (e.g. if selecting a row, one will focus on a few columns and vice versa). This ensures whether or not the missing number of the selected row can be placed in a certain cell.

- The first picture shows a particular row with numbers at focus. By determining where the 2 goes, one places their attention towards the first two empty cells and sees whether or not a 2 already occupies both columns the empty cells are a part of. Since there is a 2 in both columns, the empty cells of the selected row can't be a 2. This leaves one option in the centre-right square, so that is where the 2 goes.

- This process can even involve 3 x 3 squares as shown in the second picture. There is already a 7 in the centre-right square so the two empty cells of the focused column within that square can't be a 7. This adds to a 7 not being in the first empty cell as a 7 already occupies the row. So the 7 can only go at the bottom cell of the focused column.

- One can even determine where a number goes based on whether or not other missing numbers can go there. Take the third picture for instance. This focused row was missing a 1, 5 and 6. The column of the first empty cell (where the 5 is), already has two of the missing numbers in 1 and 6. This means neither can go in that cell. So the only other number that can go in the cell is 5.

Single Cell Technique

In the midst of solving a puzzle, I may now and then use this technique when the others don't seem to be working for me. This technique involves choosing a particular empty cell and looking at what is around it. We take a look at each number and see whether they are in the same row, column or 3 x 3 square as the empty cell. This helps eliminate certain numbers. Sometimes it can even take us straight to an answer. Look at the example below. Pretend that the nine isn't there and see whether any other number can go in that particular cell. In this situation, no other number can:

- 1 can't go in the green cell because a 1 is already in the column.

- 2 can't go in the green cell because a 2 is already in the row.

- 3 can't go in the green cell because a 3 is already in the row, column and 3 x 3 square.

- 4 can't go in the green cell because a 4 is already in the row.

- 5 can't go in the green cell because a 5 is already in the 3 x 3 square.

- 6 can't go in the green cell because a 6 is already in both the row and the column.

- 7 can't go in the green cell because a 7 is already in the column.

- 8 can't go in the green cell because an 8 is already in the row.

All of this means that only one number can go in the green cell; 9.

Jigsaw Sudoku

Jigsaw Sudoku is pretty much like regular Sudoku. We're to place each number once in every row column and group of nine cells. However, there is one significant difference. Instead of 3 x 3 squares, we are dealing with irregular jigsaw-like shapes (hence the name 'Jigsaw Sudoku'). Another minor difference about these puzzles compared to standard Sudoku, is that the shapes are symmetrical rather than the given numbers. These puzzles are slightly more complicated due to the design and the only techniques (from above) we can really use for them are the second and the third. They require a set of strong eyes and they get one thinking the tiniest bit harder. But I find them to be a lot more fun to solve. Jigsaw Sudoku is not a common puzzle and one won't stumble across it that regularly. But the design is nothing short of fascinating. From a personal perspective, I would highly recommend that people try it out for themselves.

NOTE: This picture is merely an example of what a Jigsaw Puzzle looks like and is NOT by any means an actual puzzle. Any attempt to solve it will likely fail due to inaccuracy and need for guesswork.

Killer Sudoku (Addoku)

Killer Sudoku is a hybrid puzzle that combines elements of regular Sudoku and another Japanese puzzle called Kakuro. It requires the solver to use their head a little more, as it involves calculating and mental arithmetic. We start out with the usual 9 x 9 Sudoku grid. But this time instead of given numbers, we have smaller subsections divided by either dotted lines or different colours. These are called cages. Each cage is represented by a number in the top corner of the first cell in that cage going across. This number is the total of all the numbers in a particular cage. The rules remain as they are. One is to place the numbers 1 through to 9 once on each row, column and 3 x 3 square, while also ensuring that all the numbers in the cages add up to the given total. One must also NOT repeat any numbers within a cage, even if they don't occupy the same row, column or 3 x 3 square. This type of puzzle can seem hard when you first look at it and it may remain that way. But it primarily depends on the difficulty and whether we have the right level of skill.

Allow me to share with you a very handy tip that is key to solving these puzzles both quickly and efficiently. With this puzzle you will always be focusing on the totals. Always look at the both the lowest totals and highest totals first. Knowing that numbers cannot be duplicated in cages, it makes room for obvious answers:
- If a cage covers two cells and the total is a 3, the only numbers that can occupy the two cells in that cage are 1 and 2 (as they both add up to make 3). A cage with 3 is only ever going to cover two cells.
- If a cage covers two cells and the total is a 4, the only numbers that can occupy the two cells in that cage are 1 and 3 (since 2 and 2 is repeating the same number). A cage with 4 is only ever going to cover two cells.
- If a cage covers two cells and the total is 17, the only numbers that can occupy the two cells in that cage are 8 and 9 (as they are the only two numbers that can reach the total).
- If a cage covers two cells and the total is 16, the only numbers that can occupy the two cells in that cage are 7 and 9 (since 8 and 8 is repeating the same number).
- Here are a few extra tips, though these may rarely occur:
1. A three-cell cage with a total of 6 = 1, 2 and 3
2. A three-cell cage with a total of 7 = 1, 2 and 4
3. A four-cell cage with a total of 10 = 1, 2, 3 and 4
4. A four-cell cage with a total of 11 = 1, 2, 3 and 5
5. A three-cell cage with a total of 24 = 7, 8 and 9
6. A three-cell cage with a total of 23 = 6, 7 and 9
7. A four-cell cage with a total of 30 = 6, 7, 8 and 9
8. A four-cell cage with a total of 29 = 5, 7, 8 and 9
These tips help narrow down options and provide answers. Once an answer is found, the rest of the answers will follow. Sort of like a chain reaction. No guesswork is required.

Arrow Sudoku

Arrow Sudoku is much like normal Sudoku and has a couple of similarities to Killer Sudoku. As usual, each number from 1 to 9 goes in every row, column and 3 x 3 square. This time however, many starting numbers are replaced with a set of arrows crossing over multiple cells. The arrows are joint by a circle that occupies a single cell. The number in this circle is the sum of each number on the arrow line. Numbers can be repeated on an arrow line so long as they are on a different row, column and 3 x 3 square. Arrow Sudoku is extremely challenging and requires one to have a strong level of concentration. They can take as long as a couple of hours to completely solve and answers are not as easy to find here compared to the other puzzles. I've often found myself having problems whilst attempting to solve these ones. I consider them to be my least favourite as a result of this. But then again, it depends on the solver having the mind for this type of game.

Despite my struggle with Arrow Sudoku, I have still managed to pick up a few strategies. These strategies are very helpful and will take a bit of pressure off the solver:
- A cell with a circle is never going to be a 1, as that is the smallest number in the puzzle. Nothing can add up to make 1 here.
- In most cases, one can rule out a 2 being in a circle as this is extremely rare. The only time this can happen is if the arrow crosses over two cells that do not share the same row, column or 3 x 3 square.
- The same goes for every even number. Even totals can have two of the same number placed along an arrow line, but only when that arrow crosses over two cells which do not share the same row, column or 3 x 3 square.
- The number 9 can never be placed on an arrow as it is the highest number one can use.

Calcudoku

Calcudoku is one of the more recent creations in Japanese logic puzzles. It usually involves a 6 x 6 grid with all 36 cells separated into cages of 2, 3 or 4. These cages are too accompanied by a number along with an operation sign right next to it. This number is a target and the operation sign represents the process we have to use in order to reach the target. For example, a cage of two cells with a target number of 10 and a + sign means the two numbers within the cage must add up to 10 (which in this case, can only be 4 and 6). To solve this puzzle, one must follow the target numbers and processes while still following the common rule of each number from 1 to 6 appearing once in every row and column. It's much like Killer Sudoku, except it is often smaller, excludes 3 x 3 squares and uses all four basic mathematical operations. This puzzle primarily tests our ability to calculate in our heads. It's not overly difficult, but does require some great focus.

It is not only design that sees Calcudoku being similar to Killer Sudoku. Both of the logic puzzles share a significant solving method. That being the need to focus on the smallest target numbers along with the largest. This method in Calcudoku however can be affected by the shape of any particular cage. Unlike Killer Sudoku, this puzzle allows for the same digit to appear in a cage twice (so long as the digit doesn't meet in both the same row and same column). Completing these ones generally require us to play around with the numbers and see which ones reach certain targets. The process of elimination for cells can play a role here as well, though there is always one obvious answer in front of us from start to finish. Here are a couple of tips one can take into a Calcudoku puzzle:

1. Focus on the cages first and try to see which group of numbers go where. Then look at the cells.

2. Here are a few obvious answers I gathered for a standard 6 x 6 Calcudoku puzzle:

2-Cell Cages

3+, 2× = 1 and 2

4÷ = 1 and 4

5÷ = 1 and 5

5-, 6÷ = 1 and 6

10× = 2 and 5

15× = 3 and 5

18× = 3 and 6

10+ = 4 and 6

20× = 4 and 5

11+, 30× = 5 and 6

3-Cell Cages

6+ = 1, 2 and 3 (1, 1 and 4 possible for a non-straight cage)

2- = 1, 3 and 6 (2, 2 and 6 possible for a non-straight cage)

4- = 1, 1 and 6 (only for a non-straight cage)

90× = 3, 5 and 6

108× = 3, 6 and 6 (only for a non-straight cage)

96× = 4, 4 and 6 (only for a non-straight cage)

120× = 4, 5 and 6

144× = 4, 6 and 6 (only for a non-straight cage)

150× = 5, 5 and 6 (only for a non-straight cage)

17+, 180× = 5, 6 and 6 (only for a non-straight cage)

NOTE: A straight 3-Cell cage is an 'I' shape. A non-straight 3-cell cage is an 'L' shape

Takuzu (Binary)

This is generally one of the much easier puzzles to solve. Takuzu only ever involves using two symbols. Most of the time it's the two digits that represent the common binary number system; zero ('0') and one ('1'). The aim is to simply have an even number of zeros and ones in every column and row while avoiding the same number appearing next to each other more than twice. Each row and column must also be different from one another. However, this won't be as much of a worry when following the small steps. Binary puzzles with the standard 10 x 10 grid usually take around approximately 10 to 20 minutes for me to solve depending on the day. Despite how easy they are to solve though, I personally find Takuzu a tad boring. There is minimal detail and it's nothing but two digits being used. That being said, I wouldn't stop others from solving these if they wanted to. There is every chance that they will enjoy them more than I do.

When solving Takuzu puzzles, there are four major methods to follow. These methods take all the rules into consideration and allow for further answers to be revealed. Without them, there is no solving a puzzle other than purely guessing which digit occupies which cell.
NOTE: Each method is matched to a picture underneath by the number. These examples are also based on a standard 10 x 10 grid.
1. The cell in-between two adjacent ones with the same number will always be the other number, since we cannot have three of the same number next to each other.
(e.g. 1-?-1 = 1-0-1, 0-?-0 = 0-1-0)
2. When two of the same number appear in adjacent cells, the cells on either end will always be the other number. (e.g. ?-0-0-? = 1-0-0-1, ?-1-1-? = 0-1-1-0)
3. Each row or column must have an equal number of the two digits. With the matching picture below, there are five ones and four zeros. This means the last cell in the row has to be a zero. (e.g. 1-0-0-1-0-1-1-0-0-1)
4. Most times in any row or column with three empty cells next to each other remaining, an answer can already be given. With the matching picture below, there are three zeros and fours ones given. This leaves two zeros and a single one left. If the very bottom cell of the column was a one, then that would leave the two zeros to fit the two cells directly above it. This would make for three zeros next to each other. Since this cannot happen, the very bottom cell has to be a zero.

Futoshiki

The final Japanese logic puzzle I am discussing here is none other than Futoshiki. This one is arguably the easiest of them all and only takes around 5 minutes to complete (referring to the standard 5 x 5 puzzle). All one has to do is list the numbers from 1 to 5 at least once in each column and each row so that all the sequences are different. But also coming with this puzzle are inequality constraints in the form of arrows representing both 'greater than' and 'less than'. These arrows must be followed in order to solve the puzzle correctly. Sounds like quite bit to take in, but it isn't. There are only 25 boxes with some already occupied by a few given numbers to work with. Plus the inequality arrows are more of an assistance than a constraint. With plenty of these arrows and a couple of tips in hand, one should really have no problem trying to solve a standard Futoshiki puzzle. It's a nice game to kill a few minutes off, whenever one is left waiting.

For anybody interested in Futoshiki, I'd recommended you take into account these four easy tips:
1. Since 5 is the greatest number in a standard 5 x 5 grid and there is no larger number, it won't ever be seen in a box with an arrow pointing to it.
2. Since 1 is the lowest number in any Futoshiki puzzle and there is no smaller number, it won't ever be seen in a box with an arrow pointing away from it.
3. Any box with a 2 and an arrow pointing away from it, tells us the box that same arrow is pointing to is a 1.
4. Any box with a 4 and an arrow pointing to it, tells us the box that same arrow is pointing away from is a 5.



My message to people is simple. Give these puzzles a go (or any puzzles for that matter). They are not school or work papers. They are actually a game that helps keep our brain active through concentration and logical thinking. They keep us occupied at times of boredom or when patience is required. These Japanese number puzzles are not as hard as they look and the rules are not as complicated as some make them out to be. Take it from someone who has done so many of them in the past few months. Despite my struggles with the occasional one or two over time, I generally have very little problem with most that I solve. And believe it or not, I managed to pick up a few new strategies when working on these puzzles (and numbers in general). Others will most likely learn a thing or two as well. Just try Sudoku out. Try all of these out. I don't expect them to be everybody's cup of tea, but it's worth the time. Consider this as me caring for the health everyone's mind.

Travis "TJ" James