Sep 202017
 

 Games and Us

We all play various games in our life. Right from the childhood, when we used to play outdoor games way back in the 80’s and 90’s to the indoor digital games which we play currently. The games included Cricket, football, Badminton, Chess etc in those days whereas currently all these games are digitized.

Digitization of games has its own advantages and disadvantages. The main disadvantage is that we tend to reduce the movement of our body, which normally we associate with these games. But the advantage is that we get to play against the world community as against the local community. This can help us develop our skill in a particular game, much better.

This is mostly true for certain indoor games which require more use of brain than muscle. No one can replace physical sports like football with digitized games and yet maintain the level of physical involvement required. Or may be I am wrong, time will tell.

Here in this post, I will help you learn to play Sudoku. Sudoku is primarily a number game. It involves use of basic math reading, no calculation required. If you know which numbers lie between 1 and 9, you qualify for taking this lesson.

Sudoku primarily appeared in newspapers but programmers have digitized this game. They have also added certain difficulty measures to it, one of them being time constrain. Playing Sudoku under time constrain will help you in improving your logical thought process and keeps your brain active. This also helps reduce the chance Alzheimer. And it’s fun too.

So let’s begin.

Playing Sudoku

 The view

Once you launch Sudoku in your computer or mobile phone, the screen will show a square subdivided in to 9 equal sub-squares. Each of these smaller squares are further subdivided in to 9 equal cells. This 9 X 9 configuration is a standard configuration in any version of Sudoku. Refer picture on left.

You can see few digits entered in cells. Note that the numbers are completely random. But still there exists a logic in their placement. You will understand it once we move ahead.

As you can see, the big outer square is sub divided in to nine smaller sub-squares. I have marked one of them in green. Each of these smaller sub-squares is subdivided in to nine smaller cells. I have marked two of them in red. We must fill up the blank cells to complete the puzzle.

 Game Rules

The rules for the game are pretty simple. All you should do is fill up the empty cells with following constrains in mind:

  • Each sub-square(green) must contain the numbers from 1 to 9 without repetition.
  • Also, each vertical column must contain the numbers from 1 to 9 without repetition.
  • And each horizontal row must contain the numbers from 1 to 9 without repetition.

Straight forward,isn’t it? It is if you follow certain tips and tricks. The level of difficulty you select while launching the game defines this. The difficulty level depends more on which cells are pre-filled with respect to blank cells rather than the number of pre-filled cells. I suggest that a new user should start with easier levels, to get a hang of it.

For the sake of explanation, I have numbered the cells as below. If you use excel, you will be very familiar with this cell address scheme. You may or may not see this numbering scheme in the game depending the developer. We refer to the first row first column as a1, first row second column as a2 and so on up to i9.

Game Play Tips and Tricks

This game is played using the process of elimination. First of all, look up for any sub-square which has the maximum pre-filled digits. You can see in our example above that there quite a few sub-squares. Pick up any one of these sub squares and start counting from 1 to 9 while checking which number is missing.

Playing the Sub-Squares

Let’s say the we are playing with the very first sub-square contained by the cells a1 to c3. We see that the number 1 is missing. There are 5 empty cells in the square a1-c3. But when we take in to consideration the rules, only two cells qualify to accommodate the number 1. These cells are a1 and c1. The cell b2 cannot contain the number 1 because the cell d2 contains the number 1. Similarly a3 cannot contain the number on because the cell g3 contains the number 1. If we place the number 1 in b2 or a3, this would be repetition, which is against the rules.

So now we have the cells a1 and c1 where we can possibly place the number 1. But there is no way at this moment to tell where we should place number 1 without having a conflict in future. So we move forward.

Counting ahead, numbers, 2, 3, 4 and 5 are already present in the sub-square. Number 6 is not present. We can place number 6 in either a1 or a3, but we are not sure even in this case whether there will be future conflict. Same is the case with numbers 7 and 8. Number 9 is already present in the sub-square. So we move forward to analyzing sub-square a4 to c6.

In this, while counting we find that numbers 1, 4, 5, 8, 9 are in same situation as previous sub-square and numbers 2, 3, 6, 7 are already present.

We keep on moving forward among these sub-squares. In sub-square a7-c9 we are able to fill in number 3 at cell b8. This is because it is the only cell which allows the missing 3 to be entered without conflicting with all the already present 3s highlighted in red.

We can keep on analyzing in this way and we come up the final result as below.

Since we have entered few numbered in blank cells in the first iteration, we have to go back and carry out second iteration. Since we have filled up some numbers, they might help us to determine those cells where we not sure previously. We keep on repeating these iterations till we are not able to enter any single number in the entire iteration.

The final matrix after multiple iterations in example above is as below.

Playing the Columns

Since the difficulty level for the puzzle above was easy, we solved this by analyzing the sub-squares. But as the difficulty increases, analyzing the sub-squares alone will not be sufficient and in such case we need to start analyzing using rows or columns method.

Let’s say we tried iterations number of times but were unable to fill up the matrix as below. Then we can go for the next method.

In this case we start analyzing either each row or each column, one by one. Let’s pick up column 1. We again start counting and checking whether the numbers 1 to 9 are present in that column. If any number is absent, we search for the possible cell where we can fill that number. This is done by checking the corresponding row for each cell.

For example, if we want to check if we can fill a missing number, let’s say number 1 in the above case,  in cell a1, we check cells a2- to a9 for the presence of number 1. If number 1 is not present in cells from a2 to a9, then the cell a1 becomes a possible location for number 1. Now we need to check for any other possible locations in column 1 where we can place number 1. If there is only one cell location in column 1 where we can fill the number 1, then we should fill it. If there are more then one possible locations to fill in the missing number 1, we can’t fill it and we should move ahead analyzing the next number.

Once we analyze one column, we analyze the next column in the same way. We can continue this for number of iteration till we either solve the puzzle or we are not able to fill up any number in a single iteration.

Playing the Rows

Once we are not able to fill up any number in a single column iteration but are are left with blank cells, we should start analyzing rows.

Analyzing the rows and filling them ups is same as analyzing the columns as explained above. In this we check the possibility of filling up each cell of the row by cross checking them against the corresponding column. Once done with one row, we mode on to the next row.

Spotting the Numbers

Another method which we can use along with the above three is singling out an individual number and checking their position in the matrix. This method, though similar to analyzing each sub-square, is different from it because in this method, we analyze a particular number. The presence and position of this number in corresponding horizontal and vertical sub-squares determine the position in the sub-square where it is not present.

Let’s take an example of number 5.

You can see that the number 5 appears in each sub-square except in the sub-square a4 to c6. There are four cells empty in a4 to c6. These cells are a4, a6, b5 and b6. Cell a4 abd a6 cannot contain number 5 because cells g5, a8, d6 conflicts. Similarly cell b6 cannot contain number 5 because cell d6 conflicts. So cell b5 is the only cell where we can place number 5.

This analysis can be done starting from number 1 to 9 in sequence.

Mixing it Up

We can even opt for mixing these methods instead of carrying out multiple iteration of each method. For example, we can start with analysis of rows, complete one iteration then move to next method, say column analysis for one iteration and then sub-squares for one iteration and number analysis. Mixing and matching can keep things interesting.

Endgame

So you see, Sudoku is not a difficult game. It just needs few tricks and some practice.

If this article has helped you learn Sudoku, kindly share it across. Leave comments if any help needed.

 

Mar 272016
 

Mar 192016
 

Jun 112014
 

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Another two days and you will be able to watch your favorite teams competing in Brazil.  I assume die hard fans like you have already made your flight, hotel and ticket reservations for the games in Brazil. If not yet, you may still have a chance to book the tickets. Check out the Fifa website.

Oh what!! Your boss doesn’t sanction you the leave for games. So cruel of him. First the appraisals and not the world cup!! Anyway, catch the action at your local pub or sports bar if such is the case. But you also want to create and environment for the games No problem, head over to Amazon India to buy Football Merchandise.

You can keep track of all the football action at Liv Sports. Catch the action on the go on Android and iphone

Go ahead. Live the moment. It’s a once in a four year experience!!

Any idea about any new animal replacing Paul the Psychic to do the predictions?

Apr 062012
 

After the onslaught from the politicians in India, renaming everything in sight to gain political mileage, it’s the turn of our past rulers, the Britain to follow(for once, other countries are following us)

All the 361 London tube stations have been renamed after the past and present great sportspersons of the olympic games. A rare and bold feat, ahead of the opening of the 30th games on 27th July this year. Legends like Muhammad Ali, Michael Phelps, Carl Lewis, Magic Johnson, Michael Jordan, Nadia Comaneci figure in this list.

The point of interest for us Indians is the inclusion of 3 great players of Indian hockey, Dhyan Chand, Roop Chand and Leslie Walter Claudius. Dhyan Chand, Hockey ka Jyadugar( the wizard of hockey), is a well known name in Indian households. Anecdotes about how he was asked to change the hockey stick during a game, fearing that it had some kind of magnetic power in it, are well known. We even had a lesson in our hindi text, entirely dedicated to him. I remember the name Roop Chand referred in some context, I think in one of the Kaun Banega Crorepati episode. But I am not sure. I definitely did not hear about Leslie Walter Claudius. After reading about his exploits in the Olympic games, I was surprised that I read the name for the first time. Or maybe it’s me who is ignorant. And the worst of all, I didn’t know the details about their exploits. Nor did I try to find out, with wikipedia being at hand. Such is the pitiful state of the knowledge of our national game among the current generation. I hate cricket, for being a bat-centric game. I always feel that hockey is being neglected by the current generation. I myself do not take much interest in watching the game. Hockey has been neglected. I believe, or have been led to believe that the team is being mis-managed.

It is heartening to find out that the people who were left mesmerized by the great Indian sportsmen, have not forgotten them. The gesture of renaming the stations is really sporting and I hope that the inclusion of Indian names will rekindle the flame for Hockey amongst the youth of India.

Read Details : The Times of India

Mar 192012
 

My lord, I rise before you in defense of my client, though he has not signed me up. I ask you to grand me special permission to defend my client who has been labeled with lot of names since about a year, but has remained silent bearing the torments. It was the humble opinion of my client that answering or back answering his tormentors would have given enough fuel to the fire and it would have been difficult to silence them. He chose to remain silent but I refuse to bear this injustice. I will defend him, as I know he has done no wrong.

Thank you my lord.

I begin with the backdrop for this defense. My client has been playing this game for a long time. In-fact, the longest anyone has ever played. He has earned himself a fame, which other players would envy for. Any child who lifts a bat in his hand yearns to be as famous as my client. In-fact, people have been so obsessed by his style, elegance, success in batting that they have altogether neglected the other avenue of expertise, bowling as I had mentioned in one of my previous case. Nothing wrong in trying to be him. That instills a passion and love for this game which is a necessity is we need a quality batsman. Of course, that hampers the development of a good bowler, but that’s besides point today and my client has no hand in this unbalance.

Then there came time when my client was compared with God. My client, humble as ever, rejected such a title, knowing fully well the enormous responsibilities that came with it. He kept on stating that he was a mere creation of God. But the general public did not give up. They even compared him with the great batsman of yesteryears, and one such players, who has been very successful during his times, managed to see his own image in my client. People relentlessly decorated him with titles like the little master, the master blaster etc. The latest of it being “The Centurion”. My client finally accepted that the people had their own way of showering affection and gave up. Still I would state for the record that neither of this titles have been given to my client on his request, or acquired by any illegal means.

But off-late my client has been on the receiving end of the public wrath. People have tried o tarnish his image in whichever way possible. This has happened due to certain events a year back.

As you might very well know, a player scoring a 100 runs in a single inning of a match, gets it recorded as a century against his name. My client has been master at it. His technique, concentration, game flow has been very good all through this years. He has managed to suppress all the batting records of this game and raised the bar to a level, very much difficult for any current player. He has done it during past 22 years of his career playing this game. Yes my lord, 22 years, that’s how long he has been playing. No other player has managed such a feat during their times. The above fact highlights the fitness levels of my client for such a long period. Others have played and weathered. Not my client. He makes himself available.

But some elements in the society seem to be against my client playing the game. It all began about a year back when my client scored the 99th century of his career. It was very much anticipated at that time that he would score the 100th one, the century of the century, very soon. But my client had failed to do so until very recently. This has led to a public backlash against him, humiliating him in public media, without giving due consideration to all that he has done for his country. I try to defend him on three grounds, Social, Psychological and Statistical.

If you have a superhero in front of you, you tend to have high expectations from him. This happened with my client. My first line of defense presents him as merely a victim of social expectations. As the public elevated him to the  level of God, their expectations rose high. It was expected from him to score larger amount of runs each time he took to crease. He was just human and he demonstrated that, though not willingly or voluntarily, by making a low score in number of matches. It went unnoticed each time since along the way he kept on reaching some milestone or the other, which kept the general public engaged. He wanted to pile runs for the team. They wanted milestones. There were many centuries along the way but after the 99th one, people focused on the next milestone, the 100th. It was obvious that people had this as the target, and the human, my client, flunked number of times in trying to reach the target. Meanwhile the public discounted  his failure hoping that he would succeed in the next game. This expectation was then served by media the way they treat hot news. Spiced up and peppered. Along with this they added a zing of a news which hinted to his retirement after his 100th. My client initially neglected this and went along with his game, scoring runs as they came by. But the expectations gradually were converted to taunts, then anger and finally full blown hatred against my client. Every match was treated as being scheduled for his century and every failure was treated as incompetency on his part. Children who didn’t know how to clean their nose, started commenting on how “that particular delivery” should have been played by my client. Whenever my client came close to scoring hundred, people started taking note of the exact number of balls “wasted”. Commentators meanwhile added fuel to public anger when they replayed the delivery again and again and analyzed how my client should have played it successfully. They forgot that as against the comforts of their air-conditioned cabin, my client as standing in that sweltering heat, in a noisy stadium where concentration was easy to lose. Finally they decided that it was time for my client to retire and well known sportsmen and analystsstated that his age was preventing him from going any further. They compared his fitness with their fitness at his age. Little did they know that my client follows a very strict fitness regime. The ghosts from the closet came out saying that my client scoring a century was a bad omen for our country and we rarely won. This is untrue my lord, as will be proven by me further. I would just like to state here that the society raised the bar for him a bit too high, and though no one amongst them have ever reached there, they expected my client to conquer it each time.

My second line for defense revolves around the psychological effect on my client. My client was well aware of the public expectations and though he very much wanted to fulfill them each time, he was and always will be of the opinion that he should play his natural game and success will come along. He has done it all throughout his life successfully. He knew that the century of he century was looming nearby but did not want to haste it as it would adversely affect the performance of the team. He played the game ball by ball during last one year and came close to the target set by people number of times. And failed to reach it. But people did not notice his score. People noticed his lost opportunity. And they kept on counting them. Then their expectations grew very high and that was voiced through media. My client duly noted it and knew time was ripe to bring joy to the people. But as he has rightly said, he is not God. So the opponents who were stronger managed to defeat him on number of occasions. The ghosts from the closet came out again saying that all his previous records were of no use to the country and he played for his own selfish motives and so on and blah blah. My client did not respond. He knew better. But this did get on to him a number of times. He decided to just get over with it by hook or crook and again failed at it number of times. The last time he got close to the public expectations, he decided that enough was enough and played the slowest game of his life. He finally managed to achieve what public wanted but at a price. A price which later cost our team the match. Naturally, people again pointed out that his “centuries” meant no good to the team. Maybe it was time for him to retire, they said. It was expected that his centuries alone should be match winners. Little did they realize that there are 10 more players in the team who have to perform. Winning the game is a team effort, not an individual one.

My third line of defense focuses on pure statistics. Just take the case of his centuries. Hundred of them in-fact. It is normally said that each time he scores, our team loses. Untrue. He has scored 51 centuries in tests. Of which we won 20, have drawn 20, lost 11. Is that too bad? Out of 49 centuries that my client has scored, the team has won and amazing 34 times. We have lost 13 times, tied once and had no result once. If I may take the liberty, I recollect many lost matched where he has scored but the entire team has failed to support him. So why blame him for their failure? There is also an unverified fact floating around that my client scores only against weak teams. Let’s get this straight. He has scored the best against the strong teams. His highest number of centuries is against Australia, Sri Lanka, South Africa, England, New Zealand, Zimbabwe, West Indies, Pakistan in that order. The last time I checked, these were very strong teams. There are many other statistics to reveal, all which will point to the high level of integrity, competency and fitness of my client. It will take a lot of the courts time to reveal then, but if required, they will be presented.

I request your honor to pass an order preventing the general public and the special “experts” from harassing my client into retirement. This will be a big loss for the team and the country. His selection in the team will always depend on sole discretion of the selectors. Similarly, his retirement should he his decision. He will be available whenever his country demands such and will not bow to cheap mudslinging. I have utmost respect for your judiciary wisdom and expect that you will pass a favorable verdict.

I rest my case…….

Dec 292011
 

All those missed hours of my morning sleep were waste. I am on a holiday and yet I woke up enthusiastically to watch the “Agnipath” series. And it has all been for nothing. Except for the Australians, no one else has played good cricket. I even fail to understand the meaning of he word “Agnipath” in this context. Or were the promoters of this series aware of the fact that it would be a road full of fire for Indians?

India has been consistently helping the cause of he opposing batsman or the bowlers for that matter. Ponting, the out of form man has come to his senses due to some sloppy bowling by the Indians. Hilfunhaus had been out of form and the team for quite a while. This match has done good for both these players. The Australian tail-enders got the much needed batting practice, and their team, the much needed runs.

Go for the kill, would have been a good punch line for the “Agnipath”. When the captain spreads out the field for the tail-enders and hope for a miracle edge, there will be none to come. Miracles have to be made; they don’t come cheap. Attack the last batsmen, put in slips, put men in catching positions. That’s what the great analysts of the game kept on saying. But I discount Dhoni due to the fact that walky talkies are not allowed in the game. So how could he know?

Early today morning, before the Indian innings started, my brother predicted that the match would end today with us losing. Its headed that way and I will be surprised if Dhoni manages to keep the other batsman alive for the day. Or if he manages to stay alive himself. I had a feeling in my mind that Tendulkar would get his 100th today and that would be the only medicine to the bruises. That too out of the window with his wicket.

And someone please explain to Gambhir that you cannot get out twice in a similar manner. Bowlers tend to take this as your weakness and capitalise on that in the next games. It has become a habit for the Indian players to forget about their past mistakes and never learn from them.

Full marks to Zaheer Khan and Umesh Yadav. They have done their part brilliantly. Ishant, well, not much to speak, apart from his 152.2 Kmph delivery, “fastest” by any Indian bowler till date!

Nothing is lost yet. Not atleast keeping in mind the entire series. Dravid and Laxman, the masters of the away game can still make a difference. And we have the above praised Zaheer and Umesh. But then, that’s only four players to depend on. The team is normally made of 11 in form players.

Before I finish off, a reminder. Whenever a series has been given a fancy name, we have failed to even level the series.

Jun 032011
 

Rejoice all ye F1 fans!! A double bonanza has been announced by FIA today. As we all know, Bahrain was cancelled at the beginning of the season due to political turmoil. Also the decision on Indian GP was either ways. FIA has finally announced today that Bahrain race will take place on the dates fixed initially for Indian GP. They have also confirmed that Indian GP will be the season finisher.

What a great deal we got. We get to see the full quota of races as planned earlier. Above that, people like me in India, can look forward to finally be able to see the race live. And that too a possible tense season finale. Delhi’s got a great opportunity to prove itself.

Rejoice!!

Mar 122011
 

The big man of the cricket, also called as the Master Blaster, Sachin Tendulkar is in the heat of the action all throughout the world cup until now. He is either busy getting 100’s and 50’s(these are just another numbers for him, but for us they are achievements) or sliding and diving around the field saving runs, doing both the things for the team. But there have been speculations all the time before the world cup, that he might quit after the tournament.

No matter what the results for India, he is sure to be asked the question after this tournament. Is he quitting from the international cricket? Does he thinks that he has had enough of cricket for life and may want to settle with his family?

Sachin-Tendulkar1

 

I think I know what his answer will be. “Where did you get that idea? Why do you think I should retire? Am I not doing it right for India?”

It is an impression amongst the self proclaimed gurus of the game, or of any other game for that matter, that a sportsperson should retire at the peak of his career. That way, he goes graciously and is remembered for a long time.

But, why can’t a player who is performing well and is confident about his fitness, stay on with the game for a longer time? Why should age factor come in the way? If he performs well, can he not put himself well above in the achievements’ charts in that particular sport?

Michael Schumacher did not retire at the peak of his career. But does that wipe off his 7 championships? Is he not remembered for that? Tiger Woods continue to play, and may underperform at times, but does he not perform miracles in the dying stage of any tournament? If health and age should have been considered as retirement factor, Lance Armstrong should have given up on cancer, shouldn’t he? Age is just a condition against which these players fought and continue to fight.

So now should Sachin Tendulkar quit? Give one reason. Not the age one…..Not the fitness one. Because those become invalid arguments.

Or better still. Give one player to the Indian team who has Tendulkar’s commitment, fitness, desire to better his game and his sporting spirit. Give one player who attends all the practice sessions, sober, and ready to bat(left and right handed), bowl and field. Give one player who, even after having all the above qualities, have not been distracted by the endorsement industry. If you find one, Sachin might consider making the room.

Else, quit suggesting him to quit!!

Feb 222011
 

With two numbers performed live by Bryan Adams, and a very low quality theme song, the world cup was inaugurated at Dhaka on 18th Feb. 2011. The very first match between the co-hosts, India and Bangladesh, gave a very fair idea of how the world cup will turn out to be. Far away from the lush green outfields, and the grassy pitches of Australia, England or South Africa, the dust bowls of the Indian subcontinent(including India, Sri Lanka and Bangladesh) are the venues for all the matched of this edition. It will be a little surprise that the matched will be high scoring ones, with very little for the bowler. Sehwag and Kohli, affirmed this belief on saturday.

sketch_batting

It is said that the there were huge revenue losses in the previous edition of the world cup due to the early exit of India. Now, India is considered as one of the major revenue generating country for the cricketing world, and the disqualification of their home team(due to their poor performance) would be enough reason for loss of revenue. The organisers wanted to be double sure that this doesn’t happen again. India has to stay in the game till the very end, so what do we do? Make sure that the pitches are batsman friendly, given that India has one of the strongest batting line up, and conversely, one of the weakest bowling lineup. The pitches will be one of the most favorable thing for the India team in the Indian subcontinent, and captains will be heard complaining that the bowlers were not up to the mark, after each match.

The only thing against India might be the Duckworth Lewis system, which has never ever favored India.

Except for one game, all the games up till now have been high scoring ones. Even the Netherlands managed to score a very respectable 292, and were choking the mighty England. Eventually, England managed to beat them, but with very few overs to spare, and though they lost, Netherland showed us that they could do it. Either that, or they got lost of help from the pitch. Because, England is poor player on such field.

In olden times, cricket used to be a test of mental and physical abilities for both batsman and the bowler. It used to be a one on one encounter. Batsman like Sunil Gavaskar, Arvinda D’silva, Sir Donald Bradman, Sachin Tendulkar, Viv Richards, Salim Malik, Garry Kirsten, Steve Waugh, the Flower Brothers(Andy and Grant) and many more legends of our times would be pitched against the legendary bowlers like Dennis Lilee, Courtney Walsh, Ambrose, Malcolm Marshall, Kapil Dev, Imran Khan, Wasim Akram, Glen Mcgrath, Sharne Warne etc. They were friends in the dressing room and enemies on the field. They would share their beer, but not give away anything during the game. Each wicket was earned, and each run was ran for. There were no hand outs. But times have changed. The game has become batting centered. Maybe that’s because people love runs being made, big scores being posted. A six, hit out of the stands, is more exciting for them then the batsman being bowled out by a precisely placed Yorker. This attitude towards the game has lead to the batsman centered game.

Sachin Tendulkar, or the Master Blaster, has innocently and unknowingly, shaped the way cricket is seen nowadays. Not that he is to be blamed for that. He has played his part. But the major cause of worry is that it is only he who is considered as the true success of the game, and is adored, and worshipped and followed. To an extent that everyone aspires to be him. No one wants to be the Kapils or the Lilees of the game. They all want to be the Tendulkars of the game. And that’s leading to formation of weak teams, which can compete nowhere else, other than their home ground, which are custom made to suit their style.

How bat-centric a game, cricket has become in recent times, can be judged by the world cup anthem this year. De Ghumaake, meaning “Swing it” were the words used heavily in the entire lyrics. Not that it was any great song. Infact, there was nothing much in it except 3 idiots dancing around on the stage, singing the same four lined lyrics, again and again, till everyone was tired of it. How it went past the organising committee, I have no idea. Anyway, the point was that, it has no mention about what the bowler has to do during the matched. It only instructs the batsman to “De Ghumaake”, i.e.. swing it. In other words, slog.

I just hope that in he near future, some youngsters aspire to become the Kapil Devs and Imran Khans of the game, so that the an equal balance is maintained.

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