A completed Sudoku grid is a special type of Latin square with the additional property of no repeated values in any partition of the 9×9 block into contiguous 3×3 blocks. The relationship between the two theories is now completely known, after Denis Berthier proved in his recent book, "The Hidden Logic of Sudoku", that a first order formula that does not mention blocks (also called boxes or regions) is valid for Sudoku if and only if it is valid for Latin Squares (this property is trivially true for the axioms and it can be extended to any formula).
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The first known calculation of the number of classic 9×9 Sudoku solution grids was posted on the USENET newsgroup rec.puzzles in September 2003[11] and is 6,670,903,752,021,072,936,960 (sequence A107739 in OEIS). This is roughly 1.2×10−6 times the number of 9×9 Latin squares. A detailed calculation of this figure was provided by Bertram Felgenhauer and Frazer Jarvis in 2005.[12] Various other grid sizes have also been enumerated—see the main article for details. The number of essentially different solutions, when symmetries such as rotation, reflection and relabelling are taken into account, was shown by Ed Russell and Frazer Jarvis to be just 5,472,730,538[13] (sequence A109741 in OEIS).
The maximum number of givens provided while still not rendering a unique solution is four short of a full grid; if two instances of two numbers each are missing and the cells they are to occupy form the corners of an orthogonal rectangle, and exactly two of these cells are within one region, there are two ways the numbers can be assigned. Since this applies to Latin squares in general, most variants of Sudoku have the same maximum. The inverse problem—the fewest givens that render a solution unique—is unsolved, although the lowest number yet found for the standard variation without a symmetry constraint is 17, a number of which have been found by Japanese puzzle enthusiasts,[14][15] and 18 with the givens in rotationally symmetric cells. Over 47,000 examples of Sudokus with 17 givens resulting in a unique solution are known.
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Showing posts with label Education. Show all posts
Showing posts with label Education. Show all posts
Tuesday, August 20, 2019
Sunday, August 4, 2019
Improving Spelling With Games
You got it! You can do just about any type of learning for a child or an individual learning a second language through the use of various computer games. You are sure to find something that will fit with their needs. You are also able to find a game that will keep them interested. Let's take spelling as an example.
Many kids struggle each and every year at school with that dreaded Friday spelling test. It doesn't get any easier because chances are good that the words just keep getting harder. For many parents, spelling is often a challenge to teach as well. The English language is nothing simple. But, what if you could teach them through the use of a PC game? That would be excellent, wouldn't it?
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Think about this. The next time your child comes home with that awful list of twenty words they just have to know, you can easily say to them, "Why not go play a game on the computer." Yes, you can do this!
There are a number of games that are just perfect for teaching children the art of spelling. For example, you might want to try a word puzzle game like Beesly's Buzzwords. Or, if Spiderman happens to be your child's favorite character, you have games like Spider-Man 2: Web of Words. In this game, you child can advance through the levels by correctly spelling words. Its fun, rewarding, and most of all, it will help to improve their spelling capabilities.
The spelling games are not boring, dull, and difficult. To the opposite, these games will hold your child's attention so that they can get the knowledge they need. That is what makes these games different. If you are thinking back to your school days and those boring computer programs you were allowed to play and wondering how your technology loving child is going to play with something like that, don't worry. These games are much different. They are made to stimulate your child's knowledge without even allowing them to realize that they are. To them, they are simply playing a Spider Man game.
The value of these games is huge. In fact, there are more than just spelling games, as we will see down the line. They are great ways to feed your child the knowledge that they need without boring them. When it is fun, it will get played more often. The more that it gets played, the more they can learn from it.
So, then, what is the bottom line? You can easily allow your child to play some computer games but of course, you still need to monitor their usage. And, yes, you may have to practice those specific spelling words each week, but it may just get easier as time goes on. Here's a thought. Replace their favorite computer game with one of these for a week. They still get computer time and they still get to play a fun game. But, you get the satisfaction of knowing that they are playing an educational game as well. All in all, we think these games may be a great way to boost confidence and knowledge. Consider them for any age of child. You'll be happy that you did.
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About the Author: Steve is a member of the GrandMatrix team. They provide a broad range of games, puzzles, articles and reviews. Read more articles, download and play the latest PC games for free plus enjoy thousands of user submitted puzzles, quizzes and word games at: http://www.grandmatrix.com
Source: www.isnare.com by Steve Hall
Many kids struggle each and every year at school with that dreaded Friday spelling test. It doesn't get any easier because chances are good that the words just keep getting harder. For many parents, spelling is often a challenge to teach as well. The English language is nothing simple. But, what if you could teach them through the use of a PC game? That would be excellent, wouldn't it?
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More Spelling
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Think about this. The next time your child comes home with that awful list of twenty words they just have to know, you can easily say to them, "Why not go play a game on the computer." Yes, you can do this!
There are a number of games that are just perfect for teaching children the art of spelling. For example, you might want to try a word puzzle game like Beesly's Buzzwords. Or, if Spiderman happens to be your child's favorite character, you have games like Spider-Man 2: Web of Words. In this game, you child can advance through the levels by correctly spelling words. Its fun, rewarding, and most of all, it will help to improve their spelling capabilities.
The spelling games are not boring, dull, and difficult. To the opposite, these games will hold your child's attention so that they can get the knowledge they need. That is what makes these games different. If you are thinking back to your school days and those boring computer programs you were allowed to play and wondering how your technology loving child is going to play with something like that, don't worry. These games are much different. They are made to stimulate your child's knowledge without even allowing them to realize that they are. To them, they are simply playing a Spider Man game.
The value of these games is huge. In fact, there are more than just spelling games, as we will see down the line. They are great ways to feed your child the knowledge that they need without boring them. When it is fun, it will get played more often. The more that it gets played, the more they can learn from it.
So, then, what is the bottom line? You can easily allow your child to play some computer games but of course, you still need to monitor their usage. And, yes, you may have to practice those specific spelling words each week, but it may just get easier as time goes on. Here's a thought. Replace their favorite computer game with one of these for a week. They still get computer time and they still get to play a fun game. But, you get the satisfaction of knowing that they are playing an educational game as well. All in all, we think these games may be a great way to boost confidence and knowledge. Consider them for any age of child. You'll be happy that you did.
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More Spelling
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About the Author: Steve is a member of the GrandMatrix team. They provide a broad range of games, puzzles, articles and reviews. Read more articles, download and play the latest PC games for free plus enjoy thousands of user submitted puzzles, quizzes and word games at: http://www.grandmatrix.com
Source: www.isnare.com by Steve Hall
Saturday, June 8, 2019
Exercise Your Brain: Quick Brain Teasers to Test Your Memory and Thinking Skills
Here's a quick quiz to test your memory and thinking skills, which should work out important parts of your brain. See how you do! (Answers are below).
1. - Name the one sport in which neither the spectators nor the participants know the score or the leader until the contest ends.
2. - What famous North American landmark is constantly moving backward?
3. - Of all vegetables, only two can live to produce on their own for several growing seasons. All other vegetables must be replanted every year. What are the only two perennial vegetables?
4. - What fruit has its seeds on the outside?
5. - In many liquor stores, you can buy pear brandy, with a real pear inside the bottle. The pear is whole and ripe, and the bottle is genuine; it hasn't been cut in any way. How did the pear get inside the bottle?
6. - Only three words in Standard English begin with the letters "dw" and they are all common words. Name two of them.
7. - There are 14 punctuation marks in English grammar. Can you name at least half of them?
8. - Name the one vegetable or fruit that is never sold frozen, canned, processed, cooked, or in any other form except fresh.
9. - Name 6 or more things that you can wear on your feet beginning with the letter "S."
Answers To Quiz:
1. The one sport in which neither the spectators, nor the participants, know the score or the leader until the contest ends: boxing
2. The North American landmark constantly moving backward: Niagara Falls (the rim is worn down about two and a half feet each year because of the millions of gallons of water that rush over it every minute.)
3. Only two vegetables that can live to produce on their own for several growing seasons: asparagus and rhubarb.
4. The fruit with its seeds on the outside: strawberry.
5. How did the pear get inside the brandy bottle? It grew inside the bottle. (The bottles are placed over pear buds when they are small and are wired in place on the tree. The bottle is left in place for the entire growing season. When the pears are ripe, they are snipped off at the stems.)
6. Three English words beginning with "dw": dwarf, dwell, and dwindle.
7. Fourteen punctuation marks in English grammar: period, comma, colon, semicolon, dash, hyphen, apostrophe, question mark, exclamation point, quotation marks, brackets, parenthesis, braces, and ellipses.
8. The only vegetable or fruit never sold frozen, canned, processed, cooked, or in any other form but fresh: lettuce.
9. Six or more things you can wear on your feet beginning with "s": shoes, socks, sandals, sneakers, slippers, skis, skates, snowshoes, stockings, stilts.
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Copyright (c) 2008 SharpBrains
Alvaro Fernandez is the CEO and Co-Founder of SharpBrains.com, which covers the brain games and brain health fields. SharpBrains has been recognized by Scientific American Mind, Newsweek, Forbes. Alvaro holds MA in Education and MBA from Stanford University, and teaches The Science of Brain Health at UC-Berkeley Lifelong Learning Institute. You can learn more at http://www.sharpbrains.com/
Article Source: http://www.upublish.info
1. - Name the one sport in which neither the spectators nor the participants know the score or the leader until the contest ends.
2. - What famous North American landmark is constantly moving backward?
3. - Of all vegetables, only two can live to produce on their own for several growing seasons. All other vegetables must be replanted every year. What are the only two perennial vegetables?
4. - What fruit has its seeds on the outside?
5. - In many liquor stores, you can buy pear brandy, with a real pear inside the bottle. The pear is whole and ripe, and the bottle is genuine; it hasn't been cut in any way. How did the pear get inside the bottle?
6. - Only three words in Standard English begin with the letters "dw" and they are all common words. Name two of them.
7. - There are 14 punctuation marks in English grammar. Can you name at least half of them?
8. - Name the one vegetable or fruit that is never sold frozen, canned, processed, cooked, or in any other form except fresh.
9. - Name 6 or more things that you can wear on your feet beginning with the letter "S."
Answers To Quiz:
1. The one sport in which neither the spectators, nor the participants, know the score or the leader until the contest ends: boxing
2. The North American landmark constantly moving backward: Niagara Falls (the rim is worn down about two and a half feet each year because of the millions of gallons of water that rush over it every minute.)
3. Only two vegetables that can live to produce on their own for several growing seasons: asparagus and rhubarb.
4. The fruit with its seeds on the outside: strawberry.
5. How did the pear get inside the brandy bottle? It grew inside the bottle. (The bottles are placed over pear buds when they are small and are wired in place on the tree. The bottle is left in place for the entire growing season. When the pears are ripe, they are snipped off at the stems.)
6. Three English words beginning with "dw": dwarf, dwell, and dwindle.
7. Fourteen punctuation marks in English grammar: period, comma, colon, semicolon, dash, hyphen, apostrophe, question mark, exclamation point, quotation marks, brackets, parenthesis, braces, and ellipses.
8. The only vegetable or fruit never sold frozen, canned, processed, cooked, or in any other form but fresh: lettuce.
9. Six or more things you can wear on your feet beginning with "s": shoes, socks, sandals, sneakers, slippers, skis, skates, snowshoes, stockings, stilts.
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Gold Box - New Deals Every Hour!
Copyright (c) 2008 SharpBrains
Alvaro Fernandez is the CEO and Co-Founder of SharpBrains.com, which covers the brain games and brain health fields. SharpBrains has been recognized by Scientific American Mind, Newsweek, Forbes. Alvaro holds MA in Education and MBA from Stanford University, and teaches The Science of Brain Health at UC-Berkeley Lifelong Learning Institute. You can learn more at http://www.sharpbrains.com/
Article Source: http://www.upublish.info
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