Mathdoku is a task that challenges you to fill a four by four grid with numbers from 1 to 4, such that each row and column has only one of each number. You need to use the …NRICH - explore the home of rich mathematicsNRICH - explore the home of rich mathematicsKenKen and KenDoku are trademarked names for a style of arithmetic and logic puzzle invented in 2004 by Japanese math teacher Tetsuya Miyamoto, who intended the puzzles to be an instruction-free method of training the brain. The name derives from the Japanese word for cleverness (賢, ken, kashiko (i)). The names Calcudoku and …This Mathdoku belongs to a set, which also contains 4 by 4, 5 by 5 and 6 by 6 grid sizes. If you are considering sending us solutions, we are particularly interested to hear about any elegant strategies you used when you were stuck, and you think are worth sharing. ...This is how I worked out this 3x3 mathdoku: Firstly, I filled in the numbers that are already given to me, 1 and 2. Since they are in the same column, I can deduce that the bottom left corner box would be 3. Now that I know that is 3, I have to minus 1, which is 2.Don't worry though, we've provided a calculator that you can use as much as you like without any penalty to your score. About MathDoku. KenKen players love MathDoku, the best free online version of the popular game. Test your number logic skills in games ranging from easy to hard! Top Categories.MathDoku players also enjoy: See More Games. See All. Crystal Collapse. Arkadium's Bubble Shooter. 10x10. Mahjongg Candy Cane. MathDoku Overview. KenKen players love MathDoku, the best free online version of the popular game. Test your number logic skills in games ranging from easy to hard!The first step with a Mathdoku puzzle is always to enter pencil marks for those cells that don't have many combinations. For example, the top-left cell with the clue '5x' is a great example. There is only way to satisfy that clue, i.e. 1x5 = 5. So we can enter 1 and 5 for the pencil marks for those two cells.Play MathDoku, a variation of Sudoku with math symbols, or try other classic and new games like solitaire, mahjong, and crossword. No download or registration required, just …WELCOME TO MATHDOKU. At MathDoku you can play this highly addicting logic and math puzzle game. It is available in both online and printable formats for free. Are you up for the challenge?. The games at MathDoku are is loosely similar to killer sudoku and based on the same rules of KENKEN™, an educational puzzle invented by Tetsuya Miyamoto in …The first step with a Mathdoku puzzle is always to enter pencil marks for those cells that don't have many combinations. For example, the top-left cell with the clue '5x' is a great example. There is only way to satisfy that clue, i.e. 1x5 = 5. So we can enter 1 and 5 for the pencil marks for those two cells.Among free sudoku games online there are number puzzles which provide additional challenge. This brain-teaser combines rules of the classic sudoku game and Math puzzles. Not only you have to fill in the grid with numbers unique in their row and line, but also meet the condition of each segment separated by thick borders.The first step with a Mathdoku puzzle is always to enter pencil marks for those cells that don't have many combinations. For example, the top-left cell with the clue '5x' is a great example. There is only way to satisfy that clue, i.e. 1x5 = 5. So we can enter 1 and 5 for the pencil marks for those two cells.MathDoku. Es una variante de Sudoku al que se le añaden las operaciones básicas matemáticas (suma, resta, multiplicación y división). No se puede repetir ningún número en la misma fila y columna, y los segmentos marcados con trazos más gruesos han de estar ocupados por números que formen la cifra exacta mediante la operación indicada. KenKen players love MathDoku, the best free online version of the popular game. Test your number logic skills in games ranging from easy to hard! To solve the puzzle you must place 1 to 6, or 1 to whatever the size of the puzzle is, once each into every row and column, while also solving each of the bold-lined regions. Look at the solved puzzle on the left. The 11+ region at the top-left must sum to 11, so the 1+6+4 given here is valid. The 8times; on the top row works because 2×4=8 ... The games at MathDoku are is loosely similar to killer sudoku and based on the same rules of KENKEN™, an educational puzzle invented by Tetsuya Miyamoto in Japan. MathDoku games go by a number of names including KenKen™, KenDoKu™, kenduko, cancan, square wisdom, minuplu, calcudoku, and/or latincalc. MathDoku is a math puzzle similar to Sudoku. Your goal is to correctly fill the entire square field with numbers. Fields come in varying sizes: from 3×3 to 9×9. To fill a cell, select it …To solve the puzzle you must place 1 to 6, or 1 to whatever the size of the puzzle is, once each into every row and column, while also solving each of the bold-lined regions. Look at the solved puzzle on the left. The 11+ region at the top-left must sum to 11, so the 1+6+4 given here is valid. The 8times; on the top row works because 2×4=8 ...Mathdoku is a logic puzzle game where you fill a grid with numbers from 1 to 4 or 5, following certain rules and targets. Learn how to play, download the app, and choose …Instantly play your favourite free online games including card games, puzzles, brain games & dozens of others, brought to you by Daily MailDescription. Welcome to MathDoku! MathDoku is a math puzzle similar to Sudoku. Your goal is to correctly fill the entire square field with numbers. Fields come in varying sizes: from 3×3 to 9×9. To fill a cell, select it (using a keyboard or mouse), then select the number. You can type the number from the keyboard or use the panel buttons.Every Killer Sudoku puzzle only ever has one possible solution, and it can always be reached via reasonable logical deduction. In other words, guessing is never required. Killer Sudoku puzzles on puzzlemix appear at a wide range of sizes and difficulties. Usually they are 6x6, 8x8 or 9x9. In each respective case you must place 1-6, 1-8 or 1-9 ...MathDoku. Learning should be fun and on Wordgames.com you can find lots of games like MathDoku that make practice a joy. Play now one our our best sudoku games! Learn the basic math operations the fun way, with the help of Wordgames.com and MathDoku, in a game that combines mathematics and the classic puzzle experience that sudoku offers.How to Play MathDoku. All the same rules as standard sudoku apply, but segments are now unique to each puzzle instead of always being nonets. This spin on the game tests your arithmetic skills by adding target numbers with operators …Mathdoku Puzzles can be solved by combining the four main mathematical functions of addition, subtraction, multiplication and division. To train the brain the puzzles are offered without any instruction. There are important keys to be found but no fixed starting place and no method of progression that can be learned as a strategy.Mathdoku (Same as KENKEN) is an instruction-free Puzzle for training the brain.As in Sudoku, the goal of each puzzle is to fill a grid with digits –– 1 throu... MathDoku Overview. KenKen players love MathDoku, the best free online version of the popular game. Test your number logic skills in games ranging from easy to hard! Play MathDoku online from USA TODAY. MathDoku is a fun and engaging online game. Play it and other games online at games.usatoday.com. KenKen players love MathDoku, the best free online version of the popular game. Test your number logic skills in games ranging from easy to hard! Daily Extra Large Mathdoku Puzzle Saturday 13th January 2024. Daily puzzle Archive Rules. Difficulty: SCORE: [R]eset Puzzle [S]ave Puzzle Create [P]encil Marks ⚙ Settings Print version Actions: ⎌ ⎌ Mathdoku leaderboard. All-time ...Mathdoku 1.5a APK download for Android. Mathdoku is an arithmetic puzzle that combines elements of sudoku and math.About this game. Mathdoku (known as KenKen, Calcudoku) is an arithmetic puzzle that combines elements of sudoku and math. The rules of Mathdoku are …Play MathDoku and enjoy a a mix of classic sudoku games and math puzzles free online. People in Ukraine wanted peace, but war came to their home. Learn how you can help: ua-aid-centers.comKenKen Mathdoku Challenge - Play Free. KenKen, also known as Mathdoku or Calcudoku, is a math logic puzzle similar to Sudoku. This game is part of the free online brain games collection. To begin, click the Small, Medium, or Large button under the picture of the game. This opens the game in a pop-up window. KenKen players love MathDoku, the best free online version of the popular game. Test your number logic skills in games ranging from easy to hard! Don't worry though, we've provided a calculator that you can use as much as you like without any penalty to your score. About MathDoku. KenKen players love MathDoku, the best free online version of the popular game. Test your number logic skills in games ranging from easy to hard! Top Categories. Jimmy wants to make sure you enjoy the game. He'll adapt to make it a little easier, or a little harder, depending on how you play. Try playing an online chess game against a top chess computer. You can set the level from 1 to 10, from easy to grandmaster. If you get stuck, use a hint or take back the move. When you are ready to play games with ... Calcudoku, a popular Sudoku variant, was originally invented in 2004 by Japanese math teacher Tetsuya Miyamoto. You can play Calcudoku by Razzle Puzzles on your phone and tablet. Enjoy Calcudoku online or in offline mode! For support please contact us at [email protected] or visit RazzlePuzzles.com.For Mathdoku puzzles, you can choose which way round the numbers go. So, in the bottom left we have the clues '3 -' and '3 ÷', it doesn't matter which way round the two numbers go in the cells. (It does of course matter for the general 'Sudoku' rule that each row/column must contain each number once and only once). This is another ... This Mathdoku belongs to a set, which also contains 3 by 3, 5 by 5 and 6 by 6 grid sizes. If you would prefer to work away from the computer, you can print out these grids: Mathdoku grids of difficulty 1, Mathdoku grids of difficulty 2, Mathdoku grids of difficulty 3. For Mathdoku puzzles, you can choose which way round the numbers go. So, in the bottom left we have the clues '3 -' and '3 ÷', it doesn't matter which way round the two numbers go in the cells. (It does of course matter for the general 'Sudoku' rule that each row/column must contain each number once and only once). This is another ...MathDoku Overview. KenKen players love MathDoku, the best free online version of the popular game. Test your number logic skills in games ranging from easy to hard! Play MathDoku instantly online. MathDoku is a fun and engaging Online game from The Independent. Play it and other games from The Independent. MathDoku Overview. KenKen players love MathDoku, the best free online version of the popular game. Test your number logic skills in games ranging from easy to hard! MathDoku is a free online math puzzle game, much like Sudoku, but is more of a challenge to complete. See if you can conquer it today at Dictionary.com! Need a brain challenge? MathDoku adds an extra layer of math to the classic puzzle format. Can you solve this game and get to the AARP Leaderboard? The games at MathDoku are is loosely similar to killer sudoku and based on the same rules of KENKEN™, an educational puzzle invented by Tetsuya Miyamoto in Japan. MathDoku games go by a number of names including KenKen™, KenDoKu™, kenduko, cancan, square wisdom, minuplu, calcudoku, and/or latincalc. The first step with a Mathdoku puzzle is always to enter pencil marks for those cells that don't have many combinations. For example, the top-left cell with the clue '5x' is a great example. There is only way to satisfy that clue, i.e. 1x5 = 5. So we can enter 1 and 5 for the pencil marks for those two cells. MathDoku is a mathematical and logical puzzle based on KenKen™ and loosely similar to sudoku. Puzzlescan be solved by combining the four main mathematical functions of addition, subtraction, multiplication and division. To train the brain the puzzles are offered without any instruction. The first step with a Mathdoku puzzle is always to enter pencil marks for those cells that don't have many combinations. For example, the top-left cell with the clue '5x' is a great example. There is only way to satisfy that clue, i.e. 1x5 = 5. So we can enter 1 and 5 for the pencil marks for those two cells. Server time: Wednesday 24 April 2024, 3:20:38 Central European Time. Page processing time: 0.045 sec. Page load time sec. sec.MathDoku players also enjoy: See More Games. See All. Mahjongg Solitaire. Arkadium's Bubble Shooter. Mahjongg Candy. Block Champ. MathDoku Overview. KenKen players love MathDoku, the best free online version of the popular game. Test your number logic skills in games ranging from easy to hard!Play MathDoku and enjoy a a mix of classic sudoku games and math puzzles free online. People in Ukraine wanted peace, but war came to their home. Learn how you can help: ua-aid-centers.comA simple KenKen puzzle, with answers filled in as large numbers. KenKen and KenDoku are trademarked names for a style of arithmetic and logic puzzle invented in 2004 by Japanese math teacher Tetsuya Miyamoto, [1] who intended the puzzles to be an instruction-free method of training the brain. [2] The name derives from the Japanese …How To Solve Kenken - A 5x5 Puzzle in 5 Minutesalso called Kendoku, Calcudoku and Mathdoku KenKen and KenDoku are trademarked names for a style of arithmetic... MathDoku is a mathematical and logical puzzle based on KenKen™ and loosely similar to sudoku. Puzzlescan be solved by combining the four main mathematical functions of addition, subtraction, multiplication and division. To train the brain the puzzles are offered without any instruction. Jimmy wants to make sure you enjoy the game. He'll adapt to make it a little easier, or a little harder, depending on how you play. Try playing an online chess game against a top chess computer. You can set the level from 1 to 10, from easy to grandmaster. If you get stuck, use a hint or take back the move. When you are ready to play games with ... When you start this Mathdoku app, The Back-Key of your Samsung phone becomes inoperative.. (when you turn Mathdoku off, the back-key works again). you need the back-key in order to make … Welcome to Puzzle Baron's Calcudokus! Whether you know them as Calcudoku, Mathdoku or KenKen TM, we've got thousands and thousands of unique puzzles here for you to solve. You can play for fun, or register a free account and compete against other players for the Calcudoku Hall of Fame ! Rules For Playing KenKen® The numbers you use in a KenKen puzzle depend on the size of the grid you choose. A 3 x 3 grid (3 squares across, 3 squares down) means you use the numbers 1, 2, and 3.MathDoku. MathDoku, known also under the name 'KenKen', is an interesting grid game. The rules are in a way similar to the Sudoku, however, you are also required to put a bit more thought into it as it requres you do simple maths. Like in the Sudoku, you have to fill each of the columns and rows with the numbers 1 to n, where n is the length of ...MathDoku Overview. KenKen players love MathDoku, the best free online version of the popular game. Test your number logic skills in games ranging from easy to hard! Play MathDoku instantly online. MathDoku is a fun and engaging Online game from Evening Standard. Play it and other games from The Evening Standard.Mathdoku is a mathematical and logical puzzle loosely similar to sudoku. It was invented by a Japanese mathematics teacher Tetsuya Miyamoto. The objective is to fill the grid in with the digits 1 … The games at MathDoku are is loosely similar to killer sudoku and based on the same rules of KENKEN™, an educational puzzle invented by Tetsuya Miyamoto in Japan. MathDoku games go by a number of names including KenKen™, KenDoKu™, kenduko, cancan, square wisdom, minuplu, calcudoku, and/or latincalc. MathDoku is a mathematical and logical puzzle based on KenKen™ and loosely similar to sudoku. Puzzlescan be solved by combining the four main mathematical functions of addition, subtraction, multiplication and division. To train the brain the puzzles are offered without any instruction. See full list on mathdoku.com Mathdoku grids are a motivating context for learners to develop fluency with number bonds, and factors and multiples, as well as providing an opportunity to reason mathematically. Possible approach. The 4 by 4 version of this problem featured in the NRICH Primary and Secondary webinar in October 2022.About this game. Mathdoku (known as KenKen, Calcudoku) is an arithmetic puzzle that combines elements of sudoku and math. The rules of Mathdoku are …Mathdoku is a mathematical and logical puzzle loosely similar to sudoku. It was invented by a Japanese mathematics teacher Tetsuya Miyamoto. The objective is to fill the grid in with the digits 1 …Mathdoku (Same as KENKEN) is an instruction-free Puzzle for training the brain.As in Sudoku, the goal of each puzzle is to fill a grid with digits –– 1 throu... Printable 4 by 4 difficult level MathDoku, KenKen like, math puzzles for kids. Click puzzle below for free download. Click puzzle above for free download. Our printable logic and number puzzles are based on Japanese Nikoli puzzles, such as Sudoku, Kakuro and many more. Many of our puzzles involve and stimulate math skills. Our printable logic ... Printable Mathdoku Puzzles. At PuzzleAndBrains.com we have hundreds of printable Mathdoku math puzzles for you. Mathdoku puzzles follow the same rules as the …WELCOME TO MATHDOKU. At MathDoku you can play this highly addicting logic and math puzzle game. It is available in both online and printable formats for free. Are you up for the challenge?. The games at MathDoku are is loosely similar to killer sudoku and based on the same rules of KENKEN™, an educational puzzle invented by Tetsuya Miyamoto in …MathDoku is a logic and arithmetic game that challenges your math skills and requires you to find a mathematical solution using the operator and target in each cage. Choose from … The first step with a Mathdoku puzzle is always to enter pencil marks for those cells that don't have many combinations. For example, the top-left cell with the clue '5x' is a great example. There is only way to satisfy that clue, i.e. 1x5 = 5. So we can enter 1 and 5 for the pencil marks for those two cells. MathDoku gebruikt code.google.com voor het hosten van de broncode repository. Je kunt de broncode ophalen, en direct beginnen met hacken. Localisatie. Als je kunt babbelen in een taal die MathDoku nog niet spreekt, kun je een localisatie opsturen die dan in het spel zal worden opgenomen. Lees translations voor meer informatie. To solve the puzzle you must place 1 to 6, or 1 to whatever the size of the puzzle is, once each into every row and column, while also solving each of the bold-lined regions. Look at the solved puzzle on the left. The 11+ region at the top-left must sum to 11, so the 1+6+4 given here is valid. The 8times; on the top row works because 2×4=8 ...MathDoku players also enjoy: See More Games. See All. Mahjongg Solitaire. Arkadium's Bubble Shooter. Mahjongg Candy. Block Champ. MathDoku Overview. KenKen players love MathDoku, the best free online version of the popular game. Test your number logic skills in games ranging from easy to hard!The first step with a Mathdoku puzzle is always to enter pencil marks for those cells that don't have many combinations. For example, the top-left cell with the clue '5x' is a great example. There is only way to satisfy that clue, i.e. 1x5 = 5. So we can enter 1 and 5 for the pencil marks for those two cells.Mathdoku + Calcudoku is arithmetic and logic puzzle similar to Sudoku and based on rules of Kendoku ® and KenKen ® Fill the grid so that each row and column only have one of each available number (1 to N). The table is separated into groups that are calculated together. Each group's total is dis…MathDoku is a logic and arithmetic game that challenges your math skills and requires you to find a mathematical solution using the operator and target in each cage. Choose from …A collection of videos used on the nrich.maths.org websiteMathdoku (Same as KENKEN) is an instruction-free Puzzle for training the brain.As in Sudoku, the goal of each puzzle is to fill a grid with digits –– 1 throu... The first step with a Mathdoku puzzle is always to enter pencil marks for those cells that don't have many combinations. For example, the top-left cell with the clue '5x' is a great example. There is only way to satisfy that clue, i.e. 1x5 = 5. So we can enter 1 and 5 for the pencil marks for those two cells. WELCOME TO MATHDOKU. At MathDoku you can play this highly addicting logic and math puzzle game. It is available in both online and printable formats for free. Are you up for the challenge?. The games at MathDoku are is loosely similar to killer sudoku and based on the same rules of KENKEN™, an educational puzzle invented by Tetsuya Miyamoto in …The first step with a Mathdoku puzzle is always to enter pencil marks for those cells that don't have many combinations. For example, the top-left cell with the clue '5x' is a great example. There is only way to satisfy that clue, i.e. 1x5 = 5. So we can enter 1 and 5 for the pencil marks for those two cells.Rules For Playing KenKen® The numbers you use in a KenKen puzzle depend on the size of the grid you choose. A 3 x 3 grid (3 squares across, 3 squares down) means you use the numbers 1, 2, and 3.The first step with a Mathdoku puzzle is always to enter pencil marks for those cells that don't have many combinations. For example, the top-left cell with the clue '5x' is a great example. There is only way to satisfy that clue, i.e. 1x5 = 5. So we can enter 1 and 5 for the pencil marks for those two cells.Daily Extra Large Mathdoku Puzzle Saturday 13th January 2024. Daily puzzle Archive Rules. Difficulty: SCORE: [R]eset Puzzle [S]ave Puzzle Create [P]encil Marks ⚙ Settings Print version Actions: ⎌ ⎌ Mathdoku leaderboard. All-time ...Mathdoku grids are a motivating context for learners to develop fluency with number bonds, factors and multiples, as well as providing an opportunity for learners to reason mathematically. Having experience of creating chains of reasoning provides an excellent basis on which to create proofs. Possible approach9 by 9 MathDoku Puzzles. Fill in the numbers 1 to 9 in such that each number appears only once in each row and colum. The grid is divided in so called cages with operators and target numbers. The numbers in each cages must produce the target number by using the operator of that cage. 2÷.
MathDoku players also enjoy: See More Games. See All. Mahjongg Solitaire. Arkadium's Bubble Shooter. Mahjongg Candy. Block Champ. MathDoku Overview. KenKen players love MathDoku, the best free online version of the popular game. Test your number logic skills in games ranging from easy to hard!. Pikes peak ymca
Get Mathdoku old version APK for Android. Download. About Mathdoku. English. Endless and addictive mathbased puzzle fun. Try to solve the math based puzzles while keeping these rules in mind... The math for each group should be correct. A value can not reappear in the same row.Mathdoku is a free puzzle game available on Android developed by Verschueren Geert. The game is categorized under Puzzle games and is a perfect combination of math and puzzles. The objective of the game is to solve math-based puzzles while keeping certain rules in mind. The math for each group should be correct, a value … How to Play MathDoku. All the same rules as standard sudoku apply, but segments are now unique to each puzzle instead of always being nonets. This spin on the game tests your arithmetic skills by adding target numbers with operators in the top left corner of each segment. The numbers in the segment must produce the exact target based on the ... MathDoku players also enjoy: See More Games. See All. Crystal Collapse. Arkadium's Bubble Shooter. 10x10. Mahjongg Candy Cane. MathDoku Overview. KenKen players love MathDoku, the best free online version of the popular game. Test your number logic skills in games ranging from easy to hard!Mathdoku is a task that challenges you to fill a four by four grid with numbers from 1 to 4, such that each row and column has only one of each number. You need to use the …This Mathdoku Editor allows you to create your own Mathdokus. Clicking on the purple cog in the top right corner allows you to choose the grid size. If you are not familiar with the Mathdoku Editor, you may like to start by watching this introductory video. Once you have created your own Mathdoku, click on the 'Share' button and paste the code ...For Mathdoku puzzles, you can choose which way round the numbers go. So, in the bottom left we have the clues '3 -' and '3 ÷', it doesn't matter which way round the two numbers go in the cells. (It does of course matter for the general 'Sudoku' rule that each row/column must contain each number once and only once). This is another ...For Mathdoku puzzles, you can choose which way round the numbers go. So, in the bottom left we have the clues '3 -' and '3 ÷', it doesn't matter which way round the two numbers go in the cells. (It does of course matter for the general 'Sudoku' rule that each row/column must contain each number once and only once). This is another ...Introducing Mathematical Sudokus. We are introducing a variation of the well-known Sudoku, by including mathematical constraints which challenge students to apply their knowledge of the four operations. For each grid size, there are four different puzzles, at each of three levels of difficulty, so plenty for your students to get stuck into! To ...How To Solve Kenken - A 5x5 Puzzle in 5 Minutesalso called Kendoku, Calcudoku and Mathdoku KenKen and KenDoku are trademarked names for a style of arithmetic...To solve the puzzle you must place 1 to 6, or 1 to whatever the size of the puzzle is, once each into every row and column, while also solving each of the bold-lined regions. Look at the solved puzzle on the left. The 11+ region at the top-left must sum to 11, so the 1+6+4 given here is valid. The 8times; on the top row works because 2×4=8 ...MathDoku (also known as KenKen) is a game similar to Sudoku, but with different rules involving maths. Why one solver for both? I had made a Sudoku solver, with the rules incorporated inside the solving algorithm. When I heard of MathDoku (via F-Droid), I could not do the same because there are different rules.About this game. Mathdoku (known as KenKen, Calcudoku) is an arithmetic puzzle that combines elements of sudoku and math. The rules of Mathdoku are … Jimmy wants to make sure you enjoy the game. He'll adapt to make it a little easier, or a little harder, depending on how you play. Try playing an online chess game against a top chess computer. You can set the level from 1 to 10, from easy to grandmaster. If you get stuck, use a hint or take back the move. When you are ready to play games with ... How To Solve Kenken - A 5x5 Puzzle in 5 Minutesalso called Kendoku, Calcudoku and Mathdoku KenKen and KenDoku are trademarked names for a style of arithmetic...This Mathdoku belongs to a set, which also contains 3 by 3, 4 by 4 and 6 by 6 grid sizes. If you are considering sending us solutions, we are particularly interested to hear about any elegant strategies you used when you were stuck, and you think are worth sharing.Play tons of games and quizzes at USA TODAY. With a wide variety of online web games there's something for everyone.Play the best free games on MSN Games: Solitaire, word games, puzzle, trivia, arcade, poker, casino, and more! MathDoku is a mathematical and logical puzzle based on KenKen™ and loosely similar to sudoku. Puzzlescan be solved by combining the four main mathematical functions of addition, subtraction, multiplication and division. To train the brain the puzzles are offered without any instruction. The first step with a Mathdoku puzzle is always to enter pencil marks for those cells that don't have many combinations. For example, the top-left cell with the clue '5x' is a great example. There is only way to satisfy that clue, i.e. 1x5 = 5. So we can enter 1 and 5 for the pencil marks for those two cells..