Sudoku World Championship exercise

I recommend that those coming to the Sudoku World Championship solve the German Masters Sudoku. You can find them on the page: https://logic-masters.de/DSM/archiv.php From there, I recommend choosing the range 2012-2018 and solving the Qualification puzzles and Endrunde. Anleitung means instructions and there is no point in solving them. After clicking on the corresponding year, you need to select the "Puzzle" button on the right. And from there you will get the tasks. I do not recommend 2019, because in my opinion the tasks there are unreasonably difficult. Then you can do the 2019 qualification.

I'm trying to share some tricks and suggestions here that could be helpful when solving sudoku. 2.3. 0-9 Kropki sudoku - if you haven't solved kropki, then I recommend avoiding this task. But if you want to solve it, it's important to remember that one number is missing in each row and column. I recommend marking if it's clear from a row or column which number is missing. Therefore, the rest must be there. 2.4. Anti Clone - I recommend taking crayons with you and coloring similar shapes the same color and different shapes a different color. Thanks to this, you get a very good picture in front of your eyes. Different numbers must be in the same color. 2.8. Odd/even stars - I recommend drawing circles around even numbers and starting to solve sudoku so that if you are sure that it is an even number, then draw a circle around it and if you are sure that it is odd, then make a dot. It may happen that this way it is possible to mark all the even numbers in the sudoku and then you need to solve the even/odd sudoku, which is probably very easy. I recommend leaving the classic ones for last, because there are enough tasks here that should not be too unfamiliar. But it is still advisable to solve the classic ones, because they come out clearly faster compared to the rest.

3.5 and 3.6 Thermo sudoku. For longer thermometers, I recommend marking all the options. Then you will have a good overview of what can and cannot be there. (For example, if there is a 7-digit thermometer, you can write out the following options from the beginning: 123, 234, 345, 456, 567, 678, 789). And probably some given number will start to reduce these options somewhere. 3.7 and 3.8 Distance sudoku. It makes sense to start with longer distances and mark all possible options if it is only possible to place them in 2 or 3 different places in a row or column. 3.9 and 3.10 Biggest neighbours. It is difficult to give recommendations, because I have not solved it myself. But one thing I do is that if the condition is 100% fulfilled for an arrow that it points in the direction of the largest number, then I put a cross on the arrow. For example, if it is next to the number 9 and all other neighboring squares have already excluded 9, then it is guaranteed that it points towards the largest number. In Sudoku, it is very important to note all arrows where this condition is not 100% fulfilled and if crosses are drawn, then arrows without crosses stand out better.

4.1 Circles sudoku. I definitely recommend marking the variants there if the north-south and east-west directions are known. For example, in the example problem, the circle in the middle above cannot be located so that 4-1 is in the north-south direction, because the circle on the left has 4 and 1 in different directions. Consequently, 4-1 is in the east-west direction and 2-5 is in the north-south direction. The second trick is that you usually have to look for such connections. Some numbers in some direction affect some other circle and it is probably possible to determine which numbers are in which direction. 4.2. Double kropki. I recommend noting that in this problem, even and odd numbers are distinguished from each other. If you try to put an even number somewhere, for example 4. Then the odd numbers generally do not affect it. Secondly, you need to remember 4-1 and 2-8. In such cases, you need to use a black dot. 4.3. Greater than kropki. You have to look for longer chains. but otherwise it's like a regular kropki (in places where there is no inequality sign) - that is, adjacent numbers must not be consecutive and differ by 2x. 4.4. Hidden skyscrapers. It is important to remember that all arrows are given. Possible variants must be written on the arrows. Arrows near the edge of the Sudoku and pointing towards the edge must have a small number, because it cannot be greater than the number of squares in the direction of the arrow. 4.6. Little unique killer. Usually such tasks (especially German ones) are built so that somewhere on the diagonal there is a maximum or minimum possible sum (if you take into account all the numbers that you have already written somewhere in the grid). For example, on the right edge no. 35 can only be 5 6 7 8 9. It is important to remember that numbers on the marked diagonal must not be repeated here. 4.7. Quadruple. I recommend marking out the variants and then looking for overlapping parts. Apparently, sudoku that everyone should be able to do. 4.8. Star product. If you want to solve it, it is basically solved by converting all the numbers to prime numbers. For example, in the case of 240, I usually do this by first writing out 2.5 (then 24 remains) and then 2,2,2,3. If this 240 consists of three stars, then this product can be 5*8(2,2,2)*6(2,3) Another trick is, for example, to look for the locations of the number 5. 5 can only be in a place where there is a number ending in 0 or 5 in both directions. 4.9. Sum by X. It is recommended to write out possible variants in the gray boxes, how many numbers this sum can consist of (for example, 8 can consist of either 1,2 or 3 numbers). In addition, you need to use the trick that if the sum of 35 consists of 7 numbers, then the last 2 numbers must sum to 10. (because when you add up the numbers 1-9, the result is 45). 4.10. Three is a crowd. This is a very systematic sudoku. Circle the clue that is true and cross out the clue that is false. At first, look for places where the same number is represented 2 times in the same box. Consequently, one of them is false and the other is true. All the other same numbers in that direction are true and you need to circle them. If you find a place where two numbers are already circled. Then you need to cross out the third one and immediately circle all the other same numbers in the same direction. If it is no longer possible to identify true and false numbers, then you need to start solving the outside sudoku with the numbers that are circled. And then the remaining true-false numbers should also hatch.

5.1. Alternating stripes. I have drawn circles around the ones where I know there is a large number. This helps with the solution. 5.3. Between. No. 1 and 9 cannot be on a line. The numbers in the circles cannot be consecutive. It is difficult to give other tricks. 5.4. Cloned strands. If possible, you need to get the directions. And then, if necessary, you need to start writing out possible variants square by square and then later start crossing them out if they are excluded somewhere. 5.5. Counting neighbours. In my opinion, you need to pay as much attention to numbers 2, 3 and 4 as possible. Also, to those shapes that are either somewhere in the middle or on the edge of the box and write in the possible variants there. Generally, in the final phase of the solution, the numbers 5, 6, 7, 8 and circles come into play. 5.7. German whispers. This is essentially a similar sudoku to alternating stripes, because large and small always alternate. If possible, circle the large numbers and also write the possible variants on the line. 5.8. Missing arrow. The important thing here is that the circle is always at the end of the line. It is difficult to give other recommendations. You should practice arrow sudokus, which can also be found from German masters. 5.9 Mathrax. It helps if you mark the even-even numbers if you know them for sure. And then it also helps if you write all the possible variants in some places (where there is a hint). 5.10. Odd-even bridge. The length of the line gives you the sum of the numbers in the circles. And there are not many variants left. If you wish, you can also mark the even and odd numbers in sudoku, but this may not always be useful. 5.11. Palindrome. If there are longer lines, I recommend marking the middle of the line somehow. For very long lines, I recommend marking every 5th cell in some way so that it is clear which number it is in. This helps. And you should write the possible variants on the lines so that you look at the squares that must contain the same number at the same time. 5.12. Schematic diagram. Essentially consecutive sudoku. Just presented differently. 5.13. Search 9. I recommend drawing circles around the 9s. At first, you should start looking for possible locations without 9s and write possible numbers on the arrows. Most of the 9s should come out and you may have to solve a little sudoku to get the last 9s.

GT Consecutive. Basically non-consecutive sudoku. This is an important thing to keep in mind when starting to solve hybrid sudoku. You should look for longer chains and find what options there are to complete them. Max Ascending. I usually just draw some lines in places where there is a longer consecutive sequence. Another option is to write inequality signs in some location where you know which way the sign is, but it is not possible to write a clear number there. Round off. At first, you have to write 2 possible options that can be there in all the squares above the tens. For example, is is number 40, then the tens can be 3 or 4. This makes solving much easier. Full Rank. At first, you have to go over the squares on the edge and write down as many numbers as possible. It is known that number 1 is when the clue is either 1,2,3 or 4. Number 2 goes where the clue is 5,6,7,8... etc. Once this is done, the solution is usually started from the clues in the corners and the next numbers in 9-digit numbers have to be found. I recommend crossing out or not circling the clues where the 100% condition is already met. There is no need to follow them any further. XIVI . The possible variants of VI are 15 and 24. The possible variants of XI are 29, 38, 47, 56. It is worth marking them out and solving them accordingly. If no clue is given, the combinations given above must not occur. Descriptive pairs. I recommend writing out the variants. There are 2 variants in each row with a clue. If you manage to find a number that matches the clue, I recommend crossing out the clue, it is no longer necessary to follow it. Mathrax - mark even/even. Write out the possible variants in the squares with clues. Pointing evens. It may help to mark out even and odd numbers. It may help to rule something out. Point to next. It's hard to give good tricks. It's worth keeping an eye on what's behind the arrow. This helps to rule out variants on the arrow. Next to 9. I usually circle the 9s. It helps to get the big picture better. In general, it is recommended to solve these problems in order and start with the ones preceded by a sudoku that you definitely don't want to solve. Therefore, it is important that you solve sudokus with similar rules in order. For example, I imagine that I will most likely start with a 6.6 sudoku, since full rank can be unpleasant.

7.3. 1-5-9 sudoku. At first, go over all 1,5 and 9 in the entire sudoku so that the first gray squares are definitely filled. Otherwise, solving and practicing helps. Actually, a relatively easy sudoku. 7.4. Disjoint groups. Every time you want to put a number in a box, immediately check all the other boxes to see if that number already exists in the same position or not. It is difficult to recommend others. You can practice this on the fed-sudoku.eu page under alternatives. 7.5. Biggest neighbour. Explanation for tasks 3.9 and 3.10. 7.6. Double scattered. I recommend marking the numbers that have already been used in individual squares next to them. It helps a little with solving. Otherwise, similar to a special shape. 7.8. Equal. If possible, I recommend finding out which numbers can fill these areas. It is also often possible to say how many even and odd numbers there are in a grid. For example, in three there must be one even and 2 odd numbers (E,O,O). In four (O, O, E, E). In five (E, E, E, O, O). the numbers must not be repeated. 7.10. Triangle sums you should try to find some longer chains that are formed from adjacent triangles. It also helps if you start excluding the number 9 from different boxes. 9 cannot be next to a triangle, because it is additive.

I'm skipping the team rounds for now. We can also consult there during the competition if necessary and we have to choose what someone can do and what someone likes. But round 11 then: 11.3. 0-9 Frame. If 3 sums are given, you will find out which number is missing. If 2 sums are given, it may happen that there are not many ways to find the third sum. It is worth recalculating in any case. In general, however, it is not recommended for those who do not have much experience with mathematical sudoku. 11.4 Battenburg. Mark the even (circle around, for example) and odd (dot, for example). It is possible that this sudoku will be solved in such a way that at first most of the even-odd numbers come out and then it can be solved as an even-odd sudoku. Tip: If a chess square is marked somewhere (in the middle of the 4 squares) and if there happens to be, for example, one even and one odd number next to it, then it is possible to determine the parities of the 4 squares. In other words, there must not be another chess grid where there is no sign. (Hopefully it is understandable. If not, you can also post here in the forum and ask). 11.5 Chaos=unusual 11.6 Edge product. I recommend solving. Apparently 30 points are not difficult. You just need to know the multiplication table. 11.7 First seen odd/even. Mark out the even and odd numbers even if you don't know exactly what the number should be. This helps a lot. 11.8 Magic square. A magic square is created when there is 5 in the middle and the even numbers are in the corners. It is not possible to create a magic square otherwise. More accurate solutions are created by calculation, because the sum in all directions must be 15. If you know these things, then usually a super easy sudoku. 11.9 Mini-Diagonals. A bit like Killer sudoku. The same principles must be used when solving. 11.10. Serbian Frame. I usually draw lines with a colored pencil in the rows and columns that are taken into account when creating the sums. This gives a great visual picture. Then it's important to know how good your calculation skills are with the numbers 1-9.

Basic truth 1 2 3 4 5 6 7=28 12.1A Chaos outside sums. If the sums are given at two ends, then it is also possible to figure out the sum of the three numbers between them. 12.1B Toroidal consecutive. I recommend coloring some areas (those that go over the edge to the other side). This gives a better overview. 12.1C Scattered Rank. I recommend marking the possible variants. For example, if there is a 4-digit figure, then in position 1, there can be either 1,2,3 or 4. In position 2 = 2,3,4,5 In position 3 = 3,4,5,6 In position 4 = 4,5,6,7 If the figure is larger, then there are fewer variants. 12.2A Even Sandwich. Mark out even and odd numbers. check whether there are still 3 even numbers (2,4,6) in each row and column. I would like to point out that if there is an even number somewhere and in this row, for example, a "-" is given as a hint, then the next square cannot be even. (Otherwise, the number would be between two even numbers) If the hint is an even number, then all even numbers must be in a row. 12.2B Toroidal Odd. I recommend making the transition shapes colored. It simplifies solving. 12.2C Scattered ordering. I recommend writing out the variants for the first position of all 2-digit numbers that can be there. First, write 1 next to hint no. 1. If you can also write 1 next to hint no. 2, then write 1 there too. If you can't, then write 2 there. Then take hint no. 3. If you wrote 1 for no. 2, then check if you can also write 1 next to no. 3. If not, then write 2. If you can't write 2 either, then write 3. And so on, you should go through all the hints and write the minimum possible numbers in them. And then you go back and start at 7. Then you have to mark the largest possible numbers that can go in them. Once you've gone through both, you'll have entered the maximum and minimum numbers in each box. This gives you a lot of additional information. From there it should be easier.

13.1A Numbered Rooms. Cross out the condition that is met. It is worth solving this problem 3-4 times to get the feel. It is actually not a difficult problem. 13.1B Skyscrapers. Cross out the clues that are met. Try starting with the number 9 and then with the number 8, etc. Often there are not many ways to place the number 9. 13.2A X-sums. Write out in the first square what options can be there. When you have found what fits there, I recommend drawing a line to indicate the extent to which the numbers must be added to get the desired sum. Also note that if, for example, the sum of 5 numbers is 25, then the sum of the remaining 4 numbers must be 20. 13.2B Little Killer. Here the numbers may repeat. Otherwise, more detailed tips are in point 4.6. 13.3A Outside parity. Mark out the even and odd numbers. This makes solving the puzzle much easier. For example, if the clue is 2 and the third number is even, then you know that the first 2 are even. Cross out the clue that is filled in (read: for example, the even and odd numbers in this direction are marked, which are important for this clue) 13.3B Position. Cross out the clues that are filled in. This helps to pay attention to the clues that are not yet filled in and which may be important for solving. 13.4A Edge product. A simple multiplication table. 13.4B Frame. 2 given sums in both the row, column and box provide the opportunity to calculate the third missing sum. NB!!!! In any case, I recommend starting with either Outside-parity & Position sudoku, as it is the cheapest and probably easier to grasp. Edge product & frame could also be reasonable. In the case of the remaining 2, these are probably sudokus where it is difficult to find the beginning or connections.