![]() It could happen that, for example, one cell has 3 values and two cells have 2 values, but it is important that there are N different numbers in N different cells altogether. NB: What’s important to notice is that each of the marked cells has only two pencilmark values, but there are altogether 3 different numbers there. So, what you are looking for are “n” numbers that are candidates in precisely “n” cells that fall onto the same nonet or column or row. This is essentially the same technique as the previous one, except that you take more than two cells at a time. Therefore, we remove numbers 7 and 8 from the candidates list in row 9. In this case – there is nothing to remove from nonet 7 because all other cells are already solved.īut, since those two cells also both belong to row 9, there are candidates that can be removed from that row. When you find such two cells and they belong to the same row or column or nonet – you can eliminate those two numbers from other cells in that area. So, two numbers in two cells and no other candidates for those two cells – that’s a naked pair. These numbers are “naked” – there are no other candidates for those two cells except two of them. In nonet 7, we know that numbers 7 and 8 must go into R9C1 and R9C2. So, like all remaining techniques, this technique doesn’t actually solve a cell – it only removes some candidates which then helps you in the solving process. It can also work the other way – just exchange words row and nonet and you’ll get it. In other words, you make an intersect of row 2 and nonet 2 on one particular value and remove that value from the remainder of that nonet. Whichever one of them ends up being 8, number 8 will be eliminated from the rest of nonet 2. In row 2, number 8 can appear only in R2C4 and R2C5. We again focus on nonet (“box”) 2 and row 2. BOX BREAKS (aka “row/column and nonet interactions”) they are not in the same column, row nor nonet as that cell).įor each of the remaining 3 techniques, I will be coming back to this image.ģ. For each unsolved cell, pencil in all the numbers that are still possible candidates for that cell (i.e. If we keep applying “naked” and “hidden” singles, we come to this stage:Īlright, now we must start using pencilmarks. Therefore, R1C4 = 2 – it’s a “hidden single”, because potentially there are other candidates for this cell (4, 7 and 9) and number 2 is hidden amongst them. When you look at nonet 2, there is only one cell that is not covered with red lines – it’s R1C4, so this is the only place in nonet 2 where number 2 can go into. – R5C5 = 2, so number 2 can’t go anywhere in C5. – R3C3 = 2, so number 2 can’t go anywhere in R3 – R2C7 = 2, so number 2 can’t go anywhere in R2 Red lines indicate where number 2 can’t go: Now, focus on number 2 in the top part of the puzzle. Having applied “naked singles” a few times, we come to this position: (it’s “naked” because it’s the only number that can go into one cell) Therefore, R5C3=7 and this is a naked single. Numbers 3, 4 and 6 are in the same row so they can’t go into that cell either.įinally, number 8 is in the same column, so the only remaining number is 7. Numbers 1, 2, 5 and 9 are in the same nonet so they can’t go into that cell. Have a look at row 5, column 3 (from now on, this will be marked as simply R5C3). I’m sure you know this method, but lets clearly explain it anyway. Perhaps you’ve already seen this particular puzzle: I will be using one classic Sudoku puzzle in which I will demonstrate how each of the techniques contributes to the final solution. Make sure you fully understand them before you attempt to solve the more difficult puzzles. These techniques are used in ALL sudoku puzzles – Classic, Killer, Samurai and others. Most of you are already familiar with these, but for those who aren’t – I’d like to show my explanation. ![]() It’s about time I finally explained the basic (and most common) Sudoku solving techniques.
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