Naked Triplets & Quads
Working on the same principle as Naked Pairs, Naked Triplets and Naked Quads can also help us remove candidates (pencil marks) from other cells.
Though not as easy to spot, and also not quite as common, these situations do occur. For example:
See the Naked Triplet? Itís the three cells with only 1, 5 & 9 as candidates.
Because all three cells are in the same house, and because their only candidates are 1, 5, or 9; the actual values of these three cells must be 1, 5 & 9.
For the moment, it does not matter which cell is the 1, which is the 5, or which is the 9. It only matters that we know for sure that 1, 5, & 9 go into them somehow.
Which means none of the other cells in the house could possibly be 1, 5, or 9. Therefore, we can remove those pencil marks from the other cells:
Be careful, though - these guys donít always have all three candidates in all three cells. For example:
Here, we still have three cells in the same house that can only be one of three candidates. Can you find them? Hard to see, aren't they?
They are the middle cell and the two cells on each end. Believe it or not, they make up a Naked Triplet. These cells must end up being the 5, 6, & 8, because together they share only those three candidates. The rule still applies - and you can safely remove 5, 6, & 8 from the other cells.
Naked Quads are even more rare, but they do occur on occasion, so they are at least worth mentioning. See this example:
By the same principal as Naked Triplets and Pairs, the blue cellsí only four candidates are 1, 3, 7 & 9. Therefore any other 1, 3, 7 or 9 elsewhere in the block can be removed.