| ##POTENTIAL SPOILER## I feel like I am either missing something here, or the puzzle is invalid. Because I can think of multiple, yet equally valid solutions to the puzzle after all vowels, as well as rows 1 and 5 are cleared. I spent far too much time on this and eventually looked at the solution. There, it states in item 3--that column 1 must contain either 1,2,3 or just 1,2 since a 4 or higher would force lower numbers to the right. However, we know that there is only one number in row 4--therefore, there could be any number in row 4 without the problem of a higher number to the right of it. Based on the clues available up until this point-- I see no reason why row 4 could not have a number greater than 3 in the first column? For example 1,3,4,8 could be in row 2 and in that order; 2,5,6,7 in row 3; and a 9 could be in row 4. Similarly, row 2 could contain 5,7,8,9; row 3 could then contain 1,3,4,6; and row 4 contain a 2. There are actually about a dozen solutions like this where a number higher than 3 could be in the first column that would seem to be consistent with the clues given up to this point. Since you need to know at least one(if not more) of the numbers before moving on, and since you aren't supposed to need to guess--how do we really know that column 1 must contain either 1,2,3 or 1,2 ? |