I promised to show something on the 26th column, so I'm going to do that now. Before I begin, let me do the usual and share the latest version of my spreadsheet. It can be found at: https://onedrive.live.com/redir?resid=2E6EFB80915ED5BD!9250&authkey=!ABMo7pXNYQMmPJg&ithint=file%2cxlsx
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There are six shaded cells, and the only value they can be part of is the only value in the column, the 12. There is one shaded cell in between shaded cells. The rules of the puzzle require continuous segments for each value. If the cell between the shaded cells is left unshaded, the 12 is not continuous. That means the cell in question will have to be shaded.
From here we can do our check for an overlap. I have included an image of the highest and lowest the 12 can go. Once again, we know that the cells at the top are impossible. We can mark those as unshaded.
I think we have done about all we can with the columns for now. Next time, I will look at the rows again.
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