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What are the next steps for this Kakuro? I've solved most of it, but there is an area I'm stuck on. Kakuro puzzle

Source: Puzzle Page app

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Look at the rightmost column in the part you haven't solved yet:

11 in four has got to be $1,2,3,5$ in some order. The top one must be $2$ or $4$, so now you know it must be $2$.

Then the $5$ in that column can only be in two places. Trying it in the upper possibility (just below the $2$) leads to a contradiction in the column to the left of that (two cells must be $1$ and $3$, we already have a $4$ above, so the remaining cell must be another $5$, contradiction). So the $5$ is placed, and then everything else should follow easily.

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  • $\begingroup$ Thanks for the hints! The first part is just something you have to know, I suppose. I'll know that for next time when I see 11 in four! The second part is even more difficult I think. Can you expand on it a bit further, why after trying the 5 do you deduce that two cells in the column to the left must be 1 and 3? $\endgroup$
    – Kidburla
    Jun 21 at 21:07
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    $\begingroup$ Alternatively, after determining that the top value in the 27 column is 4, the remaining entries sum to 9, which must be 6+2+1 here, eliminating the bottom 3. $\endgroup$
    – RobPratt
    Jun 21 at 21:51
  • $\begingroup$ @Kidburla 9 in three with a 5 must be 5+3+1 because 9 - 5 = 4 in two must be 3+1. $\endgroup$
    – RobPratt
    Jun 21 at 21:54
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    $\begingroup$ @Kidburla A general principle of Kakuro is that the smallest and largest possible sum-in-n always have just one possibility (like $10$ in four must be $1,2,3,4$ while $30$ in four must be $9,8,7,6$), so do the second smallest and second largest ($11$ in four must be $1,2,3,5$ while $29$ in four must be $9,8,7,5$), then the third smallest and third largest have two possibilities ($12$ in four must be $1,2,3,6$ or $1,2,4,5$ while $28$ in four must be $9,8,7,4$ or $9,8,6,5$). $\endgroup$ Jun 21 at 23:03
  • $\begingroup$ thank you @RobPratt for helping me with the final steps and RandAlThor for your tip about how to spot totals with only one possibility; with these tips I can solve this puzzle and set me in better standing for future Kakuro puzzles! $\endgroup$
    – Kidburla
    Jun 22 at 8:24

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