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Rodolfo Kurchan created a wonderful new grid puzzle called One Up that you can play on his website. There is one main rule:

Each horizontal and vertical sequence of N cells between walls, must contain every number between 1 and N, in some order.

For example, here are the possible sequences in the following grid:

enter image description here enter image description here

Here is puzzle #39 from Rodolfo's collection. Some cells have already been filled. Can you solve it? The solution is unique.

enter image description here

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2 Answers 2

5
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Final grid:

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Obvious deductions:

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More obvious deductions:

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Continuing:

enter image description here The solution of this column will prove to be crucial.

Wrapping things up gives:

enter image description here

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  • $\begingroup$ I apologize profusely in advance for my... aggressive marking practices. $\endgroup$
    – Sny
    Commented May 1 at 13:03
  • $\begingroup$ Wow you sniped me by a long shot, how did you solve it so quickly! $\endgroup$
    – PDT
    Commented May 1 at 13:35
  • $\begingroup$ thank you :) probly my agressive marking $\endgroup$
    – Sny
    Commented May 1 at 13:50
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Just an addendum to the solution above.

Silly, but I first missed that singles can be filled with 1's, so I started in a completely different but imho interesting way.

Since there are no 6- or 7-lines, all 6's, 7's and 8's must be at the intersection of 8-lines. If you mark them you quickly see they must all be filled. This leads to a number of easy deductions.

enter image description here

If then you mark the cells that can be 5, the intersections of a 5-lines with a 5- or 8-lines, you can easily place a number of 5's.

enter image description here

With this start (and finally placing the single 1's) the rest can be solved without much difficulty.

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  • 1
    $\begingroup$ Ahem puzzling.stackexchange.com/a/126301/62272 please read the comments $\endgroup$
    – PDT
    Commented May 1 at 19:41
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    $\begingroup$ I disagree with that comment. I believe the path to the solution is much more interesting than the solution itself. $\endgroup$
    – Florian F
    Commented May 1 at 19:50

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