# One Up 8x8 puzzle

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:

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

Final grid:

Obvious deductions:

More obvious deductions:

Continuing:

The solution of this column will prove to be crucial.

Wrapping things up gives:

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

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.

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.

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