Puzzle 257 (Numberlink)

This is a Numberlink puzzle.

Puzzle 257

Puzzle 257

I knew I could solve these pretty well, but this weekend I started wondering if I could learn to construct them too. I don’t know how often I’ll be posting them, but here’s my first attempt at one.

I think nikoli might have a restriction that any 10 by 10 they publish can use at most 8 pairs, since I can’t remember ever seeing a 9 in one of their puzzles that size. But considering how hard this type is to construct and that it’s my first try, I’m okay with taking some liberties.

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10 Responses to “Puzzle 257 (Numberlink)”

  1. Scott Handelman Says:

    Took some playing with the bottom left, but everything finally fell into place.

  2. Georgi Says:

    I did this on Paint with no erasing necessary 🙂 I’m sure your post the other day helped.
    I hope you do get good at constructing these, I can only imagine what a horrific, giant nightmare of a puzzle you might one day bring us.

  3. yy Says:

    Surprisingly easy. I did this with no erasing and ordered numerically, though I did even attempt to solve logically, or even logically assuming there is a solution. The fact that the puzzle is “crowded” with clues, definitely didn’t hurt.

    First step, intuition, somehow worked immediately and correctly for this puzzle.

    I’ll try to reconstruct the steps of this intuition.

    * [1] can’t go into the corner. Or around other numbers.

    * [2] can’t go through middle.

    * [4],[8],[9] are mostly together.

    * [3] is left with one option

    * [4] goes above [7]; [8] and [9] below.

    * Forcing [5],[6] around the [10]s.

    * The rest is obvious.

  4. mathgrant Says:

    Without having tried to solve the puzzle itself, I can tell you I’ve seen 9’s in 10×10 Numberlinks published by Nikoli. I haven’t seen 10’s, though.

    Nice job making it symmetrical AND not having givens on the perimeter. o.o

    • mathgrant Says:

      With the right intuitions, this puzzle fell quickly. I dread to imagine how you managed to prove the solution unique beforehand, though. o_o;

      • MellowMelon Says:

        Turned out to be amazingly easy to prove it, using the 3. If it didn’t go on the edge, it would cut off too many numbers (bit of brute forcing here, but not much). And once you draw in its correct path, to my astonishment the *entire solution* was forced logically, just from knowing that 3 and not being allowed to connect two different numbers.

      • yy Says:

        Here is a sketch of my proof of correctness. Once the puzzle is created, proving it isn’t that difficult. How to create it is a different story…

        * General direction of [10] (otherwise cuts off something completely, or [5]/[6] don’t have enough room.)

        * General direction of [1] (not enough room, or [7] blocks [4],[8],[9] or [5],[6].)

        * [2] and [3] have to follow the edge (any other way does not leave enough room.)

        * [5] will follow the edge and around [3] (otherwise [2]-[5]-[3] cuts off [6].)

        * [6] goes around [10] and [5] (or [8],[9] are cut off.)

        * Exact paths of [5],[10] are forced (to leave room for [6])

        * Exact path for [3] forced (to not block [7])

        * Exact path for [6] forced (to not block [7] on top, and [4],[8],[9] on bottom.)

        * [8],[9] are forced (otherwise they block [4] (or [7] at the top of [8]).)

        * [4] and [7] are obvious.

  5. TheSubro Says:

    Following your Numberlink “Expose'”, I am revisiting some prior puzzle and this was a nice exercise to use to keep improving. Thanks.

    Ken

  6. chaotic_iak Says:

    Great puzzle indeed.

    Going back and proving your reply to mathgrant’s…yeah, forced. Great.

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