{"id":1156,"date":"2024-05-19T01:53:48","date_gmt":"2024-05-19T08:53:48","guid":{"rendered":"https:\/\/puzzlezapper.com\/blog\/?p=1156"},"modified":"2024-05-19T09:03:25","modified_gmt":"2024-05-19T16:03:25","slug":"three-paths-to-pick-from-part-2-distant-connections","status":"publish","type":"post","link":"https:\/\/puzzlezapper.com\/blog\/2024\/05\/three-paths-to-pick-from-part-2-distant-connections\/","title":{"rendered":"Three paths to pick from, part 2: Distant connections"},"content":{"rendered":"\n

I promised two more path puzzles in part 1,<\/a> and their time has come. When I posted recently<\/a> about “starmaps” as a variation on edgematching puzzles, my variation there was actually the second puzzle inspired by them that I had found recently. The first was this set of 2\u00d72 square tiles with one cell being marked with 2 orthogonal or diagonal arrows. (The tiles can be flipped.) <\/p>\n\n\n

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Part of the inspiration to use arrows may have come from the game of Trippples, [siccc]<\/em> which uses a complete set of fixed square pieces with arrows in three directions. I recently read about Trippples in issue 7<\/a> of Abstract Games magazine<\/a>. Once I had these squares with arrows, a puzzle challenge seemed natural: connect the arrows into a single path, which may not enter any cell with arrows in any direction that does not correspond to an arrow.<\/p>\n\n\n\n

Problem 61:<\/strong> Find a closed circuit using these pieces. I spent enough time finding the path above; I suspect that a closed circuit may be solvable if you have the patience of a Lewis Patterson<\/a>, which I do not.<\/p>\n\n\n\n

One element I like to consider in puzzle design is non-locality<\/em>. A puzzle exhibits non-locality if, when you are placing a piece, you must consider pieces that are not immediately adjacent. Most polyform and edgematching puzzles are generally local. If half of a puzzle frame is filled, pieces in the interior of the filled region do not directly affect how new pieces can connect to the edge of that region. (Of course, I am eliding the fact that they reduce the set of remaining pieces that are available to place.) In the above puzzle, the empty space allows long distance connections, turning path-making into a non-local problem.<\/p>\n\n\n\n

My Color Tubes puzzle from my Edge Collection Connection set of edgematching card puzzles was also a path puzzle with non-local considerations. I neglected to introduce it on the blog back when I produced the set, so let’s remedy that now.<\/p>\n\n\n

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The configuration shown is a solution to the challenge of placing the pieces so that each tube has three segments of three different colors. Segments can break in the middle of a card, or at a connection across a card boundary with non-matching colors. (Here, the cards cannot be flipped over; the back sides of the cards contain a second, related puzzle.) Other challenges for the cards are placing them so there are two differently colored segments, or four. This was definitely more of a “designed” puzzle than a “discovered” puzzle, which was a bit of a departure for me. I’ll have another excuse to muse about the distinction in a future post, but at this point I’ve hinted at more than one future post, so they can’t all be the next one.<\/p>\n\n\n\n

With a couple of instances of non-locality under our belts, can we say anything useful about it as a puzzle design tool? In the case of Color Tubes, I think it gives it a little more depth than a typical 3\u00d73 edgematching puzzle, which would seem to be welcome. In the arrow path puzzle, it adds difficulty and complexity, but the result is a little too much difficulty and complexity, at least for my tastes. It is a spice that should be judiciously applied. But then, so is hinting at coming posts, and that won’t stop me from teasing more material about non-local puzzles in the near future!<\/p>\n","protected":false},"excerpt":{"rendered":"

I promised two more path puzzles in part 1, and their time has come. When I posted recently about “starmaps” as a variation on edgematching puzzles, my variation there was actually the second puzzle inspired by them that I had found recently. The first was this set of 2\u00d72 square tiles with one cell being … Continue reading Three paths to pick from, part 2: Distant connections<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,6],"tags":[177,269,186,262,260,197,270],"class_list":["post-1156","post","type-post","status-publish","format-standard","hentry","category-recreational-mathematics","category-puzzles","tag-arrows","tag-color-tubes","tag-edgematching","tag-path-puzzles","tag-starmaps","tag-the-edge-connection-collection","tag-trippples"],"_links":{"self":[{"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/posts\/1156","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/comments?post=1156"}],"version-history":[{"count":5,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/posts\/1156\/revisions"}],"predecessor-version":[{"id":1184,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/posts\/1156\/revisions\/1184"}],"wp:attachment":[{"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/media?parent=1156"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/categories?post=1156"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/puzzlezapper.com\/blog\/wp-json\/wp\/v2\/tags?post=1156"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}