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enter image description here Hello, I found this puzzle in an old puzzle book, it's fun. Does anyone know if this kind of puzzle has a name, I want to find more, and maybe try making some. Thanks very much!

Here is the cover of the book: enter image description here

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    $\begingroup$ Welcome to the site! Could you be more specific about that "old puzzle book"? Knowing the exact source might help us to figure out the answer to your question. $\endgroup$ Sep 19, 2023 at 14:28
  • $\begingroup$ Thanks, happy to be here. The book is called Puzzle Time Book 3, published by Grandreams Books Ltd in 2007, I found it in a second hand shop in New Zealand. It's got all sorts of word, number and picture puzzles, but no other puzzle the same as this one here. $\endgroup$
    – Rowan
    Sep 19, 2023 at 14:40
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    $\begingroup$ I'd just call this type of puzzle a "maze"; it just looks a little different and you have to use the rules to figure out where the "walls" actually are... $\endgroup$ Sep 19, 2023 at 14:47
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    $\begingroup$ ..and the walls may not be static! $\endgroup$
    – justhalf
    Sep 19, 2023 at 18:59

3 Answers 3

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I've seen this be called "Mazes With Rules" or "Logic Mazes"

see: https://www.logicmazes.com/dec99.html for Robert Abbot's take on the term, and if you want more of them he's published some online https://www.logicmazes.com/ as well as in two books https://www.logicmazes.com/super.html and https://www.logicmazes.com/mad.html

Completely agreed, they're lovely. So much more maze per maze

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    $\begingroup$ Aha you're right, the maze with the red-green-yellow dot sequence at logicmazes.com/super.html is the same concept. Thank you. I guess doing the sequence on graph paper squares like in the book really is an original idea, I love it. $\endgroup$
    – Rowan
    Sep 19, 2023 at 23:40
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Not the question, but for those curious about the answer to the maze:

enter image description here

Solve path:

Breadth first search backward eliminating dead ends, until we got:
enter image description here
Then it's forced until:
enter image description here

Then trial and error from the start to reach that square after passing through a 3. Not that hard since we get to dead ends pretty quickly in many of the branches.

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Since you mentioned creating your own such puzzles, you should take a look at this post. Ultimately the key insight is that this kind of maze can be represented by a totally ordinary maze problem on a directed graph, so standard BFS can be applied from any end.

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