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Recently, I have been amusing myself with the interesting puzzles provided by the excellent Flow Free puzzle app.

Since I couldn't find a way to bookmark my favourite puzzles, I took up a habit of screenshotting the ones I liked especially, for one reason or another. This question is an excerpt from that screenshot collection.

If you are unfamiliar with Flow Free, it's a puzzle with very simple mechanics. There's a square grid, peppered with pairs of different coloured (and optionally, lettered for the colour blind) squares, which you are supposed to connect pairwise by colouring adjacent squares, without the paths ever crossing. The resulting tangle of paths will always be the unique solution, and it will always completely fill the square grid. (There are some exceptions and variations to these rules, but all the ones I'm posting here will be of this "pure" variety.)

In so many fewer words, you are supposed to turn this

enter image description here

into this:

enter image description here

The puzzles below are not of the easiest ones, oftentimes quite the opposite actually, so if you get stuck, the app has a lot of easier ones available.


Puzzle 1 (6x6, 4 pairs):
enter image description here

Puzzle 2 (8x8, 4 pairs):
enter image description here

Puzzle 3 (8x8, 5 pairs):
enter image description here

Puzzle 4 (8x8, 5 pairs):
enter image description here

Puzzle 5 (9x9, 8 pairs):
enter image description here

Puzzle 6 (10x10, 8 pairs):
enter image description here

Puzzle 7 (10x10, 9 pairs):
enter image description here

Puzzle 8 (11x11, 7 pairs):
enter image description here


The app itself has hundreds (more likely, thousands) of puzzles like this, and it's free (as in ad-funded). Posting this is probably pretty deep in the grey area regarding both intellectual property rights and the PSE guidelines. However, since I'm pretty sure PSE likes great puzzles, and also that the app providers don't mind unpaid endorsements, I figured I'll just go ahead. Please drop a comment if you disagree.

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Here are the answers to all 8 puzzles:

enter image description here

enter image description here

enter image description here

enter image description here

enter image description here

enter image description here

enter image description here

enter image description here

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  • $\begingroup$ Well, after 2 days, your answer is still the only one with all the 8 answers, so have a tick then :-) $\endgroup$ – Bass Feb 6 '18 at 22:00
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These are called Numberlinks(letters in this case instead of numbers).

1st, 2nd, 3rd, 5th and 7th solved :


1st
1st


2nd
2nd


3rd
3rd


5th
5th


7th
7th


And similarly, one can solve all of these.


The puzzle wants to solve the given set of nodes, connecting a pair(with the same number or letter) with edges that form a (disjoint) planar graph.

The tags you have used are quite right, in my humble opinion.


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  • $\begingroup$ Oh cool, didn’t know that name for the puzzle type! Do you want to add it to the app’s wikipedia page, or should I? $\endgroup$ – Bass Feb 4 '18 at 17:15
  • $\begingroup$ @Bass You can do the honour :) $\endgroup$ – ABcDexter Feb 4 '18 at 17:17
  • $\begingroup$ Are you sure your numbers are right? The second one you solved looks like puzzle 1 $\endgroup$ – Quintec Feb 4 '18 at 18:00
  • $\begingroup$ @thecoder16 thanks for letting me know, updating the answer :) $\endgroup$ – ABcDexter Feb 4 '18 at 18:23
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    $\begingroup$ After smurfing around wikipedia's graph theory pages a bit, I think the resulting mess we call a solution can also be called a "planar regular bipartite graph of degree 1", or possibly, a "planar 1-biregular graph" :-) $\endgroup$ – Bass Feb 4 '18 at 18:40
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Solution to the 4th of these puzzles:

enter image description here

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Note: These are only the ones that ABcDexter had not yet solved at the time - go give credit!

Here is the 4th one solved:

enter image description here

...here is the 6th one solved:

enter image description here

...and here is the 8th one solved:

enter image description here

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    $\begingroup$ Argh! Looks like you just beat me to #4 :-) $\endgroup$ – Rand al'Thor Feb 4 '18 at 19:02
  • $\begingroup$ and with colour coded lines too! :)) $\endgroup$ – Jonathan Allan Feb 4 '18 at 19:02
  • $\begingroup$ I took ages on #4 because I assumed the E-line had to go around the bottom, because going over the top would cut off the upper C from the rest. It was only after a long time that I realised the E-line could loop around the lower C before going over the top. $\endgroup$ – Rand al'Thor Feb 4 '18 at 19:05
  • $\begingroup$ Nice work there, especially with the colours :D $\endgroup$ – ABcDexter Feb 5 '18 at 11:46

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