Numberlink
{{Short description|Logic puzzle}}
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| caption1 = A simple example of a Numberlink puzzle
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Numberlink is a type of logic puzzle involving finding paths to connect numbers in a grid.
Rules
The player has to pair up all the matching numbers on the grid with single continuous lines (or paths). The lines cannot branch off or cross over each other, and the numbers have to fall at the end of each line (i.e., not in the middle).
It is considered that a problem is well-designed only if it has a unique solution{{cite magazine |title=Dr. Sudoku Prescribes: Numberlink Puzzles |url=https://www.wired.com/magazine/2010/11/dr-sudoku-prescribes-numberlink-puzzles-2/ |accessdate=November 23, 2010 |author=Thomas Snyder |author-link=Thomas Snyder |magazine=Wired |date=19 November 2010}} and all the cells in the grid are filled, although some Numberlink designers do not stipulate this.
History
In 1897, a slightly different form of the puzzle was printed in the Brooklyn Daily Eagle, in a column by Sam Loyd.{{cite journal|last=Pegg Jr.|first=Ed|title=Beyond Sudoku|journal=Mathematica Journal|year=2007|volume=10|issue=3|pages=469–73|url=http://www.mathematica-journal.com/issue/v10i3/contents/NumberLink/NumberLink.pdf|accessdate=11 September 2011|archive-url=https://web.archive.org/web/20160303172350/http://www.mathematica-journal.com/issue/v10i3/contents/NumberLink/NumberLink.pdf|archive-date=3 March 2016|url-status=dead}} Another early, printed version of Number Link can be found in Henry Ernest Dudeney's book Amusements in mathematics (1917) as a puzzle for motorists (puzzle no. 252).{{cite book| last=Dudeney| first=Henry|title=Amusements in mathematics| publisher=Thomas Nelson|year=1917|contribution=Problem 252 – A Puzzle for Motorists|contribution-url=https://archive.org/stream/amusementsinmath00dude#page/72/mode/2up}} This puzzle type was popularized in Japan by Nikoli as Arukone (アルコネ, Alphabet Connection) and Nanbarinku (ナンバーリンク, Number Link). The only difference between Arukone and Nanbarinku is that in Arukone the clues are letter pairs (as in Dudeney's puzzle), while in Nanbarinku the clues are number pairs.
{{As of|2006}}, three books consisting entirely of Numberlink puzzles have been published by Nikoli.
Versions of this known as Wire Storm, Flow Free and Alphabet Connection have been released as apps for iOS, Android, Web and Windows Phone.{{cite web|url=https://itunes.apple.com/us/app/wire-storm/id588938206?ls=1&mt=8|archiveurl=https://archive.today/20130620060335/https://itunes.apple.com/us/app/wire-storm/id588938206?ls=1&mt=8|url-status=dead|title=Wire Storm - Fun and Addicting Logic Flow Puzzle Game for bigst4t22,…|date=20 June 2013|archivedate=20 June 2013|website=Archive.today|accessdate=22 November 2018}}{{cite web|url=https://apps.apple.com/us/app/flow-free/id526641427|title=Flow Free|website=App Store|access-date=22 November 2018}}{{cite web|url=https://play.google.com/store/apps/details?id=com.bigduckgames.flow|title=Flow Free - Apps on Google Play|website=Play.google.com|accessdate=22 November 2018}}{{Cite web |url=https://itunes.apple.com/us/app/alphabet-connection-arukone/id560852073?mt=8 |title=Alphabet Connection: Arukone on the App Store on iTunes |website=iTunes |access-date=2015-03-17 |archive-url=https://web.archive.org/web/20150322225047/https://itunes.apple.com/us/app/alphabet-connection-arukone/id560852073?mt=8 |archive-date=2015-03-22 |url-status=dead }}{{Cite web |url=https://play.google.com/store/apps/details?id=com.skyler.konekt.android |title=Archived copy |access-date=2013-10-29 |archive-url=https://web.archive.org/web/20150407164111/https://play.google.com/store/apps/details?id=com.skyler.konekt.android |archive-date=2015-04-07 |url-status=dead }}{{cite web|url=https://flowfree-game.com/|title=Flow Free Game|website=Flow Free Game|accessdate=27 March 2025}}{{cite web|url=https://www.microsoft.com/en-gb/store/p/flow-free/9wzdncrfj3hr|title=Get Flow Free - Microsoft Store en-GB|website=Microsoft Store|accessdate=22 November 2018}}
Computational complexity
As a computational problem, finding a solution to a given Numberlink puzzle is NP-complete.
{{citation
| last1 = Kotsuma
| first1 = Kouichi
| last2 = Takenaga
| first2 = Yasuhiko
| title = NP-Completeness and Enumeration of Number Link Puzzle
| journal = IEICE Technical Report. Theoretical Foundations of Computing
| volume = 109
| issue = 465
| pages = 1–7
|date=March 2010
| url = http://ci.nii.ac.jp/naid/110008000705
}}
NP-completeness is maintained even if "zig-zag" paths are allowed. Informally, this means paths may have "unnecessary bends" in them (see the reference for a more technical explanation).
{{citation
| last1 = Adcock
| first1 = Aaron
| last2 = Demaine
| first2 = Erik D.
| last3 = Demaine
| first3 = Martin L
| last4 = O’Brien
| first4 = Michael P.
| last5 = Villaamil
| first5 = Fernando S{\'a}nchez
| last6 = D. Sullivan
| first6 = Blair
| title = Zig-Zag Numberlink is NP-Complete
| journal = Journal of Information Processing
| volume = 23
| issue = 3
| pages = 239–245
|date=October 23, 2014
| doi = 10.2197/ipsjjip.23.239
| arxiv = 1410.5845
| s2cid = 15735280
| url = https://www.jstage.jst.go.jp/article/ipsjjip/23/3/23_239/_article
}}
See also
References
{{Reflist}}
External links
- [http://connection.ivank.net Online version of Numberlink in HTML5]