Sum in a sudoku with sum total of 15 and 45












1












$begingroup$


I have created a sudoku puzzle with the following restrictions:





  • Each row and column sum to $45$.

  • Each row and column in the nine $3$ by $3$ sub-grids sum to $15$.




Is such a sudoku unique?






grid-deduction sudoku







share|improve this question









New contributor




Aorica Ireson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$












  • $begingroup$
    "...where each row and column adds to a total of 45..." is redundant, since it is in the nature of a sudoku puzzle that its rows and columns sum to $45$. This is because each row contains the numbers $1$ through $9$, and $1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45$.
    $endgroup$
    – Hugh
    2 hours ago












  • $begingroup$
    "where each (3*3) 9 individual squares of rows and columns total a sum of 15" >>> do you mean 45?
    $endgroup$
    – Kryesec
    1 hour ago










  • $begingroup$
    @Kryesec I've assumed that that means that each of the 3 by 3 sub-grids is a magic square with "magic constant" 15. In other words, each row/column in each 3 by 3 sub-grid sums to 15.
    $endgroup$
    – Hugh
    1 hour ago


















1












$begingroup$


I have created a sudoku puzzle with the following restrictions:





  • Each row and column sum to $45$.

  • Each row and column in the nine $3$ by $3$ sub-grids sum to $15$.




Is such a sudoku unique?






grid-deduction sudoku







share|improve this question









New contributor




Aorica Ireson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$












  • $begingroup$
    "...where each row and column adds to a total of 45..." is redundant, since it is in the nature of a sudoku puzzle that its rows and columns sum to $45$. This is because each row contains the numbers $1$ through $9$, and $1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45$.
    $endgroup$
    – Hugh
    2 hours ago












  • $begingroup$
    "where each (3*3) 9 individual squares of rows and columns total a sum of 15" >>> do you mean 45?
    $endgroup$
    – Kryesec
    1 hour ago










  • $begingroup$
    @Kryesec I've assumed that that means that each of the 3 by 3 sub-grids is a magic square with "magic constant" 15. In other words, each row/column in each 3 by 3 sub-grid sums to 15.
    $endgroup$
    – Hugh
    1 hour ago
















1












1








1





$begingroup$


I have created a sudoku puzzle with the following restrictions:





  • Each row and column sum to $45$.

  • Each row and column in the nine $3$ by $3$ sub-grids sum to $15$.




Is such a sudoku unique?






grid-deduction sudoku







share|improve this question









New contributor




Aorica Ireson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




I have created a sudoku puzzle with the following restrictions:





  • Each row and column sum to $45$.

  • Each row and column in the nine $3$ by $3$ sub-grids sum to $15$.




Is such a sudoku unique?






grid-deduction sudoku




grid-deduction sudoku






share|improve this question









New contributor




Aorica Ireson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question









New contributor




Aorica Ireson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question








edited 1 hour ago









Hugh

1,6961721




1,6961721






New contributor




Aorica Ireson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 2 hours ago









Aorica IresonAorica Ireson

61




61




New contributor




Aorica Ireson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Aorica Ireson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Aorica Ireson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












  • $begingroup$
    "...where each row and column adds to a total of 45..." is redundant, since it is in the nature of a sudoku puzzle that its rows and columns sum to $45$. This is because each row contains the numbers $1$ through $9$, and $1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45$.
    $endgroup$
    – Hugh
    2 hours ago












  • $begingroup$
    "where each (3*3) 9 individual squares of rows and columns total a sum of 15" >>> do you mean 45?
    $endgroup$
    – Kryesec
    1 hour ago










  • $begingroup$
    @Kryesec I've assumed that that means that each of the 3 by 3 sub-grids is a magic square with "magic constant" 15. In other words, each row/column in each 3 by 3 sub-grid sums to 15.
    $endgroup$
    – Hugh
    1 hour ago




















  • $begingroup$
    "...where each row and column adds to a total of 45..." is redundant, since it is in the nature of a sudoku puzzle that its rows and columns sum to $45$. This is because each row contains the numbers $1$ through $9$, and $1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45$.
    $endgroup$
    – Hugh
    2 hours ago












  • $begingroup$
    "where each (3*3) 9 individual squares of rows and columns total a sum of 15" >>> do you mean 45?
    $endgroup$
    – Kryesec
    1 hour ago










  • $begingroup$
    @Kryesec I've assumed that that means that each of the 3 by 3 sub-grids is a magic square with "magic constant" 15. In other words, each row/column in each 3 by 3 sub-grid sums to 15.
    $endgroup$
    – Hugh
    1 hour ago


















$begingroup$
"...where each row and column adds to a total of 45..." is redundant, since it is in the nature of a sudoku puzzle that its rows and columns sum to $45$. This is because each row contains the numbers $1$ through $9$, and $1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45$.
$endgroup$
– Hugh
2 hours ago






$begingroup$
"...where each row and column adds to a total of 45..." is redundant, since it is in the nature of a sudoku puzzle that its rows and columns sum to $45$. This is because each row contains the numbers $1$ through $9$, and $1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45$.
$endgroup$
– Hugh
2 hours ago














$begingroup$
"where each (3*3) 9 individual squares of rows and columns total a sum of 15" >>> do you mean 45?
$endgroup$
– Kryesec
1 hour ago




$begingroup$
"where each (3*3) 9 individual squares of rows and columns total a sum of 15" >>> do you mean 45?
$endgroup$
– Kryesec
1 hour ago












$begingroup$
@Kryesec I've assumed that that means that each of the 3 by 3 sub-grids is a magic square with "magic constant" 15. In other words, each row/column in each 3 by 3 sub-grid sums to 15.
$endgroup$
– Hugh
1 hour ago






$begingroup$
@Kryesec I've assumed that that means that each of the 3 by 3 sub-grids is a magic square with "magic constant" 15. In other words, each row/column in each 3 by 3 sub-grid sums to 15.
$endgroup$
– Hugh
1 hour ago












2 Answers
2






active

oldest

votes


















4












$begingroup$


No.




Of course, there's rotation and reflection, but even beyond that you can swap any two rows within it's group of three rows (eg swap row 1 and 2 or swap 4 and 6), and you can swap a group of three with one of the other groups of three (eg swap 1,2,3 with 4,5,6), and the same applies to the columns.






share|improve this answer









$endgroup$





















    0












    $begingroup$


    I was beaten to a very similar answer, but you can create such a square based on the magic square below:

    abc
    def
    ghi

    Turn it into this:

    abcdefghi
    defghiabc
    ghiabcdef
    bcaefdhig
    efdhigbca
    higbcaefd
    cabfdeigh
    fdeighcab
    ighcabfde

    Since there are multiple possible magic squares, it's not unique. When you change the number at the very center (i), which you can, you get a different sudoku (not even a rotation or reflection).






    share









    $endgroup$













      Your Answer





      StackExchange.ifUsing("editor", function () {
      return StackExchange.using("mathjaxEditing", function () {
      StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
      StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
      });
      });
      }, "mathjax-editing");

      StackExchange.ready(function() {
      var channelOptions = {
      tags: "".split(" "),
      id: "559"
      };
      initTagRenderer("".split(" "), "".split(" "), channelOptions);

      StackExchange.using("externalEditor", function() {
      // Have to fire editor after snippets, if snippets enabled
      if (StackExchange.settings.snippets.snippetsEnabled) {
      StackExchange.using("snippets", function() {
      createEditor();
      });
      }
      else {
      createEditor();
      }
      });

      function createEditor() {
      StackExchange.prepareEditor({
      heartbeatType: 'answer',
      autoActivateHeartbeat: false,
      convertImagesToLinks: false,
      noModals: true,
      showLowRepImageUploadWarning: true,
      reputationToPostImages: null,
      bindNavPrevention: true,
      postfix: "",
      imageUploader: {
      brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
      contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
      allowUrls: true
      },
      noCode: true, onDemand: true,
      discardSelector: ".discard-answer"
      ,immediatelyShowMarkdownHelp:true
      });


      }
      });






      Aorica Ireson is a new contributor. Be nice, and check out our Code of Conduct.










      draft saved

      draft discarded


















      StackExchange.ready(
      function () {
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f79552%2fsum-in-a-sudoku-with-sum-total-of-15-and-45%23new-answer', 'question_page');
      }
      );

      Post as a guest















      Required, but never shown

























      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      4












      $begingroup$


      No.




      Of course, there's rotation and reflection, but even beyond that you can swap any two rows within it's group of three rows (eg swap row 1 and 2 or swap 4 and 6), and you can swap a group of three with one of the other groups of three (eg swap 1,2,3 with 4,5,6), and the same applies to the columns.






      share|improve this answer









      $endgroup$


















        4












        $begingroup$


        No.




        Of course, there's rotation and reflection, but even beyond that you can swap any two rows within it's group of three rows (eg swap row 1 and 2 or swap 4 and 6), and you can swap a group of three with one of the other groups of three (eg swap 1,2,3 with 4,5,6), and the same applies to the columns.






        share|improve this answer









        $endgroup$
















          4












          4








          4





          $begingroup$


          No.




          Of course, there's rotation and reflection, but even beyond that you can swap any two rows within it's group of three rows (eg swap row 1 and 2 or swap 4 and 6), and you can swap a group of three with one of the other groups of three (eg swap 1,2,3 with 4,5,6), and the same applies to the columns.






          share|improve this answer









          $endgroup$




          No.




          Of course, there's rotation and reflection, but even beyond that you can swap any two rows within it's group of three rows (eg swap row 1 and 2 or swap 4 and 6), and you can swap a group of three with one of the other groups of three (eg swap 1,2,3 with 4,5,6), and the same applies to the columns.







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 1 hour ago









          Dr XorileDr Xorile

          12.1k22567




          12.1k22567























              0












              $begingroup$


              I was beaten to a very similar answer, but you can create such a square based on the magic square below:

              abc
              def
              ghi

              Turn it into this:

              abcdefghi
              defghiabc
              ghiabcdef
              bcaefdhig
              efdhigbca
              higbcaefd
              cabfdeigh
              fdeighcab
              ighcabfde

              Since there are multiple possible magic squares, it's not unique. When you change the number at the very center (i), which you can, you get a different sudoku (not even a rotation or reflection).






              share









              $endgroup$


















                0












                $begingroup$


                I was beaten to a very similar answer, but you can create such a square based on the magic square below:

                abc
                def
                ghi

                Turn it into this:

                abcdefghi
                defghiabc
                ghiabcdef
                bcaefdhig
                efdhigbca
                higbcaefd
                cabfdeigh
                fdeighcab
                ighcabfde

                Since there are multiple possible magic squares, it's not unique. When you change the number at the very center (i), which you can, you get a different sudoku (not even a rotation or reflection).






                share









                $endgroup$
















                  0












                  0








                  0





                  $begingroup$


                  I was beaten to a very similar answer, but you can create such a square based on the magic square below:

                  abc
                  def
                  ghi

                  Turn it into this:

                  abcdefghi
                  defghiabc
                  ghiabcdef
                  bcaefdhig
                  efdhigbca
                  higbcaefd
                  cabfdeigh
                  fdeighcab
                  ighcabfde

                  Since there are multiple possible magic squares, it's not unique. When you change the number at the very center (i), which you can, you get a different sudoku (not even a rotation or reflection).






                  share









                  $endgroup$




                  I was beaten to a very similar answer, but you can create such a square based on the magic square below:

                  abc
                  def
                  ghi

                  Turn it into this:

                  abcdefghi
                  defghiabc
                  ghiabcdef
                  bcaefdhig
                  efdhigbca
                  higbcaefd
                  cabfdeigh
                  fdeighcab
                  ighcabfde

                  Since there are multiple possible magic squares, it's not unique. When you change the number at the very center (i), which you can, you get a different sudoku (not even a rotation or reflection).







                  share











                  share


                  share










                  answered 5 mins ago









                  NautilusNautilus

                  3,741523




                  3,741523






















                      Aorica Ireson is a new contributor. Be nice, and check out our Code of Conduct.










                      draft saved

                      draft discarded


















                      Aorica Ireson is a new contributor. Be nice, and check out our Code of Conduct.













                      Aorica Ireson is a new contributor. Be nice, and check out our Code of Conduct.












                      Aorica Ireson is a new contributor. Be nice, and check out our Code of Conduct.
















                      Thanks for contributing an answer to Puzzling Stack Exchange!


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid …



                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.


                      Use MathJax to format equations. MathJax reference.


                      To learn more, see our tips on writing great answers.




                      draft saved


                      draft discarded














                      StackExchange.ready(
                      function () {
                      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f79552%2fsum-in-a-sudoku-with-sum-total-of-15-and-45%23new-answer', 'question_page');
                      }
                      );

                      Post as a guest















                      Required, but never shown





















































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown

































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown







                      -

                      Popular posts from this blog

                      Knooppunt Holsloot

                      Image
                      Knooppunt Holsloot Kenmerken Wegen A37 × N34 Type knooppunt klaverblad Portaal     Verkeer & Vervoer Knooppunt Holsloot is een verkeersknooppunt op de kruising van de autosnelweg A37 en de N34 in Drenthe, tussen Emmen en Coevorden. Oorspronkelijk was deze aansluiting een afritconstructie van het type Haarlemmermeeraansluiting, zoals bij Knooppunt Hooipolder. Sinds 2002 is het knooppunt omgebouwd tot een volledig klaverblad. Als noviteit werd hier voor het eerst gebruikgemaakt van dimbare verlichting in plaats van de normale vaste tijden waarop de verlichting aan en uit gaat, wat een grote kostenbesparing opleverde. [1] Dat Holsloot als volwaardig knooppunt is uitgevoerd, waarbij alle verkeersstromen en afbuigingen ononderbroken kunnen doorgaan, is uitzonderlijk. Het betreft hier namelijk een aansluiting tussen een autosnelweg en niet-snelweg. Een vergelijkbare situatie treft men nabij Hoensbroek bij het knooppunt Ten Esschen.     Aa
                      Read more

                      Altaar (religie)

                      Image
                      Deel van de serie over kerkelijk gerei waaronder paramenten en liturgisch vaatwerk gebruikt in de liturgie Liturgisch vaatwerk Vasa sacra Miskelk · Pateen Kelklepeltje Ciborie · Monstrans Pyxis · Custodiale Vasa non sacra Ampullen · Wijwatervat Olievaatje Wierookvat · Ablutievat Paramenten Amict · Albe · Baarkleed · Cingel Tuniek · Dalmatiek · Fanon Kazuifel · Manipel · Stola Gremiale · Benedictievelum Mijter Koorkledij Rochet · Superplie Koorkap · Cappa magna Kovel Kelkgerei Bursa · Kelkvelum Ciborievelum Kerklinnen Corporale · Kelkdoekje Lavabodoekje · Palla Altaardwaal Kerkinterieur Altaar · Ambo Biechtstoel · Communiebank Doksaal · Doopvont Faldistorium Godslamp · Hoogaltaar Heilig Kruisaltaar Katheder · Preekstoel Sedilia Tabernakel · Volksaltaar Liturgische boeken Altaarmissaal Benedictionale · Brevier Evangeliarium · Evangelistarium Graduale · Kyriale Lectionarium Psalter · Rituaal Sacramentarium · Volksmissaal Overige Flambou
                      Read more

                      Gregoriusmis

                      Image
                      Een afbeelding van de Gregoriusmis uit een getijdenboek gemaakt in de zuidelijke Nederlanden tussen 1500 en 1525 Gregoriusmis, Meester van het Akense Altaar, ca. 1500-1525. Collectie Museum Catharijneconvent De Gregoriusmis of de Mis van Sint Gregorius is een motief in katholieke kunst, dat het eerst verscheen in de late Middeleeuwen en dat nog steeds werd gebruikt tijdens de contrareformatie. Paus Gregorius I (ca. 540-604) is afgebeeld, de H. Mis opdragend, terwijl Christus als de Man van Smarten verschijnt op het altaar dat voor Sint Gregorius staat. Volgens de legende had St. Gregorius gebeden om een teken voor een betwijfelaar van de transsubstantiatieleer, waarop de lijdende Christus tijdens het opdragen van de Mis verscheen om hem te overtuigen en waarbij zijn bloed in de altaarkelk liep. Vaak zijn ook de passiewerktuigen afgebeeld. Zie de categorie Mass of Saint Gregory van Wikimedia Commons voor mediabestanden over dit onderwerp. This page is onl
                      Read more