Equation to locate a square in a square












0












$begingroup$


Good evening,



I have been experimenting with different Sudoku checker and have come across a problem:



For a nxn Sudoku where n is a square number (4,6,19,25 etcc.), there would be an n number of sub-squares in a square. For example for a 9 by 9 there are 9 3x3 equal sized sub squares:



enter image description here



let column = j



let row = i



Now what I am trying to do is to come up with an equation in terms of n and sub-square number needed such that it would equal the first row number.



e.g for sub square number 3 the first row is number 3, for sub square 0 first row is 0 etc.



the issue with this is that the sub squares 0,1 and 2 all start at the same row 0 and therefore does this mean it is impossible to find an equation/algorithm or any other way to do this?



would the same apply for columns for sub squares?






recreational-mathematics problem-solving sudoku







share|cite|improve this question









$endgroup$

















    0












    $begingroup$


    Good evening,



    I have been experimenting with different Sudoku checker and have come across a problem:



    For a nxn Sudoku where n is a square number (4,6,19,25 etcc.), there would be an n number of sub-squares in a square. For example for a 9 by 9 there are 9 3x3 equal sized sub squares:



    enter image description here



    let column = j



    let row = i



    Now what I am trying to do is to come up with an equation in terms of n and sub-square number needed such that it would equal the first row number.



    e.g for sub square number 3 the first row is number 3, for sub square 0 first row is 0 etc.



    the issue with this is that the sub squares 0,1 and 2 all start at the same row 0 and therefore does this mean it is impossible to find an equation/algorithm or any other way to do this?



    would the same apply for columns for sub squares?






    recreational-mathematics problem-solving sudoku







    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      Good evening,



      I have been experimenting with different Sudoku checker and have come across a problem:



      For a nxn Sudoku where n is a square number (4,6,19,25 etcc.), there would be an n number of sub-squares in a square. For example for a 9 by 9 there are 9 3x3 equal sized sub squares:



      enter image description here



      let column = j



      let row = i



      Now what I am trying to do is to come up with an equation in terms of n and sub-square number needed such that it would equal the first row number.



      e.g for sub square number 3 the first row is number 3, for sub square 0 first row is 0 etc.



      the issue with this is that the sub squares 0,1 and 2 all start at the same row 0 and therefore does this mean it is impossible to find an equation/algorithm or any other way to do this?



      would the same apply for columns for sub squares?






      recreational-mathematics problem-solving sudoku







      share|cite|improve this question









      $endgroup$




      Good evening,



      I have been experimenting with different Sudoku checker and have come across a problem:



      For a nxn Sudoku where n is a square number (4,6,19,25 etcc.), there would be an n number of sub-squares in a square. For example for a 9 by 9 there are 9 3x3 equal sized sub squares:



      enter image description here



      let column = j



      let row = i



      Now what I am trying to do is to come up with an equation in terms of n and sub-square number needed such that it would equal the first row number.



      e.g for sub square number 3 the first row is number 3, for sub square 0 first row is 0 etc.



      the issue with this is that the sub squares 0,1 and 2 all start at the same row 0 and therefore does this mean it is impossible to find an equation/algorithm or any other way to do this?



      would the same apply for columns for sub squares?






      recreational-mathematics problem-solving sudoku




      recreational-mathematics problem-solving sudoku






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 1 at 23:16









      fredfred

      162




      162






















          2 Answers
          2






          active

          oldest

          votes


















          1












          $begingroup$

          In your example, square $k$ is in row $lfloor frac k3 rfloor$ and in column $k bmod 3$. For general $n$, replace $3$ by $n$. This shows the nice side of counting starting with zero.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Note that calculating $lfloorfrac{k}3rfloor$ in most programming languages simply requires the statement $x:=k/3;$ and $kmbox{ mod }3$ requires $x:=k%3$.
            $endgroup$
            – SmileyCraft
            Jan 1 at 23:20












          • $begingroup$
            Thank you for your response. To clarify by square do you mean each small square that hold 1 number or a sub-square which holds n numbers?
            $endgroup$
            – fred
            Jan 1 at 23:29










          • $begingroup$
            For either case, I am not exactly sure if this would work unless I am mistaken (let me know if I am!). For example if we take subsquare 8 and we do 8/3 we get the 2.66..th row.
            $endgroup$
            – fred
            Jan 1 at 23:33










          • $begingroup$
            I may not have made it clear with the picture my apologies! the lines I drew are the outlines of the square and sub squares not the rows and columns.
            $endgroup$
            – fred
            Jan 1 at 23:36










          • $begingroup$
            I assumed the rows and columns were numbered $0$ to $2$ in each direction.
            $endgroup$
            – Ross Millikan
            Jan 1 at 23:47



















          0












          $begingroup$

          Assuming the rows and columns are the numbers you wrote outside the square: If $n=m^2$ then the first row in the $k$'th sub-square would be row $m cdotlfloor frac{k}{m} rfloor$ (notice the floor function) and the first column would be $m cdot (k bmod m)$.



          So for $n=9$ the first row in e.g. the $7$'th sub-square would be row $3 cdotlfloor frac{7}{3} rfloor = 6$ and the first column would be $3 cdot (7 bmod 3)=3$.






          share|cite|improve this answer









          $endgroup$













            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: "69"
            };
            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: true,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: 10,
            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
            });


            }
            });














            draft saved

            draft discarded


















            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3058972%2fequation-to-locate-a-square-in-a-square%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









            1












            $begingroup$

            In your example, square $k$ is in row $lfloor frac k3 rfloor$ and in column $k bmod 3$. For general $n$, replace $3$ by $n$. This shows the nice side of counting starting with zero.






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              Note that calculating $lfloorfrac{k}3rfloor$ in most programming languages simply requires the statement $x:=k/3;$ and $kmbox{ mod }3$ requires $x:=k%3$.
              $endgroup$
              – SmileyCraft
              Jan 1 at 23:20












            • $begingroup$
              Thank you for your response. To clarify by square do you mean each small square that hold 1 number or a sub-square which holds n numbers?
              $endgroup$
              – fred
              Jan 1 at 23:29










            • $begingroup$
              For either case, I am not exactly sure if this would work unless I am mistaken (let me know if I am!). For example if we take subsquare 8 and we do 8/3 we get the 2.66..th row.
              $endgroup$
              – fred
              Jan 1 at 23:33










            • $begingroup$
              I may not have made it clear with the picture my apologies! the lines I drew are the outlines of the square and sub squares not the rows and columns.
              $endgroup$
              – fred
              Jan 1 at 23:36










            • $begingroup$
              I assumed the rows and columns were numbered $0$ to $2$ in each direction.
              $endgroup$
              – Ross Millikan
              Jan 1 at 23:47
















            1












            $begingroup$

            In your example, square $k$ is in row $lfloor frac k3 rfloor$ and in column $k bmod 3$. For general $n$, replace $3$ by $n$. This shows the nice side of counting starting with zero.






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              Note that calculating $lfloorfrac{k}3rfloor$ in most programming languages simply requires the statement $x:=k/3;$ and $kmbox{ mod }3$ requires $x:=k%3$.
              $endgroup$
              – SmileyCraft
              Jan 1 at 23:20












            • $begingroup$
              Thank you for your response. To clarify by square do you mean each small square that hold 1 number or a sub-square which holds n numbers?
              $endgroup$
              – fred
              Jan 1 at 23:29










            • $begingroup$
              For either case, I am not exactly sure if this would work unless I am mistaken (let me know if I am!). For example if we take subsquare 8 and we do 8/3 we get the 2.66..th row.
              $endgroup$
              – fred
              Jan 1 at 23:33










            • $begingroup$
              I may not have made it clear with the picture my apologies! the lines I drew are the outlines of the square and sub squares not the rows and columns.
              $endgroup$
              – fred
              Jan 1 at 23:36










            • $begingroup$
              I assumed the rows and columns were numbered $0$ to $2$ in each direction.
              $endgroup$
              – Ross Millikan
              Jan 1 at 23:47














            1












            1








            1





            $begingroup$

            In your example, square $k$ is in row $lfloor frac k3 rfloor$ and in column $k bmod 3$. For general $n$, replace $3$ by $n$. This shows the nice side of counting starting with zero.






            share|cite|improve this answer









            $endgroup$



            In your example, square $k$ is in row $lfloor frac k3 rfloor$ and in column $k bmod 3$. For general $n$, replace $3$ by $n$. This shows the nice side of counting starting with zero.







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Jan 1 at 23:19









            Ross MillikanRoss Millikan

            294k23198371




            294k23198371












            • $begingroup$
              Note that calculating $lfloorfrac{k}3rfloor$ in most programming languages simply requires the statement $x:=k/3;$ and $kmbox{ mod }3$ requires $x:=k%3$.
              $endgroup$
              – SmileyCraft
              Jan 1 at 23:20












            • $begingroup$
              Thank you for your response. To clarify by square do you mean each small square that hold 1 number or a sub-square which holds n numbers?
              $endgroup$
              – fred
              Jan 1 at 23:29










            • $begingroup$
              For either case, I am not exactly sure if this would work unless I am mistaken (let me know if I am!). For example if we take subsquare 8 and we do 8/3 we get the 2.66..th row.
              $endgroup$
              – fred
              Jan 1 at 23:33










            • $begingroup$
              I may not have made it clear with the picture my apologies! the lines I drew are the outlines of the square and sub squares not the rows and columns.
              $endgroup$
              – fred
              Jan 1 at 23:36










            • $begingroup$
              I assumed the rows and columns were numbered $0$ to $2$ in each direction.
              $endgroup$
              – Ross Millikan
              Jan 1 at 23:47


















            • $begingroup$
              Note that calculating $lfloorfrac{k}3rfloor$ in most programming languages simply requires the statement $x:=k/3;$ and $kmbox{ mod }3$ requires $x:=k%3$.
              $endgroup$
              – SmileyCraft
              Jan 1 at 23:20












            • $begingroup$
              Thank you for your response. To clarify by square do you mean each small square that hold 1 number or a sub-square which holds n numbers?
              $endgroup$
              – fred
              Jan 1 at 23:29










            • $begingroup$
              For either case, I am not exactly sure if this would work unless I am mistaken (let me know if I am!). For example if we take subsquare 8 and we do 8/3 we get the 2.66..th row.
              $endgroup$
              – fred
              Jan 1 at 23:33










            • $begingroup$
              I may not have made it clear with the picture my apologies! the lines I drew are the outlines of the square and sub squares not the rows and columns.
              $endgroup$
              – fred
              Jan 1 at 23:36










            • $begingroup$
              I assumed the rows and columns were numbered $0$ to $2$ in each direction.
              $endgroup$
              – Ross Millikan
              Jan 1 at 23:47
















            $begingroup$
            Note that calculating $lfloorfrac{k}3rfloor$ in most programming languages simply requires the statement $x:=k/3;$ and $kmbox{ mod }3$ requires $x:=k%3$.
            $endgroup$
            – SmileyCraft
            Jan 1 at 23:20






            $begingroup$
            Note that calculating $lfloorfrac{k}3rfloor$ in most programming languages simply requires the statement $x:=k/3;$ and $kmbox{ mod }3$ requires $x:=k%3$.
            $endgroup$
            – SmileyCraft
            Jan 1 at 23:20














            $begingroup$
            Thank you for your response. To clarify by square do you mean each small square that hold 1 number or a sub-square which holds n numbers?
            $endgroup$
            – fred
            Jan 1 at 23:29




            $begingroup$
            Thank you for your response. To clarify by square do you mean each small square that hold 1 number or a sub-square which holds n numbers?
            $endgroup$
            – fred
            Jan 1 at 23:29












            $begingroup$
            For either case, I am not exactly sure if this would work unless I am mistaken (let me know if I am!). For example if we take subsquare 8 and we do 8/3 we get the 2.66..th row.
            $endgroup$
            – fred
            Jan 1 at 23:33




            $begingroup$
            For either case, I am not exactly sure if this would work unless I am mistaken (let me know if I am!). For example if we take subsquare 8 and we do 8/3 we get the 2.66..th row.
            $endgroup$
            – fred
            Jan 1 at 23:33












            $begingroup$
            I may not have made it clear with the picture my apologies! the lines I drew are the outlines of the square and sub squares not the rows and columns.
            $endgroup$
            – fred
            Jan 1 at 23:36




            $begingroup$
            I may not have made it clear with the picture my apologies! the lines I drew are the outlines of the square and sub squares not the rows and columns.
            $endgroup$
            – fred
            Jan 1 at 23:36












            $begingroup$
            I assumed the rows and columns were numbered $0$ to $2$ in each direction.
            $endgroup$
            – Ross Millikan
            Jan 1 at 23:47




            $begingroup$
            I assumed the rows and columns were numbered $0$ to $2$ in each direction.
            $endgroup$
            – Ross Millikan
            Jan 1 at 23:47











            0












            $begingroup$

            Assuming the rows and columns are the numbers you wrote outside the square: If $n=m^2$ then the first row in the $k$'th sub-square would be row $m cdotlfloor frac{k}{m} rfloor$ (notice the floor function) and the first column would be $m cdot (k bmod m)$.



            So for $n=9$ the first row in e.g. the $7$'th sub-square would be row $3 cdotlfloor frac{7}{3} rfloor = 6$ and the first column would be $3 cdot (7 bmod 3)=3$.






            share|cite|improve this answer









            $endgroup$


















              0












              $begingroup$

              Assuming the rows and columns are the numbers you wrote outside the square: If $n=m^2$ then the first row in the $k$'th sub-square would be row $m cdotlfloor frac{k}{m} rfloor$ (notice the floor function) and the first column would be $m cdot (k bmod m)$.



              So for $n=9$ the first row in e.g. the $7$'th sub-square would be row $3 cdotlfloor frac{7}{3} rfloor = 6$ and the first column would be $3 cdot (7 bmod 3)=3$.






              share|cite|improve this answer









              $endgroup$
















                0












                0








                0





                $begingroup$

                Assuming the rows and columns are the numbers you wrote outside the square: If $n=m^2$ then the first row in the $k$'th sub-square would be row $m cdotlfloor frac{k}{m} rfloor$ (notice the floor function) and the first column would be $m cdot (k bmod m)$.



                So for $n=9$ the first row in e.g. the $7$'th sub-square would be row $3 cdotlfloor frac{7}{3} rfloor = 6$ and the first column would be $3 cdot (7 bmod 3)=3$.






                share|cite|improve this answer









                $endgroup$



                Assuming the rows and columns are the numbers you wrote outside the square: If $n=m^2$ then the first row in the $k$'th sub-square would be row $m cdotlfloor frac{k}{m} rfloor$ (notice the floor function) and the first column would be $m cdot (k bmod m)$.



                So for $n=9$ the first row in e.g. the $7$'th sub-square would be row $3 cdotlfloor frac{7}{3} rfloor = 6$ and the first column would be $3 cdot (7 bmod 3)=3$.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Jan 2 at 1:53









                JensJens

                3,71521030




                3,71521030






























                    draft saved

                    draft discarded




















































                    Thanks for contributing an answer to Mathematics 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%2fmath.stackexchange.com%2fquestions%2f3058972%2fequation-to-locate-a-square-in-a-square%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

                    Human spaceflight

                    Image
                    Human spaceflight From Wikipedia, the free encyclopedia Jump to navigation Jump to search "Space traveler" redirects here. For other uses, see Space traveler (disambiguation). @media all and (max-width:720px){.mw-parser-output .tmulti>.thumbinner{width:100%!important;max-width:none!important}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:none!important;width:100%!important;text-align:center}} Apollo 11 crewmember Buzz Aldrin on the Moon, 1969 International Space Station crewmember Tracy Caldwell Dyson views the Earth, 2010 Space Shuttle Discovery heads into space with a crew aboard, STS-121 in 2006 Inside a space suit on the Canadarm, 1993 Human spaceflight (also referred to as crewed spaceflight or manned spaceflight ) is space travel with a crew or passengers aboard the spacecraft. Spacecraft carrying people may be operated directly, by human crew, or it may be e...
                    Read more

                    Can not write log (Is /dev/pts mounted?) - openpty in Ubuntu-on-Windows?

                    Image
                    0 1 What exactly does the error message beginning with E: mean? I assume it has to do with the file structure on Ubuntu-on-Windows, but what exactly? The following package was automatically installed and is no longer required: os-prober Use 'apt-get autoremove' to remove it. The following extra packages will be installed: libxslt1.1 The following NEW packages will be installed: libxslt1.1 xmlstarlet 0 upgraded, 2 newly installed, 0 to remove and 0 not upgraded. Need to get 435 kB of archives. After this operation, 1023 kB of additional disk space will be used. Get:1 http://archive.ubuntu.com/ubuntu/ trusty/main libxslt1.1 amd64 1.1.28-2build1 [145 kB] Get:2 http://archive.ubuntu.com/ubuntu/ trusty/universe xmlstarlet amd64 1.5.0-1 [290 kB] ...
                    Read more

                    張江高科駅

                    Image
                    張江高科駅 ちょうこうこうか Zhangjiang Hi-Tech Park 所在地 中国上海市浦東新区 所属事業者 上海地鉄運営有限公司（上海軌道交通・駅詳細） 上海浦東現代有軌交通有限公司（駅詳細） テンプレートを表示 張江高科駅 各種表記 繁体字： 張江高科站 簡体字： 张江高科站 拼音 ： Zhàngjiāng Gāokē Zhàn 発音： ヂャンジャン ガオクー ヂャン 英文： Zhangjiang Hi-Tech Park Station テンプレートを表示 張江高科駅 （ちょうこうこうか-えき）は中華人民共和国上海市浦東新区に位置する、上海軌道交通2号線の駅である。 なお、張江高科駅前にある張江軌道電車の 張江地鉄駅駅 についてもここで述べる。 目次 1 利用可能な鉄道路線 2 沿革 3 駅構造 3.1 上海軌道交通 3.2 張江軌道電車 4 駅周辺 5 隣の駅 6 注釈 7 関連項目 利用可能な鉄道路線 上海軌道交通 ■ 2号線 上海浦東現代有軌交通有限公司 ■ 張江軌道電車 沿革 高架駅時代の姿 2000年12月27日 - 2号線の駅が高架駅として開業。 2010年 1月1日 - 張江軌道電車の開業に伴い、張江地鉄駅駅（停留所）を設置。 2月13日 - 駅地下化に伴い高架駅の運用停止。 2月24日 - 10日間の閉鎖を経て地下新駅の開業。 2017年2月9日 - リニューアル工事を経て再開業。乗降客の増加に対応し、ホームへのエレベーター、エスカレーターを増設、券売機エリアを拡張した [1] 。 駅構造 上海軌道交通 上海軌道交通 張江高科駅 5号口 ちょうこうこうか Zhangjiang Hi-Tech Park ◄ 竜陽路 (2.60km) (1.61km) 金科路 ► 所在地 中国上海市浦東新区松涛路 祖冲之路 （中国語版） 北緯31度12分11秒 東経121度34分50秒  /  北緯31.2...
                    Read more