9sums - a logical deduction puzzle












6












$begingroup$


Each set of minuses contains an integer in the range [1,5]. The given numbers are the sum of the surrounding 4 numbers.






---    ---    ---    ---

    13     14     11

---    ---    ---    ---

    11     10     13

---    ---    ---    ---

    11      9     14

---    ---    ---    ---



Can you solve the grid?






mathematics logical-deduction calculation-puzzle







share|improve this question









$endgroup$












  • $begingroup$
    Are there any rules on number of uses of each integer or using the same integer per row/column?
    $endgroup$
    – AHKieran
    Dec 11 '18 at 9:04










  • $begingroup$
    @AHKieran; not yet!
    $endgroup$
    – JonMark Perry
    Dec 11 '18 at 9:07
















6












$begingroup$


Each set of minuses contains an integer in the range [1,5]. The given numbers are the sum of the surrounding 4 numbers.






---    ---    ---    ---

    13     14     11

---    ---    ---    ---

    11     10     13

---    ---    ---    ---

    11      9     14

---    ---    ---    ---



Can you solve the grid?






mathematics logical-deduction calculation-puzzle







share|improve this question









$endgroup$












  • $begingroup$
    Are there any rules on number of uses of each integer or using the same integer per row/column?
    $endgroup$
    – AHKieran
    Dec 11 '18 at 9:04










  • $begingroup$
    @AHKieran; not yet!
    $endgroup$
    – JonMark Perry
    Dec 11 '18 at 9:07














6












6








6


0



$begingroup$


Each set of minuses contains an integer in the range [1,5]. The given numbers are the sum of the surrounding 4 numbers.






---    ---    ---    ---

    13     14     11

---    ---    ---    ---

    11     10     13

---    ---    ---    ---

    11      9     14

---    ---    ---    ---



Can you solve the grid?






mathematics logical-deduction calculation-puzzle







share|improve this question









$endgroup$




Each set of minuses contains an integer in the range [1,5]. The given numbers are the sum of the surrounding 4 numbers.






---    ---    ---    ---

    13     14     11

---    ---    ---    ---

    11     10     13

---    ---    ---    ---

    11      9     14

---    ---    ---    ---



Can you solve the grid?






mathematics logical-deduction calculation-puzzle




mathematics logical-deduction calculation-puzzle






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked Dec 11 '18 at 8:57









JonMark PerryJonMark Perry

18.9k63891




18.9k63891












  • $begingroup$
    Are there any rules on number of uses of each integer or using the same integer per row/column?
    $endgroup$
    – AHKieran
    Dec 11 '18 at 9:04










  • $begingroup$
    @AHKieran; not yet!
    $endgroup$
    – JonMark Perry
    Dec 11 '18 at 9:07


















  • $begingroup$
    Are there any rules on number of uses of each integer or using the same integer per row/column?
    $endgroup$
    – AHKieran
    Dec 11 '18 at 9:04










  • $begingroup$
    @AHKieran; not yet!
    $endgroup$
    – JonMark Perry
    Dec 11 '18 at 9:07
















$begingroup$
Are there any rules on number of uses of each integer or using the same integer per row/column?
$endgroup$
– AHKieran
Dec 11 '18 at 9:04




$begingroup$
Are there any rules on number of uses of each integer or using the same integer per row/column?
$endgroup$
– AHKieran
Dec 11 '18 at 9:04












$begingroup$
@AHKieran; not yet!
$endgroup$
– JonMark Perry
Dec 11 '18 at 9:07




$begingroup$
@AHKieran; not yet!
$endgroup$
– JonMark Perry
Dec 11 '18 at 9:07










7 Answers
7






active

oldest

votes


















7












$begingroup$





 2      5      3      1

    13     14     11

 3      3      3      4

    11     10     13

 4      1      3      3

    11      9     14

 5      1      4      4






share|improve this answer











$endgroup$









  • 1




    $begingroup$
    Well done! I edited the answer to make it a little more readable.
    $endgroup$
    – Christoph
    Dec 11 '18 at 9:20



















3












$begingroup$

My answer:




Not sure how to format this, but from left to right, then top to bottom, the numbers would be:

2, 5, 5, 1

5, 1, 3, 2

2, 3, 3, 5

5, 1, 2, 4







share|improve this answer









$endgroup$













  • $begingroup$
    from the looks of it there are multiple solutions, for some reason the other answer didn't appear until after I posted mine...
    $endgroup$
    – AHKieran
    Dec 11 '18 at 9:21



















3












$begingroup$

Its has many solutons, just need to start somewhere




3      3      3       1

   13     14    11

2      5      3       4

   11     10     13

2      1      1       5

   11     9     14

5      3      4       4







share|improve this answer









$endgroup$





















    3












    $begingroup$

    Here is my solution in excel:




    solution




    If you want to solve it by yourself, here is file 9sum.xlsx.






    share|improve this answer











    $endgroup$













    • $begingroup$
      Welcome to PuzzlingSE! Please include your answer in your post, and don't just link to it. This keeps it available, should you ever decide to delete the file and it does not force other people to download a file from an unknown person/source. As it stands this answer will most likely be deleted soon.
      $endgroup$
      – Christoph
      Dec 11 '18 at 11:24






    • 3




      $begingroup$
      What you could do is take a screenshot of your excel and upload it as an answer
      $endgroup$
      – AHKieran
      Dec 11 '18 at 11:25



















    2












    $begingroup$


    Also this grid is a solution :


    2 4 5 2

    3 4 1 3

    3 1 4 5

    4 3 1 4







    share|improve this answer











    $endgroup$













    • $begingroup$
      Welcome to Puzzling.SE. Take the tour. I have edited your answer to include it with a spoiler markup >!.
      $endgroup$
      – u_ndefined
      Dec 11 '18 at 10:14



















    1












    $begingroup$

    This was fun!




    For my solution, I started in the four corners and worked my way inwards, ignoring the 1-5 constraint. When I had completed the grid without constraints, I again started in the corners to adjust numbers to fit the constraints until all constraints were satisfied.



    
-3-    -4-    -4-    -1-
    
    13     14     11
    
-1-    -5-    -1-    -5-
    
    11     10     13
    
-3-    -2-    -2-    -5-
    
    11      9     14
    
-5-    -1-    -4-    -3-






    share|improve this answer









    $endgroup$





















      0












      $begingroup$




      
 2      5      3      2
      
    13     14     11
      
 3      3      3      3
      
    11     10     13
      
 3      2      2      5
      
    11      9     14
      
 4      2      3      4


      Given the multiple possible answers, it is possible to add further restrictions, such as using integers from [2, 5] only (this solution qualifies!)





      share|improve this answer









      $endgroup$













        Your Answer





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        7 Answers
        7






        active

        oldest

        votes








        7 Answers
        7






        active

        oldest

        votes









        active

        oldest

        votes






        active

        oldest

        votes









        7












        $begingroup$




        
 2      5      3      1
        
    13     14     11
        
 3      3      3      4
        
    11     10     13
        
 4      1      3      3
        
    11      9     14
        
 5      1      4      4






        share|improve this answer











        $endgroup$









        • 1




          $begingroup$
          Well done! I edited the answer to make it a little more readable.
          $endgroup$
          – Christoph
          Dec 11 '18 at 9:20
















        7












        $begingroup$




        
 2      5      3      1
        
    13     14     11
        
 3      3      3      4
        
    11     10     13
        
 4      1      3      3
        
    11      9     14
        
 5      1      4      4






        share|improve this answer











        $endgroup$









        • 1




          $begingroup$
          Well done! I edited the answer to make it a little more readable.
          $endgroup$
          – Christoph
          Dec 11 '18 at 9:20














        7












        7








        7





        $begingroup$




        
 2      5      3      1
        
    13     14     11
        
 3      3      3      4
        
    11     10     13
        
 4      1      3      3
        
    11      9     14
        
 5      1      4      4






        share|improve this answer











        $endgroup$






        
 2      5      3      1
        
    13     14     11
        
 3      3      3      4
        
    11     10     13
        
 4      1      3      3
        
    11      9     14
        
 5      1      4      4







        share|improve this answer














        share|improve this answer



        share|improve this answer








        edited Dec 11 '18 at 9:19









        Christoph

        3,4161426




        3,4161426










        answered Dec 11 '18 at 9:07









        AlexAlex

        3565




        3565








        • 1




          $begingroup$
          Well done! I edited the answer to make it a little more readable.
          $endgroup$
          – Christoph
          Dec 11 '18 at 9:20














        • 1




          $begingroup$
          Well done! I edited the answer to make it a little more readable.
          $endgroup$
          – Christoph
          Dec 11 '18 at 9:20








        1




        1




        $begingroup$
        Well done! I edited the answer to make it a little more readable.
        $endgroup$
        – Christoph
        Dec 11 '18 at 9:20




        $begingroup$
        Well done! I edited the answer to make it a little more readable.
        $endgroup$
        – Christoph
        Dec 11 '18 at 9:20











        3












        $begingroup$

        My answer:




        Not sure how to format this, but from left to right, then top to bottom, the numbers would be:

        2, 5, 5, 1

        5, 1, 3, 2

        2, 3, 3, 5

        5, 1, 2, 4







        share|improve this answer









        $endgroup$













        • $begingroup$
          from the looks of it there are multiple solutions, for some reason the other answer didn't appear until after I posted mine...
          $endgroup$
          – AHKieran
          Dec 11 '18 at 9:21
















        3












        $begingroup$

        My answer:




        Not sure how to format this, but from left to right, then top to bottom, the numbers would be:

        2, 5, 5, 1

        5, 1, 3, 2

        2, 3, 3, 5

        5, 1, 2, 4







        share|improve this answer









        $endgroup$













        • $begingroup$
          from the looks of it there are multiple solutions, for some reason the other answer didn't appear until after I posted mine...
          $endgroup$
          – AHKieran
          Dec 11 '18 at 9:21














        3












        3








        3





        $begingroup$

        My answer:




        Not sure how to format this, but from left to right, then top to bottom, the numbers would be:

        2, 5, 5, 1

        5, 1, 3, 2

        2, 3, 3, 5

        5, 1, 2, 4







        share|improve this answer









        $endgroup$



        My answer:




        Not sure how to format this, but from left to right, then top to bottom, the numbers would be:

        2, 5, 5, 1

        5, 1, 3, 2

        2, 3, 3, 5

        5, 1, 2, 4








        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered Dec 11 '18 at 9:20









        AHKieranAHKieran

        5,0081040




        5,0081040












        • $begingroup$
          from the looks of it there are multiple solutions, for some reason the other answer didn't appear until after I posted mine...
          $endgroup$
          – AHKieran
          Dec 11 '18 at 9:21


















        • $begingroup$
          from the looks of it there are multiple solutions, for some reason the other answer didn't appear until after I posted mine...
          $endgroup$
          – AHKieran
          Dec 11 '18 at 9:21
















        $begingroup$
        from the looks of it there are multiple solutions, for some reason the other answer didn't appear until after I posted mine...
        $endgroup$
        – AHKieran
        Dec 11 '18 at 9:21




        $begingroup$
        from the looks of it there are multiple solutions, for some reason the other answer didn't appear until after I posted mine...
        $endgroup$
        – AHKieran
        Dec 11 '18 at 9:21











        3












        $begingroup$

        Its has many solutons, just need to start somewhere




        3      3      3       1

           13     14    11

        2      5      3       4

           11     10     13

        2      1      1       5

           11     9     14

        5      3      4       4







        share|improve this answer









        $endgroup$


















          3












          $begingroup$

          Its has many solutons, just need to start somewhere




          3      3      3       1

             13     14    11

          2      5      3       4

             11     10     13

          2      1      1       5

             11     9     14

          5      3      4       4







          share|improve this answer









          $endgroup$
















            3












            3








            3





            $begingroup$

            Its has many solutons, just need to start somewhere




            3      3      3       1

               13     14    11

            2      5      3       4

               11     10     13

            2      1      1       5

               11     9     14

            5      3      4       4







            share|improve this answer









            $endgroup$



            Its has many solutons, just need to start somewhere




            3      3      3       1

               13     14    11

            2      5      3       4

               11     10     13

            2      1      1       5

               11     9     14

            5      3      4       4








            share|improve this answer












            share|improve this answer



            share|improve this answer










            answered Dec 11 '18 at 9:21









            Naeem ShaikhNaeem Shaikh

            829410




            829410























                3












                $begingroup$

                Here is my solution in excel:




                solution




                If you want to solve it by yourself, here is file 9sum.xlsx.






                share|improve this answer











                $endgroup$













                • $begingroup$
                  Welcome to PuzzlingSE! Please include your answer in your post, and don't just link to it. This keeps it available, should you ever decide to delete the file and it does not force other people to download a file from an unknown person/source. As it stands this answer will most likely be deleted soon.
                  $endgroup$
                  – Christoph
                  Dec 11 '18 at 11:24






                • 3




                  $begingroup$
                  What you could do is take a screenshot of your excel and upload it as an answer
                  $endgroup$
                  – AHKieran
                  Dec 11 '18 at 11:25
















                3












                $begingroup$

                Here is my solution in excel:




                solution




                If you want to solve it by yourself, here is file 9sum.xlsx.






                share|improve this answer











                $endgroup$













                • $begingroup$
                  Welcome to PuzzlingSE! Please include your answer in your post, and don't just link to it. This keeps it available, should you ever decide to delete the file and it does not force other people to download a file from an unknown person/source. As it stands this answer will most likely be deleted soon.
                  $endgroup$
                  – Christoph
                  Dec 11 '18 at 11:24






                • 3




                  $begingroup$
                  What you could do is take a screenshot of your excel and upload it as an answer
                  $endgroup$
                  – AHKieran
                  Dec 11 '18 at 11:25














                3












                3








                3





                $begingroup$

                Here is my solution in excel:




                solution




                If you want to solve it by yourself, here is file 9sum.xlsx.






                share|improve this answer











                $endgroup$



                Here is my solution in excel:




                solution




                If you want to solve it by yourself, here is file 9sum.xlsx.







                share|improve this answer














                share|improve this answer



                share|improve this answer








                edited Dec 13 '18 at 13:28









                S. M.

                953419




                953419










                answered Dec 11 '18 at 10:44









                cluster_mastercluster_master

                313




                313












                • $begingroup$
                  Welcome to PuzzlingSE! Please include your answer in your post, and don't just link to it. This keeps it available, should you ever decide to delete the file and it does not force other people to download a file from an unknown person/source. As it stands this answer will most likely be deleted soon.
                  $endgroup$
                  – Christoph
                  Dec 11 '18 at 11:24






                • 3




                  $begingroup$
                  What you could do is take a screenshot of your excel and upload it as an answer
                  $endgroup$
                  – AHKieran
                  Dec 11 '18 at 11:25


















                • $begingroup$
                  Welcome to PuzzlingSE! Please include your answer in your post, and don't just link to it. This keeps it available, should you ever decide to delete the file and it does not force other people to download a file from an unknown person/source. As it stands this answer will most likely be deleted soon.
                  $endgroup$
                  – Christoph
                  Dec 11 '18 at 11:24






                • 3




                  $begingroup$
                  What you could do is take a screenshot of your excel and upload it as an answer
                  $endgroup$
                  – AHKieran
                  Dec 11 '18 at 11:25
















                $begingroup$
                Welcome to PuzzlingSE! Please include your answer in your post, and don't just link to it. This keeps it available, should you ever decide to delete the file and it does not force other people to download a file from an unknown person/source. As it stands this answer will most likely be deleted soon.
                $endgroup$
                – Christoph
                Dec 11 '18 at 11:24




                $begingroup$
                Welcome to PuzzlingSE! Please include your answer in your post, and don't just link to it. This keeps it available, should you ever decide to delete the file and it does not force other people to download a file from an unknown person/source. As it stands this answer will most likely be deleted soon.
                $endgroup$
                – Christoph
                Dec 11 '18 at 11:24




                3




                3




                $begingroup$
                What you could do is take a screenshot of your excel and upload it as an answer
                $endgroup$
                – AHKieran
                Dec 11 '18 at 11:25




                $begingroup$
                What you could do is take a screenshot of your excel and upload it as an answer
                $endgroup$
                – AHKieran
                Dec 11 '18 at 11:25











                2












                $begingroup$


                Also this grid is a solution :


                2 4 5 2

                3 4 1 3

                3 1 4 5

                4 3 1 4







                share|improve this answer











                $endgroup$













                • $begingroup$
                  Welcome to Puzzling.SE. Take the tour. I have edited your answer to include it with a spoiler markup >!.
                  $endgroup$
                  – u_ndefined
                  Dec 11 '18 at 10:14
















                2












                $begingroup$


                Also this grid is a solution :


                2 4 5 2

                3 4 1 3

                3 1 4 5

                4 3 1 4







                share|improve this answer











                $endgroup$













                • $begingroup$
                  Welcome to Puzzling.SE. Take the tour. I have edited your answer to include it with a spoiler markup >!.
                  $endgroup$
                  – u_ndefined
                  Dec 11 '18 at 10:14














                2












                2








                2





                $begingroup$


                Also this grid is a solution :


                2 4 5 2

                3 4 1 3

                3 1 4 5

                4 3 1 4







                share|improve this answer











                $endgroup$




                Also this grid is a solution :


                2 4 5 2

                3 4 1 3

                3 1 4 5

                4 3 1 4








                share|improve this answer














                share|improve this answer



                share|improve this answer








                edited Dec 11 '18 at 10:11









                u_ndefined

                2,638436




                2,638436










                answered Dec 11 '18 at 9:53









                richardrichard

                211




                211












                • $begingroup$
                  Welcome to Puzzling.SE. Take the tour. I have edited your answer to include it with a spoiler markup >!.
                  $endgroup$
                  – u_ndefined
                  Dec 11 '18 at 10:14


















                • $begingroup$
                  Welcome to Puzzling.SE. Take the tour. I have edited your answer to include it with a spoiler markup >!.
                  $endgroup$
                  – u_ndefined
                  Dec 11 '18 at 10:14
















                $begingroup$
                Welcome to Puzzling.SE. Take the tour. I have edited your answer to include it with a spoiler markup >!.
                $endgroup$
                – u_ndefined
                Dec 11 '18 at 10:14




                $begingroup$
                Welcome to Puzzling.SE. Take the tour. I have edited your answer to include it with a spoiler markup >!.
                $endgroup$
                – u_ndefined
                Dec 11 '18 at 10:14











                1












                $begingroup$

                This was fun!




                For my solution, I started in the four corners and worked my way inwards, ignoring the 1-5 constraint. When I had completed the grid without constraints, I again started in the corners to adjust numbers to fit the constraints until all constraints were satisfied.



                
-3-    -4-    -4-    -1-
                
    13     14     11
                
-1-    -5-    -1-    -5-
                
    11     10     13
                
-3-    -2-    -2-    -5-
                
    11      9     14
                
-5-    -1-    -4-    -3-






                share|improve this answer









                $endgroup$


















                  1












                  $begingroup$

                  This was fun!




                  For my solution, I started in the four corners and worked my way inwards, ignoring the 1-5 constraint. When I had completed the grid without constraints, I again started in the corners to adjust numbers to fit the constraints until all constraints were satisfied.



                  
-3-    -4-    -4-    -1-
                  
    13     14     11
                  
-1-    -5-    -1-    -5-
                  
    11     10     13
                  
-3-    -2-    -2-    -5-
                  
    11      9     14
                  
-5-    -1-    -4-    -3-






                  share|improve this answer









                  $endgroup$
















                    1












                    1








                    1





                    $begingroup$

                    This was fun!




                    For my solution, I started in the four corners and worked my way inwards, ignoring the 1-5 constraint. When I had completed the grid without constraints, I again started in the corners to adjust numbers to fit the constraints until all constraints were satisfied.



                    
-3-    -4-    -4-    -1-
                    
    13     14     11
                    
-1-    -5-    -1-    -5-
                    
    11     10     13
                    
-3-    -2-    -2-    -5-
                    
    11      9     14
                    
-5-    -1-    -4-    -3-






                    share|improve this answer









                    $endgroup$



                    This was fun!




                    For my solution, I started in the four corners and worked my way inwards, ignoring the 1-5 constraint. When I had completed the grid without constraints, I again started in the corners to adjust numbers to fit the constraints until all constraints were satisfied.



                    
-3-    -4-    -4-    -1-
                    
    13     14     11
                    
-1-    -5-    -1-    -5-
                    
    11     10     13
                    
-3-    -2-    -2-    -5-
                    
    11      9     14
                    
-5-    -1-    -4-    -3-







                    share|improve this answer












                    share|improve this answer



                    share|improve this answer










                    answered Dec 11 '18 at 12:10









                    MarvMarv

                    1134




                    1134























                        0












                        $begingroup$




                        
 2      5      3      2
                        
    13     14     11
                        
 3      3      3      3
                        
    11     10     13
                        
 3      2      2      5
                        
    11      9     14
                        
 4      2      3      4


                        Given the multiple possible answers, it is possible to add further restrictions, such as using integers from [2, 5] only (this solution qualifies!)





                        share|improve this answer









                        $endgroup$


















                          0












                          $begingroup$




                          
 2      5      3      2
                          
    13     14     11
                          
 3      3      3      3
                          
    11     10     13
                          
 3      2      2      5
                          
    11      9     14
                          
 4      2      3      4


                          Given the multiple possible answers, it is possible to add further restrictions, such as using integers from [2, 5] only (this solution qualifies!)





                          share|improve this answer









                          $endgroup$
















                            0












                            0








                            0





                            $begingroup$




                            
 2      5      3      2
                            
    13     14     11
                            
 3      3      3      3
                            
    11     10     13
                            
 3      2      2      5
                            
    11      9     14
                            
 4      2      3      4


                            Given the multiple possible answers, it is possible to add further restrictions, such as using integers from [2, 5] only (this solution qualifies!)





                            share|improve this answer









                            $endgroup$






                            
 2      5      3      2
                            
    13     14     11
                            
 3      3      3      3
                            
    11     10     13
                            
 3      2      2      5
                            
    11      9     14
                            
 4      2      3      4


                            Given the multiple possible answers, it is possible to add further restrictions, such as using integers from [2, 5] only (this solution qualifies!)






                            share|improve this answer












                            share|improve this answer



                            share|improve this answer










                            answered Dec 14 '18 at 5:52









                            kwypstonkwypston

                            1763




                            1763






























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