numbers_1-9_triangle_sum_17_v1.c

/*

    numbers_1-9_triangle_sum_17_v1.c

    How to fill the triangle with 1, 2, 3, 4, 5, 6, 7, 8 and 9
    to get the sum of each side equal to 17 ?

                x4
            x3      x5
        x2              x6
    x1      x9      x8      x7

    https://web.facebook.com/photo.php?fbid=130470831905101&set=gm.2637750503211777&type=3&theater

    Brute force algorithm.


    You can find all my C programs at Dragan Milicev's pastebin:

    https://pastebin.com/u/dmilicev

*/

#include <stdio.h>

int main(void)
{
    int i, j, different, count=0, x[9];
    unsigned number_of_attempts=0;

    for( x[0]=1; x[0]<=9; x[0]++)
     for( x[1]=1; x[1]<=9; x[1]++)
      for( x[2]=1; x[2]<=9; x[2]++)
       for( x[3]=1; x[3]<=9; x[3]++)
        for( x[4]=1; x[4]<=9; x[4]++)
         for( x[5]=1; x[5]<=9; x[5]++)
          for( x[6]=1; x[6]<=9; x[6]++)
           for( x[7]=1; x[7]<=9; x[7]++)
            for( x[8]=1; x[8]<=9; x[8]++)
            {
                number_of_attempts++;
                different=1;

                for( i=0; i<9; i++)     // Check that all numbers 1 to 9 are different
                {
                    for( j=i+1; j<9; j++)
                    {
                        if( x[i] == x[j] )
                            different=0;
                    }
                    if(different==0)
                        break;
                }

                if(different)           // if they are different
                {                       // and if they satisfy the condition
                    if( x[0] + x[1] + x[2] + x[3] == 17 &&
                        x[3] + x[4] + x[5] + x[6] == 17 &&
                        x[6] + x[7] + x[8] + x[0] == 17     )
                    {
                            count++;    // count and display them
                            printf("\n---%3d. solution: --------\n\n", count);
                            printf("............%d\n", x[3]);
                            printf("........%d.......%d\n", x[2],x[4]);
                            printf("....%d...............%d\n", x[1],x[5]);
                            printf("%d.......%d.......%d.......%d\n", x[0],x[8],x[7],x[6]);
                    }
                } // if(different)
            } // for( x[8]=1; x[8]<=9; x[8]++)


    printf("\n Number of attempts is 9^9 = %ld \n", number_of_attempts);
    printf("\n There are %d solutions. \n", count);

    return 0;

} // main()

/*

The computer program I created to accomplish this task says that there are 96 solutions, which are:

---  1. solution: ------

............3
........9......5
....4..............7
1......8......6......2

---  2. solution: ------

............3
........9......5
....4..............7
1......6......8......2

---  3. solution: ------

............3
........9......7
....4..............5
1......8......6......2

---  4. solution: ------

............3
........9......7
....4..............5
1......6......8......2

---  5. solution: ------

............2
........9......4
....5..............8
1......7......6......3

---  6. solution: ------

............2
........9......4
....5..............8
1......6......7......3

---  7. solution: ------

............2
........9......8
....5..............4
1......7......6......3

---  8. solution: ------

............2
........9......8
....5..............4
1......6......7......3

---  9. solution: ------

............3
........7......4
....6..............8
1......9......5......2

--- 10. solution: ------

............3
........7......4
....6..............8
1......5......9......2

--- 11. solution: ------

............3
........7......8
....6..............4
1......9......5......2

--- 12. solution: ------

............3
........7......8
....6..............4
1......5......9......2

--- 13. solution: ------

............2
........8......5
....6..............7
1......9......4......3

--- 14. solution: ------

............2
........8......5
....6..............7
1......4......9......3

--- 15. solution: ------

............2
........8......7
....6..............5
1......9......4......3

--- 16. solution: ------

............2
........8......7
....6..............5
1......4......9......3

--- 17. solution: ------

............3
........6......4
....7..............8
1......9......5......2

--- 18. solution: ------

............3
........6......4
....7..............8
1......5......9......2

--- 19. solution: ------

............3
........6......8
....7..............4
1......9......5......2

--- 20. solution: ------

............3
........6......8
....7..............4
1......5......9......2

--- 21. solution: ------

............2
........6......5
....8..............7
1......9......4......3

--- 22. solution: ------

............2
........6......5
....8..............7
1......4......9......3

--- 23. solution: ------

............2
........6......7
....8..............5
1......9......4......3

--- 24. solution: ------

............2
........6......7
....8..............5
1......4......9......3

--- 25. solution: ------

............3
........4......5
....9..............7
1......8......6......2

--- 26. solution: ------

............3
........4......5
....9..............7
1......6......8......2

--- 27. solution: ------

............3
........4......7
....9..............5
1......8......6......2

--- 28. solution: ------

............3
........4......7
....9..............5
1......6......8......2

--- 29. solution: ------

............2
........5......4
....9..............8
1......7......6......3

--- 30. solution: ------

............2
........5......4
....9..............8
1......6......7......3

--- 31. solution: ------

............2
........5......8
....9..............4
1......7......6......3

--- 32. solution: ------

............2
........5......8
....9..............4
1......6......7......3

--- 33. solution: ------

............3
........8......6
....4..............7
2......9......5......1

--- 34. solution: ------

............3
........8......6
....4..............7
2......5......9......1

--- 35. solution: ------

............3
........8......7
....4..............6
2......9......5......1

--- 36. solution: ------

............3
........8......7
....4..............6
2......5......9......1

--- 37. solution: ------

............3
........7......4
....5..............9
2......8......6......1

--- 38. solution: ------

............3
........7......4
....5..............9
2......6......8......1

--- 39. solution: ------

............3
........7......9
....5..............4
2......8......6......1

--- 40. solution: ------

............3
........7......9
....5..............4
2......6......8......1

--- 41. solution: ------

............1
........9......6
....5..............7
2......8......4......3

--- 42. solution: ------

............1
........9......6
....5..............7
2......4......8......3

--- 43. solution: ------

............1
........9......7
....5..............6
2......8......4......3

--- 44. solution: ------

............1
........9......7
....5..............6
2......4......8......3

--- 45. solution: ------

............1
........8......4
....6..............9
2......7......5......3

--- 46. solution: ------

............1
........8......4
....6..............9
2......5......7......3

--- 47. solution: ------

............1
........8......9
....6..............4
2......7......5......3

--- 48. solution: ------

............1
........8......9
....6..............4
2......5......7......3

--- 49. solution: ------

............3
........5......4
....7..............9
2......8......6......1

--- 50. solution: ------

............3
........5......4
....7..............9
2......6......8......1

--- 51. solution: ------

............3
........5......9
....7..............4
2......8......6......1

--- 52. solution: ------

............3
........5......9
....7..............4
2......6......8......1

--- 53. solution: ------

............3
........4......6
....8..............7
2......9......5......1

--- 54. solution: ------

............3
........4......6
....8..............7
2......5......9......1

--- 55. solution: ------

............3
........4......7
....8..............6
2......9......5......1

--- 56. solution: ------

............3
........4......7
....8..............6
2......5......9......1

--- 57. solution: ------

............1
........6......4
....8..............9
2......7......5......3

--- 58. solution: ------

............1
........6......4
....8..............9
2......5......7......3

--- 59. solution: ------

............1
........6......9
....8..............4
2......7......5......3

--- 60. solution: ------

............1
........6......9
....8..............4
2......5......7......3

--- 61. solution: ------

............1
........5......6
....9..............7
2......8......4......3

--- 62. solution: ------

............1
........5......6
....9..............7
2......4......8......3

--- 63. solution: ------

............1
........5......7
....9..............6
2......8......4......3

--- 64. solution: ------

............1
........5......7
....9..............6
2......4......8......3

--- 65. solution: ------

............2
........8......5
....4..............9
3......7......6......1

--- 66. solution: ------

............2
........8......5
....4..............9
3......6......7......1

--- 67. solution: ------

............2
........8......9
....4..............5
3......7......6......1

--- 68. solution: ------

............2
........8......9
....4..............5
3......6......7......1

--- 69. solution: ------

............1
........9......6
....4..............8
3......7......5......2

--- 70. solution: ------

............1
........9......6
....4..............8
3......5......7......2

--- 71. solution: ------

............1
........9......8
....4..............6
3......7......5......2

--- 72. solution: ------

............1
........9......8
....4..............6
3......5......7......2

--- 73. solution: ------

............2
........7......6
....5..............8
3......9......4......1

--- 74. solution: ------

............2
........7......6
....5..............8
3......4......9......1

--- 75. solution: ------

............2
........7......8
....5..............6
3......9......4......1

--- 76. solution: ------

............2
........7......8
....5..............6
3......4......9......1

--- 77. solution: ------

............1
........7......5
....6..............9
3......8......4......2

--- 78. solution: ------

............1
........7......5
....6..............9
3......4......8......2

--- 79. solution: ------

............1
........7......9
....6..............5
3......8......4......2

--- 80. solution: ------

............1
........7......9
....6..............5
3......4......8......2

--- 81. solution: ------

............2
........5......6
....7..............8
3......9......4......1

--- 82. solution: ------

............2
........5......6
....7..............8
3......4......9......1

--- 83. solution: ------

............2
........5......8
....7..............6
3......9......4......1

--- 84. solution: ------

............2
........5......8
....7..............6
3......4......9......1

--- 85. solution: ------

............1
........6......5
....7..............9
3......8......4......2

--- 86. solution: ------

............1
........6......5
....7..............9
3......4......8......2

--- 87. solution: ------

............1
........6......9
....7..............5
3......8......4......2

--- 88. solution: ------

............1
........6......9
....7..............5
3......4......8......2

--- 89. solution: ------

............2
........4......5
....8..............9
3......7......6......1

--- 90. solution: ------

............2
........4......5
....8..............9
3......6......7......1

--- 91. solution: ------

............2
........4......9
....8..............5
3......7......6......1

--- 92. solution: ------

............2
........4......9
....8..............5
3......6......7......1

--- 93. solution: ------

............1
........4......6
....9..............8
3......7......5......2

--- 94. solution: ------

............1
........4......6
....9..............8
3......5......7......2

--- 95. solution: ------

............1
........4......8
....9..............6
3......7......5......2

--- 96. solution: ------

............1
........4......8
....9..............6
3......5......7......2

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

*/