Turkish Project Euler Question 18 Largest Sum Path 1

Starting from the top of the triangle below, the greatest sum that can be obtained by progressing with connected numbers in the rows below is 23.

3

7 4

2 4 6

8 5 9 3

Like this: 3 + 7 + 4 + 9 = 23.

Find the maximum sum that can be obtained from top to bottom in the triangle below:

75

95 64

17 47 82

18 35 87 10

20 04 82 47 65

19 01 23 75 03 34

88 02 77 73 07 63 67

99 65 04 28 06 16 70 92

41 41 26 56 83 40 80 70 33

41 48 72 33 47 32 37 16 94 29

53 71 44 65 25 43 91 52 97 51 14

70 11 33 28 77 73 17 78 39 68 17 57

91 71 52 38 17 14 91 43 58 50 27 29 48

63 66 04 68 89 53 67 30 73 16 69 87 40 31

04 62 98 27 23 09 70 98 73 93 38 53 60 04 23

NOTE: Since there are only 16,384 different paths, it is possible to solve this problem by trying all possibilities. However, question 67 is the same problem with a triangle of 100 rows; therefore, it cannot be solved by brute force and requires a clever method. ;o)