The guidelines for Project Euler say that

Each problem has been designed according to a “one-minute rule”, which means that although it may take several hours to design a successful algorithm with more difficult problems, an efficient implementation will allow a solution to be obtained on a modestly powered computer in less than one minute.

which makes me think that my solution to problem 15,

Starting in the top left corner of a 22 grid, there are 6 routes (without backtracking) to the bottom right corner.

How many routes are there through a 2020 grid?

which has been running since Wednesday, is less than optimal (makes me think I don’t quite deserve the 9% genius rating). I am sure it is going to find the right answer and I calculated that it would take three days. When it is done, I’ll try to get it down to a minute. That’s part of the fun.

Since #15 is taking such a long time, I skipped to some later problems. #18 was fun:

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

3

7 5

2 4 6

8 5 9 3That is, 3 + 7 + 4 + 9 = 23.

Find the maximum total from top to bottom of the triangle below

My recursive solution below the fold (no peeking until you have solved it).

```
``````
input = "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"
@triangle = input.split(/\n/).collect { |line|
line.split(/\s/).collect{ |number| number.to_i }
}
def total row, col
total = @triangle[row][col]
return total if row == @triangle.size - 1
left = total(row+1, col)
right = total(row+1, col+1)
return total + right if right > left
return total + left
end
before = Time.now
puts total(0,0)
after = Time.now
puts "time=#{after - before}"
```

My solution to #15 ended up taking half an hour, I think. Then I got to look at the forum solutions, of course, which were educational. There is a quick way to solve it, but I would have never guessed it, I don’t think. I’ve put off #18 because it hints at a “trick” to it, and I haven’t figured out anything but brute force. I solved a couple later ones instead :). The problems are definitely getting harder to solve.