My solution for Project Euler problem #2 came out a little fugly mainly because of the global variables, but it works. The “secret” to getting the program to run in a reasonable amount of time is to store the values of the fibonacci sequence as you compute them instead of processing the same data over again.

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

Find the sum of all the even-valued terms in the sequence which do not exceed four million.

My Solution

```
max = 4_000_000
total = 0
$stack = []
def fib n
if n == 0
return 1
end
if n == 1
return 2
end
return $stack[n - 1] + $stack[n - 2]
end
max.times do |i|
$stack[i] = fib i
if $stack[i] > max
break
end
if $stack[i] & 1 == 0
total += $stack[i]
end
end
puts total
```

As is quickly becoming the case, Olathe’s solution was *much* more elegant than mine:

```
x, y, sum = 1, 1, 0
while sum < 1_000_000
sum += (x + y)
x, y = x + 2*y, 2*x + 3*y
end
puts "Sum is #{ sum }."
```