Question

Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:

21 22 23 24 25
20  7  8  9 10
19  6  1  2 11
18  5  4  3 12
17 16 15 14 13

It can be verified that the sum of the numbers on the diagonals is 101.

What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?

main :: IO ()
main = print $foldr (+) 1 [4*n^2 - 6*n + 6 | n <- [3,5..1001]] $ ghc -O2 -o spiral spiral.hs
$time ./spiral real 0m0.001s user 0m0.000s sys 0m0.000s Python #!/usr/bin/env python def sum_diagonals_of_spiral(size): n = 1 step = 2 total = 0 since_last = 0 while n <= size**2: total += n n += step since_last += 1 if since_last == 4: step += 2 since_last = 0 return total print(sum_diagonals_of_spiral(1001)) $ time python3 spiral.py
real   0m0.035s
user   0m0.024s
sys    0m0.008s

Ruby

#!/usr/bin/env ruby
i = 1
sum = i
step = 2
until i >= 1001**2
4.times { sum += i += step }
step += 2
end
puts sum
\$ time ruby spiral.rb
real   0m0.036s
user   0m0.028s
sys    0m0.004s

Questions? Comments? Send me an email: z@chdenton.com