Problem 28
Statement
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 both diagonals is 101.
What is the sum of both diagonals in a 1001 by 1001 spiral formed in the same way?
Solution
class Spiral
def initialize(size)
@size = size
end
def sum_first_diagonal
sum = 0
nb = 1
inc = 0
(@size).times do |i|
nb += inc
sum += nb
inc += 2
end
return sum
end
def sum_second_diagonal
sum = 0
nb = 1
inc = 0
(@size).times do |i|
nb += inc
sum += nb
inc += 4 if i%2==0
end
return sum
end
def sum_diagonals
sum_first_diagonal+sum_second_diagonal-1
end
end
spiral = Spiral.new(1001)
puts spiral.sum_diagonals
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