problem174.rb

# We shall define a square lamina to be a square outline with a square "hole" so that the shape possesses vertical and horizontal symmetry.
# 
# Given eight tiles it is possible to form a lamina in only one way: 3x3 square with a 1x1 hole in the middle. However, using thirty-two tiles it is possible to form two distinct laminae.
# 
# If t represents the number of tiles used, we shall say that t = 8 is type L(1) and t = 32 is type L(2).
# 
# Let N(n) be the number of t ≤ 1000000 such that t is type L(n); for example, N(15) = 832.
# 
# What is ∑ N(n) for 1 ≤ n ≤ 10?

max = 1000000
l_array = [0]*(max+1)

[8,12].each do |start|
    a_0 = start
    while a_0 <= max
	current = a_0
	sum = current
	while sum <= max
	    l_array[sum] += 1
	    current += 8
	    sum += current
	end
	a_0 += 8
    end
end

puts l_array.reject{|x| x < 1 or x > 10}.length