Problem 42

Projekt Euler w Ruby
1

Problem 42

The n-th term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, …

By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is 19 + 11 + 25 = 55 = t10. If the word value is a triangle number then we shall call the word a triangle word.

Using words.txt , a 16K text file containing nearly two-thousand common English words, how many are triangle words?

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[code=ruby]T = []

def is_triangle?(n)
T[n] ||= (delta = 1 + 8*n) > 0 && (s=Math.sqrt(delta)).to_i == s && (((-1 - s.to_i) / 2).integer? || ((-1 + s.to_i) / 2).integer?)
end

p File.read(‘words.txt’).split(’,’).map{|w| w.gsub(/"/, “”)}.select {|w|
is_triangle? w.each_byte.map{|e| e - 64}.inject(:+)
}.size[/code]