This week's quiz was fairly easy. The hardest part was finding and choosing a way to turn the numbers into their English equivalents. Initially I used an array that extended to TWENTY, but that was insufficient. I had solved Ruby Quiz #25 and some of the other old ones myself a while ago, but lost it due to a harddrive crash and couldn't find a copy. I then just picked someone else's solution to Ruby Quiz #25 that added a to_en method to Integer.

Here's my solution, minus the Integer#to_en method. I commented out the code to print out the elements of the cycle, as it turns out the cycle is about 430 elements long!

def count_and_say(str)
  ('A'..'Z').map{|l| (str.count(l) > 0) ? 
    [str.count(l).to_en.upcase, l] : ""}.join(' ').squeeze(' ')
end

order = ARGV[0].chomp.to_i
prev_results = {}
element = "LOOK AND SAY"
for n in (0..order)
  if prev_results[element]
    puts "Cycle of length #{n-prev_results[element]} starting" +
      " at element #{prev_results[element]}"
    #puts "Cycle's elements are:"
    #puts (prev_results[element]...n).to_a.map{|n| prev_results.invert[n]}
    break
  else
    prev_results[element] = n
  end
  element = count_and_say(element)
end

----- Original Message ----
From: Ruby Quiz <james / grayproductions.net>
To: ruby-talk ML <ruby-talk / ruby-lang.org>
Sent: Thursday, September 6, 2007 7:00:20 AM
Subject: [QUIZ] Count and Say (#138)

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by Martin DeMello

Conway's "Look and Say" sequence
(http://en.wikipedia.org/wiki/Look-and-say_sequence) is a sequence of numbers in
which each term "reads aloud" the digits of the previous term. For instance, the
canonical L&S sequence starts off 1, 11, 21, 1211, 111221, ..., because:

    * 1 is read off as "one 1" or 11.
    * 11 is read off as "two 1's" or 21.
    * 21 is read off as "one 2, then one 1" or 1211.
    * 1211 is read off as "one 1, then one 2, then two 1's" or 111221.
    * 111221 is read off as "three 1, then two 2, then one 1" or 312211.

Over on rec.puzzles, Eric A. proposed a variant in which the letters of a
sentence are grouped, then "counted aloud", omitting the "s"s for the plural
form. Thus, seeding the sequence with "LOOK AND SAY", we get:

    0. LOOK AND SAY
    1. TWO A ONE D ONE K ONE L ONE N TWO O ONE S ONE Y
    2. ONE A ONE D SIX E ONE K ONE L SEVEN N NINE O ONE S TWO T TWO W ONE Y
    3. ONE A ONE D TEN E TWO I ONE K ONE L TEN N NINE O THREE S THREE T ONE V
       THREE W ONE X ONE Y

and so on. (Note the difference between this and the L&S sequence--the letters
are counted rather than read in order). Eric wants to know when the sequence
enters a cycle, and how long that cycle is. Well?






       
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