Phone riddle for Karl Leswing. See karl.rb for more details.

hint.rb

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karl.rb

#!/usr/bin/ruby

require "puzzle"

# Hi Karl! Welcome to your phone number riddle, Ruby style. You'll need both karl.rb and
# puzzle.rb (see below) in the same directory to solve things correctly, but the only
# file you should edit is karl.rb.

# Solve the following riddles. By running this Ruby script and answering the questions
# correctly, you'll generate the phone number of a certain person you know.
#
# //----------//
# // PART ONE //
# //----------//
# 
# Replace each question mark with the integer which is the answer to the statement above.

# Hint: all answers lie in the range 0 to 6 inclusive, and no two answers are the same.
s = Array.new(7)

# ?: Square root of Miley Cyrus's age as of November 21, 2009.
s[ ? ] = [*(5..7).map{|i| i * 10 + 7}]

# ?: Number of games won by UVA's football team as of November 20, 2009.
s[ ? ] = [*(1..3).map{|i| i * 10 + 7}]

# ?: Maximum legal length of a high school lacrosse goalie's stick, in feet.
s[ ? ] = [*(84..86)]

# ?: Smallest odd number which cannot be expressed as the sum of the proper
# divisors of any other number. Proper divisors are numbers which divide
# another number with no remainder; for example, [1, 2, 3] are the proper
# divisors of 6.
s[ ? ] = [*(5..7).map{|i| i * 10 + 3}]

# ?: Cardinality of the empty set.
s[ ? ] = [*(4..6)]

# ?: Baker's dozen minus a dozen.
s[ ? ] = [*(1..3).map{|i| i * 10 + 3}]

# ?: Solve for n: 1 + 1/n + 1/n^2 + ... = n.
s[ ? ] = [*(44..46)]

#
# //----------//
# // PART TWO //
# //----------//
#
# Two numbers i and j are coprime if they share no prime factors other than 1; for
# example 12 [2 * 2 * 3] and 35 [5 * 7] are coprime.
#
# Many integers can be expressed as the difference between another integer and the
# number of coprimes below that integer. For example, if you let CP(x) be the number
# of coprimes below x, then 6 is such a number: 10 - CP(10) = 10 - 4 = 6.
#
# Replace the question mark below with the smallest positive integer that cannot be
# expressed as the difference between any integer and the total number of coprimes
# below that integer. 
# 
sz = ?

# At this point, run "ruby karl.rb". If your answers are right, give the resulting
# phone number a call. Good luck, and happy Thanksgiving!

d = [
  s[0]|s[1]|s[3]|s[4]|s[5]|s[6],
  s[0]|s[2]|s[3]|s[4]|s[6],
  s[1]|s[2]|s[3]|s[4],
  s[0]|s[1]|s[2]|s[4]|s[6],
  s[1]|s[2]|s[5]|s[4]|s[6],
  s[0]|s[1]|s[2]|s[3]|s[4]|s[5]|s[6],
  s[0]|s[1]|s[2]|s[3]|s[4]
].map { |el| Grid.from_indices(sz, el) }

[d[2], d[1], d[2], d[5], d[0], d[4], d[3], d[6], d[1], d[5]].each { |d|
  d.display
}

puzzle.rb

#!/usr/bin/ruby

# Quick class I wrote to do some stuff. Hooray.

class Grid
  attr_accessor :size, :grid
  class << self
    attr_reader :f, :t
  end
  @f = '0'
  @t = '1'

  def self.from_array(arr)
    raise "can't use nil array" if arr.nil?
    raise "must be square grid" if arr.length != arr[0].length unless arr.empty?
    g = Grid.new(arr.length)
    g.grid = arr
    g
  end

  def self.from_indices(grid_size, arr = [])
    raise "can't use nil array" if arr.nil?
    g = Grid.new(grid_size)
    g.grid = []
    (grid_size).times { g.grid << self.f * grid_size }
    arr.each { |el| g[el / g.size, el % g.size] = self.t }
    g
  end

  def initialize(size = 12)
    @size = size
  end

  def self.from_rule(grid_size, &bl)
    g = Grid.new(grid_size)
    bl ||= lambda { |c,i| false }
    g.grid = []
    (s = self.f * grid_size * grid_size).split('').each_with_index { |c, i|
      s[i] = self.t if bl.call(c, i)
    }
    g.grid += s.scan(/.{1,#{grid_size}}/)

    g
  end

  def display(spacing = 1, chars = {:t => '#', :f => ' ', :spacer => ' '})
    mapping = chars[:f].to_s + chars[:t].to_s
    spacer = chars[:spacer] * spacing
    border = "+" + ("-" * @size * (chars[:spacer].length + spacing)) + "+"

    puts border
    @grid.each { |row|
      puts "|" + row.split('').map{|i| (i == self.class.t) ? chars[:t] : chars[:f]}
      .join(spacer) + spacer + "|"
    }
    puts border
    return
  end

  def [](i, j)
    self.grid[i][j]
  end

  def []=(i, j, val)
    self.grid[i][j] = val
  end

  def &(o)
    self.op(o) { |l, r, i| l == self.class.t && r == self.class.t }
  end

  def |(o)
    self.op(o) { |l, r, i| l == self.class.t || r == self.class.t }
  end

  def op(o, &bl)
    l = self.grid
    r = o.grid
    
    Grid.from_array(
      l.zip(r).map { |li,ri|
        (0..li.size-1).map { |j|
          bl.call(li[j], ri[j], j) ? self.class.t : self.class.f
        }.join
      }
    )
  end
end