Trying to solve the chain problem by brute force. Uses 4 cores with the Parallel gem. https://fivethirtyeight.com/features/pick-a-number-any-number/

chain.rb

# ruby chain.rb &
# writes to /tmp/chain_results.log

require 'parallel'

def number_chain( n, range, chain)
  chain << n
  range.delete(n)

  next_numbers = []
  range.each do |r|
    next_numbers << r if ((n % r) == 0)
    next_numbers << r if ((r % n) == 0)
  end

  if next_numbers.count > 0
    next_numbers.each do |nx|
      number_chain( nx, range.dup, chain.dup )
    end
  else
    if chain.count > 45
      IO.write("/tmp/chain_results.log", "-----\n", mode: 'a')
      IO.write("/tmp/chain_results.log", "Count: #{chain.count}\n", mode: 'a')
      IO.write("/tmp/chain_results.log", "Chain: #{chain.to_s}\n", mode: 'a')
    end
  end
end

a = (1..100).to_a
Parallel.each(a, in_processes: 4) do |n|
  IO.write("/tmp/chain_results.log", "Processing #{n}\n", mode: 'a')
  number_chain(n, (1..100).to_a, [])
end