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to Collatz Conjecture in the Ruby Track

Published at Feb 14 2021 · 0 comments
Test suite

The Collatz Conjecture or 3x+1 problem can be summarized as follows:

Take any positive integer n. If n is even, divide n by 2 to get n / 2. If n is odd, multiply n by 3 and add 1 to get 3n + 1. Repeat the process indefinitely. The conjecture states that no matter which number you start with, you will always reach 1 eventually.

Given a number n, return the number of steps required to reach 1.


Starting with n = 12, the steps would be as follows:

  1. 12
  2. 6
  3. 3
  4. 10
  5. 5
  6. 16
  7. 8
  8. 4
  9. 2
  10. 1

Resulting in 9 steps. So for input n = 12, the return value would be 9.

For installation and learning resources, refer to the Ruby resources page.

For running the tests provided, you will need the Minitest gem. Open a terminal window and run the following command to install minitest:

gem install minitest

If you would like color output, you can require 'minitest/pride' in the test file, or note the alternative instruction, below, for running the test file.

Run the tests from the exercise directory using the following command:

ruby collatz_conjecture_test.rb

To include color from the command line:

ruby -r minitest/pride collatz_conjecture_test.rb


An unsolved problem in mathematics named after mathematician Lothar Collatz https://en.wikipedia.org/wiki/3x_%2B_1_problem

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.


require 'minitest/autorun'
require_relative 'collatz_conjecture'

# Common test data version: 1.2.1 d94e348
class CollatzConjectureTest < Minitest::Test
  def test_zero_steps_for_one
    # skip
    assert_equal 0, CollatzConjecture.steps(1)

  def test_divide_if_even
    assert_equal 4, CollatzConjecture.steps(16)

  def test_even_and_odd_steps
    assert_equal 9, CollatzConjecture.steps(12)

  def test_large_number_of_even_and_odd_steps
    assert_equal 152, CollatzConjecture.steps(1_000_000)

  def test_zero_is_an_error
    assert_raises(ArgumentError) do

  def test_negative_value_is_an_error
    assert_raises(ArgumentError) do
Write your code for the 'Collatz Conjecture' exercise in this file. Make the tests in
`collatz_conjecture_test.rb` pass.

To get started with TDD, see the `README.md` file in your
`ruby/collatz-conjecture` directory.

class CollatzConjecture

  def self.steps(i)
    raise ArgumentError, 'Positive Integer expected.' unless i.integer? && i.positive? 
    i > 1 ? 1 + steps(i.odd? ? i * 3 + 1 : i / 2) : 0


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