🎉 Exercism Research is now launched. Help Exercism, help science and have some fun at research.exercism.io 🎉
Avatar of Agathasta

Agathasta's solution

to Collatz Conjecture in the Ruby Track

Published at Dec 26 2020 · 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
# frozen_string_literal: true

# Calculate the number of steps to reach 1 in the Collatz Conjecture from a starting integer
class CollatzConjecture
  def self.steps(integer, steps = 0)
    raise ArgumentError if integer <= 0
    return steps if integer == 1

    steps(integer.odd? ? (integer * 3 + 1) : (integer / 2), steps + 1)

Community comments

Find this solution interesting? Ask the author a question to learn more.

What can you learn from this solution?

A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

  • What compromises have been made?
  • Are there new concepts here that you could read more about to improve your understanding?