Ruby factorial function - ruby

I'm going crazy: Where is the Ruby function for factorial? No, I don't need tutorial implementations, I just want the function from the library. It's not in Math!
I'm starting to doubt, is it a standard library function?

There is no factorial function in the standard library.

Like this is better
(1..n).inject(:*) || 1

It's not in the standard library but you can extend the Integer class.
class Integer
def factorial_recursive
self <= 1 ? 1 : self * (self - 1).factorial
end
def factorial_iterative
f = 1; for i in 1..self; f *= i; end; f
end
alias :factorial :factorial_iterative
end
N.B. Iterative factorial is a better choice for obvious performance reasons.

Shamelessly cribbed from http://rosettacode.org/wiki/Factorial#Ruby, my personal favorite is
class Integer
def fact
(1..self).reduce(:*) || 1
end
end
>> 400.fact
=> 64034522846623895262347970319503005850702583026002959458684445942802397169186831436278478647463264676294350575035856810848298162883517435228961988646802997937341654150838162426461942352307046244325015114448670890662773914918117331955996440709549671345290477020322434911210797593280795101545372667251627877890009349763765710326350331533965349868386831339352024373788157786791506311858702618270169819740062983025308591298346162272304558339520759611505302236086810433297255194852674432232438669948422404232599805551610635942376961399231917134063858996537970147827206606320217379472010321356624613809077942304597360699567595836096158715129913822286578579549361617654480453222007825818400848436415591229454275384803558374518022675900061399560145595206127211192918105032491008000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
This implementation also happens to be the fastest among the variants listed in Rosetta Code.
update #1
Added || 1 to handle the zero case.
update #2
With thanks and appreciation to Mark Thomas, here's a version that is a bit more efficient, elegant and obscure:
class Integer
def fact
(2..self).reduce(1,:*)
end
end

In math, factorial of n is just the gamma function of n+1
(see: http://en.wikipedia.org/wiki/Gamma_function)
Ruby has Math.gamma() so just use Math.gamma(n+1) and cast it back to an integer if desired.

You could also use Math.gamma function which boils down to factorial for integer parameters.

class Integer
def !
(1..self).inject(:*)
end
end
examples
!3 # => 6
!4 # => 24

I would do
(1..n).inject(1, :*)

I just wrote my own:
def fact(n)
if n<= 1
1
else
n * fact( n - 1 )
end
end
Also, you can define a falling factorial:
def fall_fact(n,k)
if k <= 0
1
else
n*fall_fact(n - 1, k - 1)
end
end

With high respect to all who participated and spent their time to help us, I would like to share my benchmarks of the solutions listed here.
Params:
iterations = 1000
n = 6
user system total real
Math.gamma(n+1) 0.000383 0.000106 0.000489 ( 0.000487)
(1..n).inject(:*) || 1 0.003986 0.000000 0.003986 ( 0.003987)
(1..n).reduce(1, :*) 0.003926 0.000000 0.003926 ( 0.004023)
1.upto(n) {|x| factorial *= x } 0.003748 0.011734 0.015482 ( 0.022795)
For n = 10
user system total real
0.000378 0.000102 0.000480 ( 0.000477)
0.004469 0.000007 0.004476 ( 0.004491)
0.004532 0.000024 0.004556 ( 0.005119)
0.027720 0.011211 0.038931 ( 0.058309)

Just call this function
def factorial(n=0)
(1..n).inject(:*)
end
examples
factorial(3)
factorial(11)

Using Math.gamma.floor is an easy way to produce an approximation and then round it back down to the correct integer result. Should work for all Integers, include an input check if necessary.

Just another way to do it, although it really isn't necessary.
class Factorial
attr_reader :num
def initialize(num)
#num = num
end
def find_factorial
(1..num).inject(:*) || 1
end
end
number = Factorial.new(8).find_factorial
puts number

You will probably find a Ruby feature request useful. It contains a nontrivial patch that includes a demo Bash script. The speed difference between a naive loop and the solution presented in the batch can be literally 100x (hundred fold). Written all in pure Ruby.

Here is my version seems to be clear to me even though it's not as clean.
def factorial(num)
step = 0
(num - 1).times do (step += 1 ;num *= step) end
return num
end
This was my irb testing line that showed each step.
num = 8;step = 0;(num - 1).times do (step += 1 ;num *= step; puts num) end;num

Why would the standard library require a factorial method, when there is a built-in iterator for this exact purpose? It is called upto.
No you do not need to use recursion, like all these other answers show.
def fact(n)
n == 0 ? 1 : n * fact(n - 1)
end
Rather, the built-in iterator upto can be used to calculate factorials:
factorial = 1
1.upto(10) {|x| factorial *= x }
factorial
=> 3628800

class Integer
def factorial
return self < 0 ? false : self==0 ? 1 : self.downto(1).inject(:*)
#Not sure what other libraries say, but my understanding is that factorial of
#anything less than 0 does not exist.
end
end

And yet another way (=
def factorial(number)
number = number.to_i
number_range = (number).downto(1).to_a
factorial = number_range.inject(:*)
puts "The factorial of #{number} is #{factorial}"
end
factorial(#number)

Just one more way to do it:
# fact(n) => Computes the Factorial of "n" = n!
def fact(n) (1..n).inject(1) {|r,i| r*i }end
fact(6) => 720

In Ruby standard library function for factorial is not available. We can make a simple function of factorial in ruby in this way.
def factorial_number(n)
if n <= 1
1
else
n * factorial_number(n-1)
end
end
puts factorial_number(6) #Output is 720 => (6*5*4*3*2*1)
puts factorial_number(8) #Output is 40320 => (8*7*6*5*4*3*2*1)

Related

Slow Ruby computation? Project Euler #5

This question references Project Euler Problem 5, so beware of spoilers!
Problem 5:
2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
I wrote the following code in Ruby as a solution to Problem 5.
num = 2520
until (1..20).all?{|x| num % x == 0}
num += 1
end
puts "#{num}"
However, whenever I run the script, it just hangs. Note that I tested the same method on the base case 2520 for the range 1 to 10 and it worked just fine.
Why does it work for the simpler case but not for the more advanced case? What can I do to fix what I have?
It's slow because the answer is more than 200 million, and you're counting up to it in steps of 1. That's going to take a while. You need a better algorithm.
You won't be able to brute force this problem as you have with others. You're going to need to find a more efficient solution for it.
SPOILER BELOW
This is a significantly more efficient way to do it (apologies if this isn't very Ruby-like):
def find_multiple
lcm = 1
(2..20).each do |i|
lcm *= i / gcd(lcm, i)
end
lcm
end
def gcd(a, b)
while b > 0
a %= b
return b if a == 0
b %= a
end
a
end
puts find_multiple
If you're looking for a more Ruby-like way to solve it, you can use the following (as suggested by steenslag in the comments):
(1..20).inject(:lcm)
A little late to the game but here's my input. If you like your code - which is succinct and pretty clear - you can make a couple of small adjustments to make it run faster. This worked for me without timing out:
num = 20
until (11..20).all?{ |i| num % i == 0 }
num +=20
end
puts num
Essentially you just increment by 20s since you know it needs to be divisible by 20, and you can skip iterating through anything in the lower 1/2 of the set.
Simplest and clean solution in ruby language.
(1..20).inject(:lcm) # output will be 232792560
Try this.
Code:
i=2520
max_product = (4..19).inject(1){|j,k| j*k}
puts max_product
while i < max_product
if( [3, 7].inject(true) do |memo, p|
memo && i%p==0
end)
if(
(4..20).inject(true) do |memo, p|
memo && i%p==0
end
)
puts i
end
end
i+=10
end

How do I generate the first n prime numbers?

I am learning Ruby and doing some math stuff. One of the things I want to do is generate prime numbers.
I want to generate the first ten prime numbers and the first ten only. I have no problem testing a number to see if it is a prime number or not, but was wondering what the best way is to do generate these numbers?
I am using the following method to determine if the number is prime:
class Integer < Numeric
def is_prime?
return false if self <= 1
2.upto(Math.sqrt(self).to_i) do |x|
return false if self%x == 0
end
true
end
end
In Ruby 1.9 there is a Prime class you can use to generate prime numbers, or to test if a number is prime:
require 'prime'
Prime.take(10) #=> [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
Prime.take_while {|p| p < 10 } #=> [2, 3, 5, 7]
Prime.prime?(19) #=> true
Prime implements the each method and includes the Enumerable module, so you can do all sorts of fun stuff like filtering, mapping, and so on.
If you'd like to do it yourself, then something like this could work:
class Integer < Numeric
def is_prime?
return false if self <= 1
2.upto(Math.sqrt(self).to_i) do |x|
return false if self%x == 0
end
true
end
def next_prime
n = self+1
n = n + 1 until n.is_prime?
n
end
end
Now to get the first 10 primes:
e = Enumerator.new do |y|
n = 2
loop do
y << n
n = n.next_prime
end
end
primes = e.take 10
require 'prime'
Prime.first(10) # => [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
Check out Sieve of Eratosthenes. This is not Ruby specific but it is an algorithm to generate prime numbers. The idea behind this algorithm is that you have a list/array of numbers say
2..1000
You grab the first number, 2. Go through the list and eliminate everything that is divisible by 2. You will be left with everything that is not divisible by 2 other than 2 itself (e.g. [2,3,5,7,9,11...999]
Go to the next number, 3. And again, eliminate everything that you can divide by 3. Keep going until you reach the last number and you will get an array of prime numbers. Hope that helps.
http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
People already mentioned the Prime class, which definitely would be the way to go. Someone also showed you how to use an Enumerator and I wanted to contribute a version using a Fiber (it uses your Integer#is_prime? method):
primes = Fiber.new do
Fiber.yield 2
value = 3
loop do
Fiber.yield value if value.is_prime?
value += 2
end
end
10.times { p primes.resume }
# First 10 Prime Numbers
number = 2
count = 1
while count < 10
j = 2
while j <= number
break if number%j == 0
j += 1
end
if j == number
puts number
count += 1
end
number += 1
end
Implemented the Sieve of Eratosthene (more or less)
def primes(size)
arr=(0..size).to_a
arr[0]=nil
arr[1]=nil
max=size
(size/2+1).times do |n|
if(arr[n]!=nil) then
cnt=2*n
while cnt <= max do
arr[cnt]=nil
cnt+=n
end
end
end
arr.compact!
end
Moreover here is a one-liner I like a lot
def primes_c a
p=[];(2..a).each{|n| p.any?{|l|n%l==0}?nil:p.push(n)};p
end
Of course those will find the primes in the first n numbers, not the first n primes, but I think an adaptation won't require much effort.
Here is a way to generate the prime numbers up to a "max" argument from scratch, without using Prime or Math. Let me know what you think.
def prime_test max
primes = []
(1..max).each {|num|
if
(2..num-1).all? {|denom| num%denom >0}
then
primes.push(num)
end
}
puts primes
end
prime_test #enter max
I think this may be an expensive solution for very large max numbers but seems to work well otherwise:
def multiples array
target = array.shift
array.map{|item| item if target % item == 0}.compact
end
def prime? number
reversed_range_array = *(2..number).reverse_each
multiples_of_number = multiples(reversed_range_array)
multiples_of_number.size == 0 ? true : false
end
def primes_in_range max_number
range_array = *(2..max_number)
range_array.map{|number| number if prime?(number)}.compact
end
class Numeric
def prime?
return self == 2 if self % 2 == 0
(3..Math.sqrt(self)).step(2) do |x|
return false if self % x == 0
end
true
end
end
With this, now 3.prime? returns true, and 6.prime? returns false.
Without going to the efforts to implement the sieve algorithm, time can still be saved quickly by only verifying divisibility until the square root, and skipping the odd numbers. Then, iterate through the numbers, checking for primeness.
Remember: human time > machine time.
I did this for a coding kata and used the Sieve of Eratosthenes.
puts "Up to which number should I look for prime numbers?"
number = $stdin.gets.chomp
n = number.to_i
array = (1..n).to_a
i = 0
while array[i]**2 < n
i = i + 1
array = array.select do |element|
element % array[i] != 0 || element / array[i] == 1
end
end
puts array.drop(1)
Ruby: Print N prime Numbers
http://mishra-vishal.blogspot.in/2013/07/include-math-def-printnprimenumbernoofp.html
include Math
def print_n_prime_number(no_of_primes=nil)
no_of_primes = 100 if no_of_primes.nil?
puts "1 \n2"
count = 1
number = 3
while count < no_of_primes
sq_rt_of_num = Math.sqrt(number)
number_divisible_by = 2
while number_divisible_by <= sq_rt_of_num
break if(number % number_divisible_by == 0)
number_divisible_by = number_divisible_by + 1
end
if number_divisible_by > sq_rt_of_num
puts number
count = count+1
end
number = number + 2
end
end
print_n_prime_number
Not related at all with the question itself, but FYI:
if someone doesn't want to keep generating prime numbers again and again (a.k.a. greedy resource saver)
or maybe you already know that you must to work with subsequent prime numbers in some way
other unknown and wonderful cases
Try with this snippet:
require 'prime'
for p in Prime::Generator23.new
# `p` brings subsequent prime numbers until the end of the days (or until your computer explodes)
# so here put your fabulous code
break if #.. I don't know, I suppose in some moment it should stop the loop
end
fp
If you need it, you also could use another more complex generators as Prime::TrialDivisionGenerator or Prime::EratosthenesGenerator. More info
Here's a super compact method that generates an array of primes with a single line of code.
def get_prime(up_to)
(2..up_to).select { |num| (2...num).all? { |div| (num % div).positive? } }
end
def get_prime(number)
(2..number).each do |no|
if (2..no-1).all? {|num| no % num > 0}
puts no
end
end
end
get_prime(100)

How can I test if a value is a prime number in Ruby? Both the easy and the hard way?

I am trying to create a program that will test whether a value is prime, but I don't know how. This is my code:
class DetermineIfPrime
def initialize (nth_value)
#nth_value = nth_value
primetest
end
def primetest
if Prime.prime?(#nth_value)
puts ("#{#nth_value} is prime")
else
puts ("This is not a prime number.")
end
rescue Exception
puts ("#{$!.class}")
puts ("#{$!}")
end
end
And every time I run that it returns this.
NameError
uninitialized constant DetermineIfPrime::Prime
I tried other ways to do the job, but I think this is the closest I can get.
I also tried this:
class DetermineIfPrime
def initialize (nth_value)
#nth_value = nth_value
primetest
end
def primetest
for test_value in [2, 3, 5, 7, 9, 11, 13] do
if (#nth_value % test_value) == 0
puts ("#{#nth_value} is not divisible by #{test_value}")
else
puts ("This is not a prime number since this is divisible by #{test_value}")
break
end
end
end
end
Or am I just doing something wrong?
Ruby has built in method to check if number is prime or not.
require 'prime'
Prime.prime?(2) #=> true
Prime.prime?(4) #=> false
def is_prime?(num)
return false if num <= 1
Math.sqrt(num).to_i.downto(2).each {|i| return false if num % i == 0}
true
end
First, we check for 0 and 1, as they're not prime. Then we basically just check every number less than num to see if it divides. However, as explained here, for every factor greater than the square root of num, there's one that's less, so we only look between 2 and the square root.
Update
def is_prime?(num)
return if num <= 1
(2..Math.sqrt(num)).none? { |i| (num % i).zero? }
end
The error you are getting is because you haven't required Primein your code, You need to do require Prime in your file.
One cool way I found here, to check whether a number is prime or not is following:
class Fixnum
def prime?
('1' * self) !~ /^1?$|^(11+?)\1+$/
end
end
10.prime?
From an algorithmic standpoint, checking if a number is prime can be done by checking all numbers up to and including (rounding down to previous integer) said number's square root.
For example, checking if 100 is prime involves checking everything up to 10.
Checking 99 means only going to 9.
** Another way to think about it **
Each factor has a pair (3 is a factor of 36, and 3's pair is 12).
The pair is on the other side of the square root (square root of 6 is 36, 3 < 6, 12 > 6).
So by checking everything until the square root (and not going over) ensures you check all possible factors.
You can make it quicker by having a list of prime numbers to compare, as you are doing. If you have a maximum limit that's reasonably small, you could just have a list of primes and do a direct lookup to see if that number is prime.
def is_prime?(num)
Math.sqrt(num).floor.downto(2).each {|i| return false if num % i == 0}
true
end
lol sorry for resurrecting a super old questions, but it's the first one that came up in google.
Basically, it loops through possible divisors, using the square root as the max number to check to save time on very large numbers.
In response to your question, while you can approach the problem by using Ruby's Prime I am going to write code to answer it on its own.
Consider that all you need to do is determine a factor that is smaller than the integer's square root. Any number larger than the integer's square root as a factor requires a second factor to render the number as the product. (e.g. square root of 15 is approx 3.8 so if you find 5 as a factor it is only a factor with the factor pair 3 and 5!!)
def isPrime?(num)
(2..Math.sqrt(num)).each { |i| return false if num % i == 0}
true
end
Hope that helps!!
(To first answer the question: yes, you are doing something wrong. As BLUEPIXY mentions, you need to put require 'prime' somewhere above the line that calls Prime.prime?. Typically on line 1.)
Now, a lot of answers have been given that don't use Prime.prime?, and I thought it might be interesting to benchmark some of them, along with a possible improvement of my own that I had in mind.
###TL;DR
I benchmarked several solutions, including a couple of my own; using a while loop and skipping even numbers performs best.
Methods tested
Here are the methods I used from the answers:
require 'prime'
def prime1?(num)
return if num <= 1
(2..Math.sqrt(num)).none? { |i| (num % i).zero? }
end
def prime2?(num)
return false if num <= 1
Math.sqrt(num).to_i.downto(2) {|i| return false if num % i == 0}
true
end
def prime3?(num)
Prime.prime?(num)
end
def prime4?(num)
('1' * num) !~ /^1?$|^(11+?)\1+$/
end
prime1? is AndreiMotinga's updated version. prime2? is his original version (with the superfluous each method removed). prime3? is Reboot's, using prime library. prime4? is Saurabh's regex version (minus the Fixnum monkey-patch).
A couple more methods to test
The improvement I had in mind was to leverage the fact that even numbers can't be prime, and leave them out of the iteration loop. So, this method uses the #step method to iterate over only odd numbers, starting with 3:
def prime5?(num)
return true if num == 2
return false if num <= 1 || num.even?
3.step(Math.sqrt(num).floor, 2) { |i| return false if (num % i).zero? }
true
end
I thought as well that it might be interesting to see how a "primitive" implementation of the same algorithm, using a while loop, might perform. So, here's one:
def prime6?(num)
return true if num == 2
return false if num <= 1 || num.even?
i = 3
top = Math.sqrt(num).floor
loop do
return false if (num % i).zero?
i += 2
break if i > top
end
true
end
Benchmarks
I did a simple benchmark on each of these, timing a call to each method with the prime number 67,280,421,310,721. For example:
start = Time.now
prime1? 67280421310721
puts "prime1? #{Time.now - start}"
start = Time.now
prime2? 67280421310721
puts "prime2? #{Time.now - start}"
# etc.
As I suspected I would have to do, I canceled prime4? after about 60 seconds. Presumably, it takes quite a bit longer than 60 seconds to assign north of 6.7 trillion '1''s to memory, and then apply a regex filter to the result — assuming it's possible on a given machine to allocate the necessary memory in the first place. (On mine, it would seem that there isn't: I went into irb, put in '1' * 67280421310721, made and ate dinner, came back to the computer, and found Killed: 9 as the response. That looks like a SignalException raised when the process got killed.)
The other results are:
prime1? 3.085434
prime2? 1.149405
prime3? 1.236517
prime5? 0.748564
prime6? 0.377235
Some (tentative) conclusions
I suppose that isn't really surprising that the primitive solution with the while loop is fastest, since it's probably closer than the others to what's going on under the hood. It is a bit surprising that it's three times faster than Prime.prime?, though. (After looking at the source code in the doc it is less so. There are lots of bells and whistles in the Prime object.)
AndreiMotinga's updated version is nearly three times as slow as his original, which suggests that the #none? method isn't much of a performer, at least in this context.
Finally, the regex version might be cool, but it certainly doesn't appear to have much practical value, and using it in a monkey-patch of a core class looks like something to avoid entirely.
If you are going to use any Prime functions you must include the Prime library. This problem can be solved without the use of the prime library however.
def isPrime?(num)
(2..Math.sqrt(num)).each { |i|
if num % i == 0 && i < num
return false
end
}
true
end
Something like this would work.
Try this
def prime?(num)
2.upto(Math.sqrt(num).ceil) do |i|
break if num%i==0
return true if i==Math.sqrt(num).ceil
end
return false
end
So most of the answers here are doing the same thing in slightly different ways which is one of the cool things about Ruby, but I'm a pretty new student (which is why I was looking this up in the first place) and so here's my version with comment explanations in the code:
def isprime n # starting with 2 because testing for a prime means you don't want to test division by 1
2.upto(Math.sqrt(n)) do |x| # testing up to the square root of the number because going past there is excessive
if n % x == 0
# n is the number being called from the program
# x is the number we're dividing by, counting from 2 up to the square root of the number
return false # this means the number is not prime
else
return true # this means the number is prime
end
end
end

Ruby Recursion doesn't work?

I was trying to make a recursive algorithm with Ruby and I couldn't do it so I kept popping the stack as it were and each time I tried a simpler recursive algorithm to see where my mistake was..
But I arrived at this:
def fact(n)
if n==0
1
else
fact(n)*fact(n-1)
end
end
puts fact(5)
and
ruby/part2.rb:81: stack level too deep (SystemStackError)
Ok what is going on?
Is it not possible to make recursive algorithms in Ruby??
your algorithm is incorrect, it should look like this
def fact(n)
if n==0
1
else
n*fact(n-1)
end
end
puts fact(5)
fact(n) * fact(n - 1) is infinite recursion. You need to reduce the problem size in each call.
def fact(n)
if n <= 0
1
else
n * fact(n - 1)
end
end
Or simply,
def fact(n)
n <= 0 ? 1 : n * fact(n - 1)
end
You have to do something like fact(n-1)*fact(n-2) because otherwise, fact(n),n=5 will be called forever.

More ruby-like solution to this problem?

I am learning ruby and practicing it by solving problems from Project Euler.
This is my solution for problem 12.
# Project Euler problem: 12
# What is the value of the first triangle number to have over five hundred divisors?
require 'prime'
triangle_number = ->(num){ (num *(num + 1)) / 2 }
factor_count = ->(num) do
prime_fac = Prime.prime_division(num)
exponents = prime_fac.collect { |item| item.last + 1 }
fac_count = exponents.inject(:*)
end
n = 2
loop do
tn = triangle_number.(n)
if factor_count.(tn) >= 500
puts tn
break
end
n += 1
end
Any improvements that can be made to this piece of code?
As others have stated, Rubyists will use methods or blocks way more than lambdas.
Ruby's Enumerable is a very powerful mixin, so I feel it pays here to build an enumerable in a similar way as Prime. So:
require 'prime'
class Triangular
class << self
include Enumerable
def each
sum = 0
1.upto(Float::INFINITY) do |i|
yield sum += i
end
end
end
end
This is very versatile. Just checking it works:
Triangular.first(4) # => [1, 3, 7, 10]
Good. Now you can use it to solve your problem:
def factor_count(num)
prime_fac = Prime.prime_division(num)
exponents = prime_fac.collect { |item| item.last + 1 }
exponents.inject(1, :*)
end
Triangular.find{|t| factor_count(t) >= 500} # => 76576500
Notes:
Float::INFINITY is new to 1.9.2. Either use 1.0/0, require 'backports' or do a loop if using an earlier version.
The each could be improved by first checking that a block is passed; you'll often see things like:
def each
return to_enum __method__ unless block_given?
# ...
Rather than solve the problem in one go, looking at the individual parts of the problem might help you understand ruby a bit better.
The first part is finding out what the triangle number would be. Since this uses sequence of natural numbers, you can represent this using a range in ruby. Here's an example:
(1..10).to_a => [1,2,3,4,5,6,7,8,9,10]
An array in ruby is considered an enumerable, and ruby provides lots of ways to enumerate over data. Using this notion you can iterate over this array using the each method and pass a block that sums the numbers.
sum = 0
(1..10).each do |x|
sum += x
end
sum => 55
This can also be done using another enumerable method known as inject that will pass what is returned from the previous element to the current element. Using this, you can get the sum in one line. In this example I use 1.upto(10), which will functionally work the same as (1..10).
1.upto(10).inject(0) {|sum, x| sum + x} => 55
Stepping through this, the first time this is called, sum = 0, x = 1, so (sum + x) = 1. Then it passes this to the next element and so sum = 1, x = 2, (sum + x) = 3. Next sum = 3, x = 3, (sum + x) = 6. sum = 6, x = 4, (sum + x) = 10. Etc etc.
That's just the first step of this problem. If you want to learn the language in this way, you should approach each part of the problem and learn what is appropriate to learn for that part, rather than tackling the entire problem.
REFACTORED SOLUTION (though not efficient at all)
def factors(n)
(1..n).select{|x| n % x == 0}
end
def triangle(n)
(n * (n + 1)) / 2
end
n = 2
until factors(triangle(n)).size >= 500
puts n
n += 1
end
puts triangle(n)
It looks like you are coming from writing Ocaml, or another functional language. In Ruby, you would want to use more def to define your methods. Ruby is about staying clean. But that might also be a personal preference.
And rather than a loop do you could while (faction_count(traingle_number(n)) < 500) do but for some that might be too much for one line.

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