# Simple Factorial Challenge [duplicate]

In light of today's date...

A factorial of a number n, is the product of all the numbers from 1 to n inclusive.

## The Challenge

Given an integer n where 0 <= n <= 420, find the sum of the digits of n!. It's that simple :P

Notes: I feel like this challenge isn't too simple, as some languages have a very hard time storing numbers that are fairly large. Also, coding a BigInteger datatype is fairly straightforward, but hard to golf.

## Examples

Input: 100. Output: 648.

Input: 200. Output: 1404.

Input: 420. Output: 3672.

## Scoring

• The input and output can be given by any convenient method.
• Either a full program or a function are acceptable. If a function, you can return the output rather than printing it.
• Standard loopholes are forbidden.
• This is so all usual golfing rules apply, and the shortest code (in bytes) wins.

EDIT: Ok, I guess it's actually easy...take a look at the Jelly answer below. Anyways, I guess we all know which one's going to be accepted. But, I'd still like to see some interesting ideas and tricks to this problem!

• This is A004152 in the OEIS. Apr 21 '18 at 1:56
• @NL628: Typically, people are trying to get the smallest byte count for a particular language. So yes, Jelly in this case has very short result; but that hardly makes the results for other languages less fun or interesting for most afficianados of PPCG! Apr 21 '18 at 2:03
• I'd like this better without the arbitrary restriction of 42<=n<=420
– Jo King
Apr 21 '18 at 3:03
• Today is Apr 21 for me. Nothing special. Apr 21 '18 at 4:00
• @JoKing The lower bound doesn't make much sense, but having an explicit upper bound (up to which all submissions must work, regardless of native types) is a good thing. Apr 21 '18 at 13:57

# (old problem) JavaScript (Node.js), 99949288868380 78 bytes

f=(x,t=[...21+Array(999)])=>x?f(s=x-1,t.map(d=>-s+(s+=(t=~~d*x+t/10|0)%10))):s


Try it online!

well, first language without large number support

Thank Arnauld for 4 bytes

f = (x, t = ['2', '1', ...','.repeat(998)]) => // init x, t=1
x ?
f( // recursive x':=x-1, t'=t*x
s = x-1, // s init to 0 when x==1, in next recursion just return
t.map (
b = // init b to NaN
d =>
-s + ( //  to return the added value
s+= ( // -s + (s + k) == k
b=
~~d*x+b/10 | 0
// ~~d converts ',' to 0
// b is initally NaN, after first iteration
// it's zero, then the last digit sum result with carry
) % 10
)
)
)
:
s // the sum from x==1

• ps. it doesn't work for 0, but the original question says >=42
– l4m2
Apr 22 '18 at 12:40
• Umm no, it says <= 420 ... Apr 22 '18 at 12:50
• First version "Given an integer n where 42 <= n <= 420, find the sum of the digits of n!"
– l4m2
Apr 22 '18 at 13:27
• Nice this is what I was looking for...a language that doesn't have the capability of storing massive amounts of digits. Could you explain how it works? Apr 22 '18 at 17:25

# Wolfram Language (Mathematica), 24 bytes

Total@IntegerDigits[#!]&


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# 05AB1E, 3 bytes

!SO


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Explanation

!     # factorial of input
S    # split to list of digits
O   # sum

• I really think O on a string/non-list should be digit sum. It's come up enough in these non-important challenges. Apr 23 '18 at 0:04

# Neim, 2 bytes

𝐓𝐬


Explanation: Factorial 𝐓; sum 𝐬.

This outgolfs 3-byte answers as the sum command is able to implicitly convert to a list.

Try it online!

# Haskell, 4240 38 bytes

f n=sum[read[d]|d<-show$product[1..n]]  Try it online! Thanks to @Laikoni for saving 2 bytes with list comprehension. • 38 bytes: f n=sum[read[d]|d<-show$product[1..n]]. Apr 21 '18 at 7:52

# Attache, 11 bytes

Sum@List@!


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Sums the List of digits in the factorial (!) of the input. Anonymous function.

# Pari/GP, 16 bytes

n->sumdigits(n!)


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• When evaluated on 42000000, gives 1311426180 (takes under three minutes on my machine). The number has 310,936,107 digits. The average contribution per digit is 4.34, a bit under the "ideal" 4.5, which is likely related to the long string of zero digits in the end. Apr 21 '18 at 16:19

# J, 13 11bytes

1#.,.&.":@!


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## Explanation:

! calculate the factorial

@ and

,.&.": convert it to a list of digits (convert to string ":, ravel ,. and convert each char back to number)

1#. find their sum by base-1 conversion

# Perl 6, 21 bytes

{[*](2..$_).comb.sum}  Try it ## Expanded: { # bare block lambda with implicit parameter ｢$_｣

[*](       # reduce using &infix:« * »

2 .. $_ # Range starting at 2 (slight optimization over 1) ).comb # split the result into digits .sum # find the sum of those digits }  # R + gmp, 66 bytes sum(strtoi(el(strsplit(paste(gamma(gmp::as.bigz(scan())+1)),""))))  Try it online! gmp is one of the several BigInteger packages available on CRAN. • sum(utf8ToInt(as.character(gmp::factorialZ(scan())))-48) should do the trick as well Apr 22 '18 at 20:24 # Python 2, 51 bytes f=lambda L,p=1:0**L*sum(map(eval,p))or f(L-1,p*L)  Try it online! We'd like to write map(int,p), but since repr(p) might have a trailing L, that won't work. Ordinarily, we'd resort to map(int,str(p)) and lose three bytes. Here, can we name our counting-down variable L, and write map(eval,p). Since L is 0 when we compute the result, the digit sum is unaffected. # Jelly, 3 bytes !DS  Try it online! !DS - main link, taking an integer e.g. 9 ! - factorial --> 362880 D - convert to decimal --> [3,6,2,8,8,0] S - sum of list --> 27  • ...you can't be serious... Apr 21 '18 at 1:42 • DENNIS WHAT DID YOU DO Apr 21 '18 at 1:43 • @NL628 Python 3 has bigint support, Jelly inherits that. Apr 21 '18 at 3:31 # Pyt, 2 bytes !Ś  Try it online! Explanation:  Implicit input ! Factorial Ś Sum of digits Implicit output  # Python 2, 5254 52 bytes f=lambda n,r=1:1/n*sum(map(int,str(r)))or f(n-1,n*r)  Try it online! -2 bytes thx to Kirill L. • Could you tell me how to make this challenger harder? I'm kind of struggling right now... Apr 21 '18 at 1:49 • I believe you need the f= as this is a recursive lambda Apr 21 '18 at 1:57 • @Giuseppe: Quite right! Thx. Apr 21 '18 at 2:01 • @NL628 don't make the challenge harder after posting it. That said, if you're looking for some hard challenges for the future, look into mathematical subjects like graph theory, or sets. Apr 21 '18 at 2:04 • @NL628 Also, you can post it to the Sandbox where it can be refined before posting it to main. – Jo King Apr 21 '18 at 9:05 # Octave with Symbolic Package, 43 42 bytes @(s)sum(char(sym(['factorial(' s 41]))-48)  Anonymous function that takes the input as a string and outputs a nubmer. Try it online! # Bash + GNU utilities, 36 • 6 bytes saved thanks to @Cowsquack seq -s*$1|bc|sed 's/\B\|\\/+&/g'|bc


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# Charcoal, 7 bytes

ＩΣΠ…¹⊕Ｎ


Try it online! Link is to verbose version of code. Explanation:

      Ｎ Input as a number
⊕  Increment
¹   Literal 1
…    Range
Π     Product
Σ      Sum (of digits)
Ｉ       Cast to string
Implicitly print


InclusiveRange(1, InputNumber()) also works but the explanation is prettier this way.

# Elixir, 54 bytes

fn n->Enum.sum Integer.digits Enum.reduce 1..n,&*/2end


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Ungolfed:

def sum_factorial(n) do
# factorial
Enum.reduce(1..n, fn(x, acc) -> x * acc end)
# sum digits
|> Integer.digits
|> Enum.sum


# C (gcc), 107 bytes

f(x){int a[999]={1},i,c;
for(;x;--x)for(c=i=0;i<999;)c=(a[i]=a[i]*x+c)/10,a[i++]%=10;
for(;i--;)x+=a[i];
i=x;}


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• a[i++]%=10 into the for
– l4m2
Apr 21 '18 at 12:48
• c;f(x){int a[999]={1},i;for(;x;--x)for(i=0;i<999;a[i++]%=10)c=(a[i]=a[i]*x+c)/10;for(;i--;)x+=a[i];i=x;}
– l4m2
Apr 21 '18 at 12:51
• c;i;f(x){int a[999]={x},n;for(;--x;)for(i=n=0;i<999;n+=a[i++]%=10)c=(a[i]=a[i]*x+c)/10;i=n;}
– l4m2
Apr 21 '18 at 12:54
• 104 bytes Apr 21 '18 at 12:57
• @l4m2 why the i=n part then? c;n;f(x){int a[999]={x},i;for(;--x;)for(i=n=0;i<999;n+=a[i++]%=10)c=(a[i]=a[i]*x+c)/10;} Though fails for x=0 now that the lower bound has been edited out of the challenge. Apr 23 '18 at 1:56

# Husk, 3 bytes

ΣdΠ


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### Explanation

ΣdΠ  Implicit input
Π  Factorial
d   Convert to list of digits
Σ    Sum


# Ruby, 33 bytes

->n{(2..n).inject(:*).digits.sum}


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# Stax, 4 bytes

║▼⌡è


Run and debug it at staxlang.xyz!

### Unpacked (5 bytes) and explanation

|FE|+
|F       Implicit input. Factorial.
E      Array of decimal digits.
|+    Sum of list. Implicit print.


Python, 75 bytes

import math
print(sum(map(int,list(str(math.factorial(int(input())))))))


# Tcl, 78 bytes

proc S n {proc F n {expr $n?($n)*\[F $n-1]:1} expr [join [split [F$n] ""] +]}


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# Java 10, 135 bytes

n->{var r=java.math.BigInteger.ONE;for(;!n.equals(r.ZERO);n=n.subtract(r.ONE))r=r.multiply(n);return(r+"").chars().map(c->c-48).sum();}


Explanation:

Try it online.

n->{                         // Method with BigInteger parameter and integer return-type
var r=java.math.BigInteger.ONE;
//  BigInteger, starting at 1
for(;!n.equals(r.ZERO);    //  Loop as long as n is not 0 yet
n=n.subtract(r.ONE))   //    After every iteration: subtract 1 from n
r=r.multiply(n);         //   Multiply r by n
return(r+"").chars()       //  Loop over the characters of r
.map(c->c-48)  //   Convert them to digits
.sum();}       //   And return the sum of those digits


## Ceylon, 98 bytes

import ceylon.whole{l=one}Integer q(Integer n)=>sum({0,*product({l,*(l:n)}).string*.offset('0')});


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## Explanation:

This is quite long, because we need to convince the compiler that we are not doing bogus stuff.

import ceylon.whole { l = one } // 1

Integer q(Integer n) => // 2
sum({0,*product({l,*(l:n)}).string *.offset('0')});
//  |   |   |       |    '3' || |    | | |         |||
//  |   |   |       '--4-----'| |    | 7 |         |||
//  |   |   '----5------------' '-6--'   '--8------'||
//  |   |   '----------------9---------------------'||
//  |   '----------------10-------------------------'|
//  '------------------------11----------------------'

1. Import the value one from the package ceylon.whole, and give it locally the name l (small L, not the digit 1 – though I choose this alias for its similarity to 1). (This alias import costs two bytes here, but saves two bytes for each of the two usages).
2. Define a function q from Integer to Integer, which maps each parameter n to the result of the following expression (calculated in steps 3 to 11). Top-level functions always need a type declaration. For local ones we could replace the return type by function, which wouldn't have saved anything here. (For inline functions, we sometimes can omit both types and the keyword, if they can be inferred from context.)
3. This is a short syntax for measure(one, n), which returns either the empty sequence [] if n is non-positive, or a Range<Whole> starting from one and having size n (i.e. all numbers from 1 to n, assuming n is a positive integer). Type: []|Range<Whole>, which is a subtype of {Whole*} (possibly empty iterable of Whole).
4. This is an iterable enumeration, with one as the first element and then all the elements of one:n (the * here expands the iterable). This has type {Whole+}, and has the only purpose to make sure the compiler knows it is non-empty. We could have used [...] instead of {...} for a tuple enumeration (which is non-lazy). No difference here apart from performance. We could have written this (l:n).follow(l), but that is longer.
5. Calculate the product of all those numbers, type Whole. product needs a non-empty iterable as a parameter to work (as the product of nothing is not defineable in a type-independent way).
6. Get the string representation of the result of step 5. (The .string attribute exists for all classes, and Whole implements it in the expected way, using decimal digits.) – type String, which is also a {Character*} (possibly empty iterable of characters).
7. The *. operator for iterables applies the the following attribute or method call to each element of the iterable and collects the result in a sequence. It can be seen as syntactic sugar for .collect(c => c.offset('0')). This is non-lazily evaluated, there is also .map(...) which is lazy.
8. The offset method of Character just calculates the difference between the unicode code points, returning an Integer. This takes advantage of the fact that the ten decimal digits are sequential starting with 0 in ASCII (and thus unicode).
9. This whole thing has now type [Integer*] (possibly empty sequence of integers – because the string is possibly empty for the compiler).
10. Same trick again as step 4, we make it an {Integer+} (nonempty iterable) by prepending a 0 (which has no effect on the following sum).
11. Sum it all up.

# CJam, 11 8 bytes

there is in fact a better way to get a list of digits

lim!Ab:+


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Explanation:

li          input, convert to integer
m!        factorial
Ab      convert to array of digits in base 10
:+    sum


Original solution:

lim!1/:i:+


Explanation:

li              input converted to integer
m!            factorial
           convert to string
1/         split into pieces of length 1
:i       convert back to integer
:+     sum
`