People keep telling me that the square of a number is the number multiplied by itself. This is obviously false. The correct way to square a number is to make it into a square, by stacking it on top of itself a number of times equal to the number of digits it has, and then reading all the numbers from the resultant square, both horizontally (from left to right only) and vertically (from up to down only), and then adding them together. So, for the number 123, you first create the square:

```
123
123
123
```

Then you take all of the rows and columns from the square, and add them together:

`123+123+123+111+222+333`

Which gives us a result of `1035`

.

For negative numbers, you stack normally (remember that you only count the number of *digits*, so the negative sign is not included in the length), and then read the horizontal numbers normally (with negative signs), and then ignore the negative signs for the vertical numbers. So, for the number `-144`

we get the square:

```
-144
-144
-144
```

Which gives us `-144-144-144+111+444+444`

, which equals `567`

For numbers with only one digit, the square is always equal to the number doubled (read once horizontally and once vertically). So `4`

gives us

`4`

Which gives us `4+4`

, which equals `8`

.

For numbers with decimal parts, stack normally (remember that only *digits* are counted in the number of times you stack the number, and therefore the decimal point is not counted), and ignore the decimal symbols when reading the vertical numbers. For example, the number `244.2`

gives us

```
244.2
244.2
244.2
244.2
```

Which gives us `244.2+244.2+244.2+244.2+2222+4444+4444+2222`

, which equals `14308.8`

.

Fractional or complex numbers cannot be squared.

I'm tired of squaring numbers my way by hand, so I've decided to automate the process. Write me a program or function that takes a float or string, whichever you prefer, as input and returns the result of squaring it my way.

```
123 -> 1035
388 -> 3273
9999 -> 79992
0 -> 0
8 -> 16
-6 -> 0
-25 -> 27
-144 -> 567
123.45 -> 167282.25
244.2 -> 14308.8
2 -> 4
-0.45 -> 997.65
0.45 -> 1000.35
```

My hands are getting cramped from writing out all those squares, and my computer doesn't support copy/paste, so the entry with the least amount of code for me to type (measured in bytes for some reason?) wins!

Erik the Outgolfer 07/29/2017.

`þSDg×+O`

Explanation

```
þSDg×+O Implicit input
þ Keep digits
S Get chars
D Duplicate
g Length
× Repeat string(s)
+ Add (implicit input added to all elements)
O Sum
```

Also I would note that the single leading zero is a requirement on the input for -1 < input < 1 (i.e. 0.45 and .45 are different inputs but the same number, only the former is acceptable)

Jonathan Allan 07/29/2017.

`fØDẋ€L$ŒV+VS`

A monadic link accepting a list of characters (a well-formed decimal number, the single leading zero being a requirement for **-1 < n < 1**) and returning a number.

14 bytes to accept and return numbers (input limited at **+/-10 ^{-5}** by

`ŒṘ`

): `ŒṘfØDẋ€L$ŒV+⁸S`

.```
fØDẋ€L$ŒV+VS - Link: list of characters e.g. "-0.45"
ØD - yield digit characters "0123456789"
f - filter keep "045"
$ - last two links as a monad:
L - length (number of digit characters) 3
ẋ€ - repeat list for €ach digit ["000","444","555"]
ŒV - evaluate as Python code (vectorises) [0,444,555]
V - evaluate (the input) as Jelly code -0.45
+ - addition (vectorises) [-0.45,443.55,554.55]
S - sum 997.65
```

Erik the Outgolfer 07/29/2017

Umm not in the 15-byte version. EDIT: 3 seconds too early I suppose...

nimi 07/29/2017.

`f s|l<-filter(>'.')s=0.0+sum(read<$>(s<$l)++[c<$l|c<-l])`

The input is taken as a string.

How it works

```
l<-filter(>'.')s -- let l be the string of all the numbers of the input string
f s = 0.0 + sum -- the result is the sum of (add 0.0 to fix the type to float)
read<$> -- turn every string of the following list into a number
s<$l -- length of l times the input string followed by
[c<$l|c<-l] -- length of l times c for each c in l
```

ETHproductions 07/29/2017.

```
o\d
l
¬xpV +V*Ng
```

```
o\d First line: Set U to the result.
o Keep only the chars in the input that are
\d digits. (literally /\d/g)
l Second line: Set V to the result.
l U.length
¬xpV +V*Ng Last line: implicitly output the result.
¬ Split U into chars.
x Sum after
pV repeating each V times.
+V*Ng Add V * first input (the sum of the horizontals) to the result.
```

Ian H. 07/31/2017.

*Saved 9 bytes thanks to @TheLethalCoder**Saved another 8 bytes thanks to @TheLethalCoder*

`a=>{var c=(a+"").Replace(".","").Replace("-","");int i=0,l=c.Length;var r=a*l;for(;i<l;)r+=int.Parse(new string(c[i++],l));return r;}`

Takes a string as an input and outputs the 'squared' number as a float.

This code follows the following algorithm:

Create a new string from the input, but without the decimal points and symbols, so we can get our length and the numbers for the columns from there.

Calculate the input times the length of the string we created at point 1.

For each column in our 'square', create a new string with the column number and the row length and add it to our result.

Example:

Input: `-135.5`

- If we replace decimal points and symbols we get the string
`1355`

, which has a length of`4`

. - The input times 4:
`-135.5 * 4 = -542`

. - Now we create new strings for each column, parse them and add them to our result:
`1111`

,`3333`

,`5555`

,`5555`

.

If we sum these numbers up we get `15012`

, which is exactly what our program will output.

1 Dada 07/31/2017

Welcome on the site, and nice first answer (the explanations in particular are appreciated!) !

Ian H. 07/31/2017

@Dada Thank you! Even tough I am rather unpleased by the bytes I gained from stuff like

`string.Replace()`

, but I guess thats the only way it works! Ian H. 07/31/2017

@TheLethalCoder Thought of that aswell, sadly indexing does not work with floats, and

`.Length`

cannot implicitly be converted to float. 1 TheLethalCoder 07/31/2017

`a=>{var c=a.Replace(".","").Replace("-","");int i=0,l=c.Length;var r=float.Parse(a)*l;for(;i<l;)r+=int.Parse(new string(c[i++],l));return r;}`

141 bytes. Might be able to save by taking input as a `float`

and casting to a string with `n+""`

but I haven't checked. Erik the Outgolfer 07/29/2017.

`{∋ịṫ}ᶠ⟨≡zl⟩j₎ᵐ;[?]zcịᵐ+`

Brachylog doesn't go well with floats...

Explanation:

```
{∋ịṫ}ᶠ⟨≡zl⟩j₎ᵐ;[?]zcịᵐ+ Takes string (quoted) input, with '-' for the negative sign
ᶠ Return all outputs (digit filter)
{ } Predicate (is digit?)
∋ An element of ? (input)
ị Convert to number (fails if '-' or '.')
ṫ Convert back to string (needed later on)
⟨ ⟩ Fork
≡ Identity
l Length
with
z Zip
ᵐ Map
₎ Subscript (optional argument)
j Juxtapose (repeat) (this is where we need strings)
; Pair with literal
[ ] List
? ?
z Zip
c Concatenate (concatenate elements)
ᵐ Map
ị Convert to number
+ Add (sum elements)
```

Zgarb 07/29/2017.

`§+ȯṁrfΛ±TṁrSR#±`

Takes a string and returns a number.Try it online!

It's a bit annoying that the built-in parsing function `r`

gives parse errors on invalid inputs instead of returning a default value, which means that I have to explicitly filter out the columns that consist of non-digits.
If it returned 0 on malformed inputs, I could drop `fΛ±`

and save 3 bytes.

```
§+ȯṁrfΛ±TṁrSR#± Implicit input, e.g. "-23"
#± Count of digits: 2
SR Repeat that many times: ["-23","-23"]
ṁr Read each row (parse as number) and take sum of results: -46
ȯṁrfΛ±T This part is also applied to the result of SR.
T Transpose: ["--","22","33"]
fΛ± Keep the rows that contain only digits: ["22","33"]
ṁr Parse each row as number and take sum: 55
§+ Add the two sums: 9
```

Mr. Xcoder 07/29/2017.

ThePirateBay 07/31/2017.

Xcali 08/05/2017.

`$_*=@n=/\d/g;for$\(@n){$_+=$\x@n}`

*Used some tricks from Dom's code to shave 4 bytes*

**Explained:**

```
@n=/\d/g; # extract digits from input
$_*=@n; # multiply input by number of digits
for$\(@n){ # for each digit:
$_+= # add to the input
$\x@n} # this digit, repeated as many times as there were digits
# taking advantage of Perl's ability to switch between strings
# and numbers at any point
```

Dom Hastings 07/31/2017

Came up with a very similar approach, but managed to get a couple of bytes off using $\ and exiting the loop: try it online!

Xcali 08/05/2017

Used some inspiration from you to shave mine down. What's the "}{" construct at the end of yours? I'm not familiar with that one.

Dom Hastings 08/05/2017

It's one I learnt from this site, basically

`-n`

and `-p`

literally wrap a `while(){...}`

around the code so `}{`

breaks out of that. This unsets `$_`

but if you use `$\ `

as your variable it'll still get printed since `$\ `

is appended to every print. Means you can stores number or something in that and disregard `$_`

. Not sure that was a great explanation, but check out the Tips for golfing g in Perl thread, I'm sure that'll explain it better! Glad to have helped your score though! Mr. Xcoder 07/29/2017.

`K@jkUTQ+smv*lKdK*lKv`

Uses a completely different approach from @EriktheOutgolfer's answer, which helped me golf 1 byte in chat, from 22 to 21.

K@jkUTQ+s.ev*lKbK*lKv K@jkUTQ - Filters the digits and assigns them to a variable K. m - Map. Iterated through the digits with a variable d v - Evaluate (convert to float). *lKd - Multiplies each String digit by the length of K. s - Sum + - Sum *lKvQ - Multipies the number by the length of the digits String

officialaimm 07/30/2017.

** -7 bytes thanks to @Mr. Xcoder**:

`'/'<i`

- Takes in integer or float, returns float.

`lambda x:sum(float(i*len(z))for z in[[i for i in`x`if"/"<i]]for i in[x]+z)`

Say `123.45`

is given as input. `[i for i in`x`if"/"<x]`

gives a list of stringified integers `['1','2','3','4','5']`

(which is also `z`

). Now we iterate through `[x]+z`

i.e. `[123.45,'1','2','3','4','5']`

, multiplying each element by `len(z)`

, here `5`

and converting each to a Float (so that strings also convert accordingly), yielding `[617.25,11111.0,22222.0,33333.0,44444.0,55555.0]`

. Finally we calculate the `sum(...)`

and obtain `167282.25`

.

74 bytes. You can replace

`i.isdigit()`

with `"/"<i`

, in fact, because both `.`

and `-`

have lower ASCII codes than digits, adn `/`

is in between them Bruce Forte 07/30/2017.

Thanks a lot @TomCarpenter for teaching me that assignments have a return value and saving me `18`

bytes!

`@(v)(n=nnz(s=strrep(num2str(abs(v)),'.','')-'0'))*v+sum(sum(s'*logspace(0,n-1,n)))`

```
function f=g(v)
s=strrep(num2str(abs(v)),'.','')-'0'; % number to vector of digits (ignore . and -)
n=nnz(s); % length of that vector
f=n*v+sum(sum(s'*logspace(0,n-1,n))) % add the number n times and sum the columns of the square
end
```

The way this works is that we basically need to add the number itself `n`

times and then add the sum of the columns. Summing `s' * logspace(0,n-1,n)`

achieves the sum of columns, for example if `v=-123.4`

that matrix will be:

```
[ 1 10 100 1000;
2 20 200 2000;
3 30 300 3000;
4 40 400 4000 ]
```

So we just need to `sum`

it up and we're done.

You can save 18 bytes by smushing it all into an anonymous function

`@(v)(n=nnz(s=strrep(num2str(abs(v)),'.','')-'0'))*v+sum(sum(s'*logspace(0,n-1,n)))`

. Try it online! Mr. Xcoder 07/30/2017.

`func f(s:String){let k=s.filter{"/"<$0};print(Float(s)!*Float(k.count)+k.map{Float(String(repeating:$0,count:k.count))!}.reduce(0,+))}`

`func f(s:String)`

- Defines a function`f`

with an explicit String parameter`s`

.`let k=s.filter{"/"<$0}`

- Filters the digits: I noticed that both`-`

and`.`

have smaller ASCII-values than all the digits, and`/`

is between`.`

,`-`

and`0`

. Hence, I just checked if`"/"`

is smaller than the current character, as I did in my Python answer.`print(...)`

- Prints the result.`Float(s)!*Float(k.count)`

- Converts both the String and the number of digits to Float and multiplies them (Swift does not allow Float and Int multiplication :()). So it adds the number`x`

times, where`x`

is the number of digits it contains.`k.map{Int(String(repeating:$0,count:k.count))!`

-`k.map{}`

maps over`k`

with the current value`$0`

.`String(repeating:$0,count:k.count)`

takes each digit, creates a String of`x`

identical digits and`Float(...)!`

converts it to a Floating-point number.`.reduce(0,+)`

- Gets the sum of the list above.And finally

`+`

sums the two results.

Say our String is `"0.45"`

. First off, we filter the digits, so we are left with `0, 4, 5`

. We convert `"0.45"`

to Float and multiply by the number of digits: `0.45 * 3 = 1.35`

. Then we take each digit and turn it into a String repeating that digit until it fills the width of the square (how many digits there are): `0, 4, 5 -> 000, 444, 555`

. We sum this, `000 + 444 + 555 = 999`

. Then we just add the results together: `1.35 + 999 = 1000.35`

.

TheLethalCoder 07/31/2017.

`using System.Linq;n=>{var d=(n+"").Where(char.IsDigit);return d.Sum(i=>int.Parse(new string(i,d.Count())))+new int[d.Count()].Sum(_=>n);}`

*Saved 2 bytes thanks to @Ian H.*

Full/Formatted version:

```
namespace System.Linq
{
class P
{
static void Main()
{
Func<double, double> f = n =>
{
var d = (n + "").Where(char.IsDigit);
return d.Sum(i => int.Parse(new string(i, d.Count()))) + new int[d.Count()].Sum(_ => n);
};
Console.WriteLine(f(123));
Console.WriteLine(f(-144));
Console.WriteLine(f(4));
Console.WriteLine(f(244.2));
Console.ReadLine();
}
}
}
```

Ian H. 07/31/2017

You can save 2 bytes at the beginning by using

`var d=(n+ ...`

instead of `var d = (n ...`

. TheLethalCoder 07/31/2017

@IanH. Forgot to remove all the spaces -_- That's what I get for answering whilst doing a support call.

Jenny_mathy 08/09/2017.

`(t=Length[s=#&@@RealDigits[#]//.{a___, 0}:>{a}];If[IntegerPart@#==0,t++];t#+Tr[FromDigits@Table[#,t]&/@s])&`

Titus 08/11/2017.

`for($e=preg_match_all("#\d#",$n=$argn);~$c=$n[$i++];)$s+=str_repeat($c,$e);echo$s+$n*$e;`

Run as pipe with `-nR`

.

May yield warnings in PHP 7.1. Repace `$c,$e`

with `$c>0?$c:0,$e`

to fix.

C McAvoy 07/31/2017.

`lambda n:sum(float(n)+int(_*sum(x>"/"for x in n))for _ in n if"/"<_)`

Loops over every digit character and repeats it by the number of digit characters overall, makes that into an integer, and adds that to `n`

. This way `n`

gets added `d`

times, the horizontal part of the sum, along with the digit repetition, which is the vertical part. Originally used `str.isdigit`

but `>"/"`

, thanks to others in this thread, saved a lot of bytes. Saves two bytes by taking `n`

as a string, but the output is messier.

`lambda n:sum(n+int(_*sum(x>"/"for x in str(n)))for _ in str(n)if"/"<_)`

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`244.2`

is not a float number. It cannot be converted to the string`"244.2"`

.