Pure bash (no coreutils or other utilities), 125

Standard center of mass calculation using moments about the origin:

for((;i<${#1};w=36#${1:i:1}-9,m+=w,M+=w*++i)){ :;} ((M%m))&&echo $1 DOES NOT BALANCE||echo ${1:0:M/m-1} ${1:M/m-1:1} ${1:M/m} 

Test output:

$ for t in \ > STEAD \ > CONSUBSTANTIATION \ > WRONGHEADED \ > UNINTELLIGIBILITY \ > SUPERGLUE > do ./wordbal.sh $t; done S T EAD CONSUBST A NTIATION WRO N GHEADED UNINTELL I GIBILITY SUPERGLUE DOES NOT BALANCE $ 

Python 3, 124

w=input() i=a=b=0 for c in w:n=ord(c)-64;a+=n;b+=n*i;i+=1 m=b//a print(*[w[:m],w,w[m],"DOES NOT BALANCE",w[m+1:]][b%a>0::2]) 

This code doesn't test potential fulcrums, but rather finds the "center of mass" and checks if it's an integer. It does so by summing the total mass a and the position-weighted mass b, to find the center of mass m=b/a. It then prints either the string split at position m, or the string plus "DOES NOT BALANCE", chosen by the [_::2] list-slicing trick.

CJam, 57 bytes

l_,,_f{f-W$'@fm.*:+}0#:I){ISIW$=S++t}" DOES NOT BALANCE"? 

This can still be golfed a bit.

Try it online here

JavaScript (ES6), 211 200 160 bytes

f=w=>{for(j=-w.length;j++;)if(![...w].reduce((p,v,i)=>p+(parseInt(v,36)-9)*(j+i),0))return w.slice(0,-j)+` ${w[-j]} `+w.slice(1-j);return w+` DOES NOT BALANCE`} 

Previous attempt, 200 bytes

Thanks to edc56 and nderscore for helping me golf this

f=w=>{for(j=0,r=(a,z)=>[...a][z||`reverse`]().reduce((p,v,i)=>p+(parseInt(v,36)-9)*++i,0);j++<w.length;)if(r(a=w[s=`slice`](0,j))==r(b=w[s](j+1),s))return a+` ${w[j]} `+b;return w+` DOES NOT BALANCE`} 

Demo

Firefox and Edge only for now, as it is ES6

f=w=>{for(j=1-w.length;j++;)if(!([...w].reduce((p,v,i)=>p+(parseInt(v,36)-9)*(j+i),0)))return w.slice(0,-j)+` ${w[-j]} `+w.slice(1-j);return w+` DOES NOT BALANCE`} // DEMO console.log = function(a) { document.body.innerHTML += a + "<br>"; } console.log(f('STEAD')); console.log(f('CONSUBSTANTIATION')); console.log(f('WRONGHEADED')); console.log(f('UNINTELLIGIBILITY')); console.log(f('SUPERGLUE'));

C, 236 198 192 188 180 173 bytes

a,i,j,k,L;f(char*s){L=strlen(s);for(;i<L;i++){for(a=j=0;j<L;j++)a+=(s[j]-64)*(i-j);if(!a)break;}for(;k<L;k++)printf(k-i?"%c":" %c ",s[k]);if(a)printf(" DOES NOT BALANCE");} 

Expanded with main():

#define p printf a,i,j,k,L; f(char*s) { L=strlen(s); for(;i<L;i++){ for(a=j=0;j<L;j++) a+=(s[j]-64)*(i-j); if(!a) break; } for(;k<L;k++) printf(k-i?"%c":" %c ",s[k]); if(a) printf(" DOES NOT BALANCE"); } // 83 bytes below int main(int argc, char **argv) { f(argv[1]); printf("\n"); } 

Verification:

$ ./a.out CONSUBSTANTIATION CONSUBST A NTIATION $ ./a.out WRONGHEADED WRO N GHEADED $ ./a.out A A $ ./a.out WRONG WRONG DOES NOT BALANCE $ ./a.out SUPERGLUE SUPERGLUE DOES NOT BALANCE 

CJam, 50 bytes

r_'@f-_ee::*:+\:+md"X DOES NOT BALANCEX"@?)/()@]S* 

Using the Java interpreter, this exits with an error to STDERR for non-balancing words.

If you try the code in the CJam interpreter, just ignore everything but the last line of output.

Idea

My "original idea" turned out to be the same approach @xnor posted several hours before me. Nevertheless, here it goes:

Given a list of values (v₀, … v_n), we have that v_t is the anchor of the list if and only if any of the following, equivalent conditions holds:

• tv₀ + … + 1v_t-1 == 1v_t+1 + … tv_n

• (0 - t)v₀ + … + (n - t)v_n == 0

• 0v₀ + … + nv_n == t(v₀ + … + v_n)

• t := (0v₀ + … + nv_n)/(v₀ + … + v_n) is an integer.

Code

r e# Read a whitespace separated token from STDIN. _'@f- e# Push a copy and subtract '@' from each char (pushes code point - 64). _ee e# Push a copy of the array of values and enumerate them. ::* e# Multiply each value by its index. :+ e# Add all results. \:+ e# Add the unmodified values. md e# Perform modular division. Pushes quotient and residue. "X DOES NOT BALANCEX" @ e# Rotate the quotient on top of the string. ? e# If the residue is 0, select the quotient. Otherwise, select the string. 

At this part, we start having a little fun with overloaded operators.

For the quotient, this happens:

) e# Add 1 to the quotient. / e# Split the input string into chunks of that length. ( e# Shift out the first chunk. ) e# Pop the last character of the first chunk. @ e# Rotate the rest of the string on top of the stack. ]S* e# Wrap all three parts in an array and join them, separating by spaces. 

For the string, this happens:

) e# Pop out the last char: "X DOES NOT BALANCE" 'X' / e# Split the remainder at X's: ["" " DOES NOT BALANCE"] ( e# Shift out the first chunk: [" DOES NOT BALANCE"] "" ) e# Pop out the last char. 

At this point, a runtime error happens, since "" does not have a last char. The stack gets printed and executing is aborted immediately.

Julia, 122 bytes

s->(v=[int(i)-64for i=s];m=dot(v,1:length(s))/sum(v);m==int(m)?join([s[1:m-1],s[m],s[m+1:end]]," "):s*" DOES NOT BALANCE") 

This creates an unnamed function that accepts a string as input and returns a string. To call it, give it a name, e.g. f=s->....

We treat the word like a one-dimensional system for which we need to find the center of mass. The center of mass is computed as the dot product of the masses with their locations, divided by the total mass of the system. If the computed center is an integer, it corresponds to one of the letters in the word. Otherwise the word doesn't balance.

Ungolfed + explanation:

function f(s) # Create a vector of ASCII code points -- these are the "masses" v = [int(i)-64 for i in s] # Compute the center of mass, taking the locations to be the indices m = dot(v, 1:length(s)) / sum(v) # Check whether the center corresponds to a letter's position if m == int(m) join([s[1:m-1], s[m], s[m+1:end]], " ") else m * " DOES NOT BALANCE" end end 

Examples:

julia> f("WRONG") "WRONG DOES NOT BALANCE" julia> f("STEAD") "S T EAD" julia> f("CONSUBSTANTIATION") "CONSUBST A NTIATION" 

PHP, 249 174 bytes

Takes one command-line argument.

<?for($i=-$l=strlen($w=$argv[1]);$i++;){for($k=$q=0;$l>$k;)$q+=($i+$k)*(ord($w[$k++])-64);$q?:exit(substr($w,0,-$i)." {$w[-$i]} ".substr($w,1-$i));}echo"$w DOES NOT BALANCE"; 

Initial attempt:

<?function r($a){for($i=$q=0;strlen($a)>$i;){$q+=(ord($a[$i])-64)*++$i;}return$q;}for($i=0;$i++<strlen($w=$argv[1]);)(strlen($w)<2?exit($w):(r(strrev($a=substr($w,0,$i)))==r($b=substr($w,$i+1)))?exit("$a {$w[$i++]} $b"):0);echo"$w DOES NOT BALANCE"; 

Haskell, 161 135 bytes

a#b=a*(fromEnum b-64) v=sum.zipWith(#)[1..] h![]=h++" DOES NOT BALANCE" h!(x:y)|v(reverse h)==v y=h++' ':x:' ':y|1<2=(h++[x])!y f=([]!) 

Usage example:

*Main> putStr $ unlines $ map f ["CONSUBSTANTIATION","WRONGHEADED","UNINTELLIGIBILITY","SUPERGLUE"] CONSUBST A NTIATION WRO N GHEADED UNINTELL I GIBILITY SUPERGLUE DOES NOT BALANCE 

How it works: f calls the helper function ! which takes two parameters, the left and right part of the word at a given position. It stops if both parts have equal weight (function v) or calls itself recursively with the first letter of the right part moved to the left. It ends with the DOES NOT BALANCE message if the right part is empty.

C, 183 134 bytes

h,i,a=1;c(char*s){for(;s[i++]&&a;)for(a=h=0;s[h];)a+=(s[h]-64)*(h++-i);printf(a?"%.*s DOES NOT BALANCE":"%.*s %c %s",i,s,s[--i],s+i);} 

New Version Explained:

Like the other two entries, it makes use of constant addition on one side and subtraction on the other to hopefully reach zero which is the indication of balance. My original output is reused from the first answer, albeit slightly modified.

l,h,i,a,b;c(char*s){for(l=strlen(s);h++<l&&(a^b|!a);)for(i=a=b=0;i<l;i++)i==h?a=b,b=0:(b+=(s[i]-64)*abs(i-h));printf(a==b?"%.*s %c %s":"%.*s DOES NOT BALANCE",a==b?h:l,s,s[--h],s+h);} 

Old Version Explained:

The first loop (h) is the main iterator for the length of the string. The second loop (i) accumulates (b) until h==i. Once that happens, (b) is stored in (a), reset to 0, and then continues until the end of the string is reached where (a) is compared to (b). If there's a match, the main iterator's loop is broken and the output is printed.

Ruby 175

F=->s{v=->s{(0...s.size).map{|i|(i+1)*(s[i].ord-64)}.inject :+} r="#{s} DOES NOT BALANCE" (0...s.size).map{|i|b,a=s[0...i],s[i+1..-1] v[b.reverse]==v[a]&&r=b+" #{s[i]} "+a} r} 

Test it online: http://ideone.com/G403Fv

This is a pretty straightforward Ruby implementation. Here's the readable program:

F=-> word { string_value = -> str { (0...str.size).map{|i|(i+1) * (str[i].ord - 64)}.inject :+ } result = "#{word} DOES NOT BALANCE" (0...word.size).map {|i| prefix, suffix = word[0...i], word[i+1..-1] if string_value[prefix.reverse] == string_value[suffix] result = prefix + " #{word[i]} " + suffix end } result } 

R, 190 bytes

As an unnamed function. I think I can get a few more, but that'll have to wait.

function(A){D=colSums(B<-(as.integer(charToRaw(A))-64)*outer(1:(C=nchar(A)),1:C,'-'));if(!length(E<-which(B[,D==0]==0)))cat(A,'DOES NOT BALANCE')else cat(substring(A,c(1,E,E+1),c(E-1,E,C)))} 

Ungolfed a bit with brief explanation

function(A){ D=colSums( #column sums of the outer function * character values B<-( as.integer(charToRaw(A))-64) # character values * outer(1:(C=nchar(A)),1:C,'-') # matrix of ranges eg -3:2, -1:4, etc ) if(!length( E<-which(B[,D==0]==0) # where the colsum = 0, get the index of the zero )) cat(A,'DOES NOT BALANCE') else cat(substring(A,c(1,E,E+1),c(E-1,E,C))) #cat the substrings } 

It doesn't put a newline at the end.

Test run

> f= + function(A){D=colSums(B<-(as.integer(charToRaw(A))-64)*outer(1:(C=nchar(A)),1:C,'-'));if(!length(E<-which(B[,D==0]==0)))cat(A,'DOES NOT BALANCE')else cat(substring(A,c(1,E,E+1),c(E-1,E,C)))} > > f('CONSUBSTANTIATION') CONSUBST A NTIATION > f('WRONGHEADED') WRO N GHEADED > f('UNINTELLIGIBILITY') UNINTELL I GIBILITY > f('SUPERGLUE') SUPERGLUE DOES NOT BALANCE > 

C, 142 bytes

Credit to some user for beating me to it :)

i,l=1,j;g(char*v){for(;v[i]&&l;++i)for(j=l=0;v[j];++j)l+=(i-j)*(v[j]-64);printf(l?"%.*s DOES NOT BALANCE":"%.*s %c %s",l?i:--i,v,v[i],v+i+1);} 

Java, 240 bytes

String b(String s){for(int i=-1,a=s.length(),l=0,r,m;++i<a;){for(r=i;--r>=0;l+=(s.charAt(r)-64));for(m=r=0;++m+i<a;r+=(s.charAt(m+i)-64)*m);if(l==r)return s.substring(0,i)+" "+s.charAt(i)+" "+s.substring(i+1);}return s+" DOES NOT BALANCE";}