#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };
use List::Util qw{ shuffle };

my @words = qw( this is a string with a word );
my @order = 0 .. $#words;

my %ord;
push @{ $ord{ $words[$_] } }, $_ for 0 .. $#words;  # <-- Here...

@words = shuffle(@words);
@order = @ord{@words};

print do { local $" = "\t"; "@words\n" };
say join "\t", map "[@$_]", @order;

@order = map shift @$_, @order;                     # <-- and here.
say join ' ',
    map $words[$_],
    sort { $order[$a] <=> $order[$b] }
    @order;
[download]

($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
[download]

Of course, I had no doubt you know how to do it! ;)

Just wanted to point out that the inverse of a function isn't necessarily a function again. :)

Cheers Rolf
_{(addicted to the Perl Programming Language and ☆☆☆☆ :)
Je suis Charlie!}