use strict;
use warnings;

my @orig = (1..10);
my @altered = ( [qw( 1  2  3  4  9  5  6  7  8 10)],
                [qw( 2  3  4  1  5  6  7  8  9 10)],
                [qw( 1  2  3  4 10  5  6  7  8  9)],
                [qw( 1  2  3  5  4  6  7  8  9 10)],
                [qw( 1  3  4  5  6  7  2  8  9 10)],
                [qw( 1  2  3  4  5  6  7  8 10  9)],
                [qw( 1  2  3  4  6  5  7  8  9 10)],
);


for my $test (@altered) {
    my %count = ();
    my ($val, $flag) = (undef, $orig[0] == $test->[0]);

    for my $i (0..$#orig) {
        # keep track of what the nums in each array add up to
        $count{before} += $orig[$i];
        $count{after}  += $test->[$i];
        
        if (($flag && ($count{before} != $count{after}))
                || (!$flag && ($count{before} == $count{after}))) {
            $val = ( $test->[$i] == $orig[$i+1])
                ? $orig[$i]
                : $test->[$i];
            last;
        }
    }
    print "$val moved between (@orig) and (@$test)\n";
}


##</code><code>##

The sum of a sequence of integers from x to x+n equals
    ((x+n)(x+n+1) - (x-1)(x))/2