Here is my solution:

#!/usr/bin/perl

use strict;
use warnings;

my $input_file  = 'HGDP.txt';
my $output_file = 'output.txt';

open my $fh, '<', $input_file
  or die "Unable to open for read $input_file: $!";
open my $out_fh, '>', $output_file
  or die "Unable to open for write $output_file: $!";

local $, = q{ };
local $\ = "\n";

my @rows;

my $static_i = 3;    # number of first unjoinable columns

sub print_rows {
    print {$out_fh} @{$rows[0]}[0 .. $static_i - 1], map {
        my @columns;
        foreach my $x (0 .. $#rows) {
            push @columns, $rows[$x][$_];
        }
        join q{/}, @columns;
    } $static_i .. $#{$rows[0]};
}

while (defined(my $line_1 = <$fh>)) {

    my ($x) = $line_1 =~ /^(\d+)/ or next;
    push @rows, [split q{ }, $line_1];

    while (defined(my $line_2 = <$fh>)) {
        next unless $line_2 =~ /^\d/;
        if ($line_2 =~ /^$x\b/) {
            push @rows, [split q{ }, $line_2];
        }
        else {
            print_rows();
            @rows = [split q{ }, $line_2];
            last;
        }
    }
}

print_rows();

close $fh;
close $out_fh;

__END__|Output from your example:
1 51 Brahui A/A C/C A/A A/G T/T
3 51 Brahui A/A C/C A/G G/A C/T
5 51 Brahui A/A C/C G/G A/G T/C
7 51 Brahui A/A C/C G/G A/G T/T
9 51 Brahui A/A C/C G/G G/G T/T
[download]

Note that the code it's not very efficient and is not very well written, but you can try to improve it. Good luck!