Take it in steps.

#! perl -slw
use strict;
my $data = do { local $/; <DATA>; }; #! slurp the file into a scalar.

$data =~ s/([^\n])(\n)([^\n])/$1$3/g; #! join the paras into lines
$data =~ s/\n+/\n/g; #! reduce multiple \n's to 1

my @data = split/\n/, $data; #! and split.

print for @data;

__DATA__
1   2   3   1
1   6   4   8

5   6   9   0
8   89   5   0
0   8




7   8   4   6
6   3   79   0

588   7   9   4
3   9   2   9



9   23   8   0
2   8   98   0

9   7   8   0
0
[download]

Gives

C:\test>216446
1   2   3   11   6   4   8
5   6   9   08   89   5   00   8
7   8   4   66   3   79   0
588   7   9   43   9   2   9
9   23   8   02   8   98   0
9   7   8   00
[download]