#!/usr/bin/perl
=head1 NAME
weights40.pl - check you can make each weight from 1 to 40 balance
=head1 DESCRIPTION
This doesn't solve the puzzle but does prove that the solution works.
The puzzle is you have a balance (bilancia in Italian).
And you can choose some unit weights to help weigh things.
If you get any unit weight from 1 to 40 you need to be able to determine the weight.
(You have to make the scales balance, you're not allowed to measure
it as lighter than w+1 and heavier than w-1 hence is w.)
What is the minimum number of weights you can do this in ?
If the puzzle is told properly then you probably have to bring the
balance and weights up a big mountain with dragons on top so you wish to use the absolute minimum
number of weights (or possibly minimum weight of weights - is it the same answer I wonder?)
=cut
my @weights = ( 1, 3, 9, 27 );
for(my $w=-1; $w<=41; $w++) {
# brute force, try balance all permutations, weights on both sizes
# try position of not there, left, right for each weight
my @weight_pos = ( 0, 0, 0, 0 );
my $wi = 0;
# print terrible message if not found otherwise might miss one
my $terribleness = "BAH! :( not good, no match for $w\n";
my $found = 0;
for($weight_pos[0]=0; $weight_pos[0]<3 && $found==0; $weight_pos[0]++) {
for($weight_pos[1]=0; $weight_pos[1]<3 && $found==0; $weight_pos[1]++) {
for($weight_pos[2]=0; $weight_pos[2]<3 && $found==0; $weight_pos[2]++) {
for($weight_pos[3]=0; $weight_pos[3]<3 && $found==0; $weight_pos[3]++) {
# start with $w always on left
my $left_tot = $w;
my $right_tot = 0;
my @leftside = ( $w );
my @rightside = ();
# print '$#weights is ' . $#weights . " (number of elements in weights array)\n";
# put weights on balance
for($wi=0;$wi<=$#weights;$wi++) {
#print "dbg w=$w wi=$wi pos=$weight_pos[$wi]\n";
if ($weight_pos[$wi] == 1) {
#printf "L";
push @leftside, $weights[$wi];
$left_tot += $weights[$wi];
} elsif ($weight_pos[$wi] == 2) {
#printf "R";
push @rightside, $weights[$wi];
$right_tot += $weights[$wi];
}
#$ls += "(".$weights[$wi].) ";
#$rs += "(".$weights[$wi].) ";
}
#print "dbg w: $w, balance $left_tot = $right_tot, left: @leftside - right: @rightside\n";
if ($left_tot == $right_tot) {
print "w: $w, balance $left_tot = $right_tot, left: @leftside - right: @rightside\n";
$terribleness = "";
$found = 1;
break;
}
}
}
}
}
print $terribleness;
}
perldoc is a good reference, (command-line interface to perl docs)
not on all machines but is on slaine
same stuff as is on web in lots of places of course:
http://perldoc.perl.org/perl.html
e.g. perldoc perl, perldoc perldoc (for table of contents)
perldoc perlsyn
perldoc perlre
-f or -q to get function documentation or search faq:
perldoc -f printf
perldoc -q while
After you know all that perldoc then you can start thinking about using perl modules! :D
To read perl documentation _inside_ perl scripts or modules just do e.g.:
perldoc weight40.pl
