use strict;
use warnings;

my @constraints = (
                   {mid => 20, sd => 15},
                   {mid => 30, sd => 25},
                   {mid => 50, sd => 10},
               );

my $sum;

for my $cnst (@constraints) {
    my $value = RandFlat ($cnst->{mid}, $cnst->{sd});
    $cnst->{value} = $value;
    $sum += $value;
}

# want $diff = 0
my $diff = $sum - 100;

my $adj_sum = 0;
# positive $diff means $sum is too high, go lower
if ( $diff > 0 ) {
    for my $cnst (@constraints) {
        # how far can this value be adjusted?
        my $adj = $cnst->{value} - ($cnst->{mid} - $cnst->{sd});
        $cnst->{adj} = $adj;
        $adj_sum += $adj;
    }
}
# negative $diff means $sum is too low, go higher
elsif ( $diff < 0 ) {
    for my $cnst (@constraints) {
        # how far can this value be adjusted?
        my $adj = $cnst->{mid} + $cnst->{sd} - $cnst->{value};
        $cnst->{adj} = $adj;
        $adj_sum += $adj;
    }
}

# possible adjustment vs. adjustment needed
my $scale = $adj_sum / $diff;
for my $cnst (@constraints) {
    my $adj = $cnst->{adj};
    $cnst->{value} -= $cnst->{adj} / $scale;
}

$sum = 0;
for my $cnst (@constraints) {
    my ($mid, $sd, $value) = @{$cnst}{'mid', 'sd', 'value'};

    printf "%5.1f +-%5.1f: %5.1f", $mid, $sd, $value;
    print " - bad" if ($value < ($mid - $sd)) || ($value > ($mid + $sd));
    print "\n";

    $sum += $value;
}
print "sum: $sum\n";

sub RandFlat {
    #Return a rand () value with a flat distribution about the $mean +- $stdDev
    my ($mean, $stdDev) = @_;
    my $range = 2.0 * $stdDev;
    my $value = rand ($range);
    return $value + ($mean-$stdDev);
}