Merge pull request #5789 from PerlMonk-Athanasius/branch-for-challenge-156

Perl & Raku solutions to Tasks 1 & 2 of the Weekly Challenge 156

4 files changed, 778 insertions, 0 deletions

diff --git a/challenge-156/athanasius/perl/ch-1.pl b/challenge-156/athanasius/perl/ch-1.pl
new file mode 100644
index 0000000000..285ba4872e
--- /dev/null
+++ b/challenge-156/athanasius/perl/ch-1.pl
@@ -0,0 +1,149 @@
+#!perl
+
+###############################################################################
+=comment
+
+Perl Weekly Challenge 156
+=========================
+
+TASK #1
+-------
+*Pernicious Numbers*
+
+Submitted by: Mohammad S Anwar
+
+Write a script to permute first 10 Pernicious Numbers.
+
+    A pernicious number is a positive integer which has prime number of ones in
+    its binary representation.
+
+The first pernicious number is 3 since binary representation of 3 = (11) and
+1 + 1 = 2, which is a prime.
+
+Expected Output
+
+  3, 5, 6, 7, 9, 10, 11, 12, 13, 14
+
+=cut
+###############################################################################
+
+#--------------------------------------#
+# Copyright © 2022 PerlMonk Athanasius #
+#--------------------------------------#
+
+#==============================================================================
+=comment
+
+Interface
+---------
+Although the Task specifies a target of 10, I have extended the solution to
+accept any target integer value greater than 0; but if no argument is supplied
+on the command line, the target defaults to 10.
+
+Table
+-----
+The first 100 Pernicious Numbers [1, 2]:
+
+      3,   5,   6,   7,   9,  10,  11,  12,  13,  14,
+     17,  18,  19,  20,  21,  22,  24,  25,  26,  28,
+     31,  33,  34,  35,  36,  37,  38,  40,  41,  42,
+     44,  47,  48,  49,  50,  52,  55,  56,  59,  61,
+     62,  65,  66,  67,  68,  69,  70,  72,  73,  74,
+     76,  79,  80,  81,  82,  84,  87,  88,  91,  93,
+     94,  96,  97,  98, 100, 103, 104, 107, 109, 110,
+    112, 115, 117, 118, 121, 122, 124, 127, 129, 130,
+    131, 132, 133, 134, 136, 137, 138, 140, 143, 144,
+    145, 146, 148, 151, 152, 155, 157, 158, 160, 161
+
+Algorithm
+---------
+The natural numbers, in ascending order, are filtered as follows:
+ - each natural number n is converted to its binary representation b;
+ - the 1-digits in b are counted;
+ - if the count is a primary number, n is recorded as a pernicious number;
+ - the filtering process continues until the number of pernicious numbers found
+   is equal to the given target.
+
+References
+----------
+[1] "A052294  Pernicious numbers: numbers with a prime number of 1's in their
+     binary expansion.", The On-Line Encyclopedia of Integer Sequences,
+     https://oeis.org/A052294
+[2]  Iain Fox, "Table of n, a(n) for n = 1..10000",
+     https://oeis.org/A052294/b052294.txt
+[3] "Pernicious number", Wikipedia,
+     https://en.wikipedia.org/wiki/Pernicious_number
+
+=cut
+#==============================================================================
+
+use strict;
+use warnings;
+use Const::Fast;
+use ntheory        qw( is_prime );
+use Regexp::Common qw( number );
+
+const my $TARGET => 10;
+const my $USAGE  =>
+"Usage:
+  perl $0 [<target>]
+
+    [<target>]    The required output size [default: $TARGET]\n";
+
+#------------------------------------------------------------------------------
+BEGIN
+#------------------------------------------------------------------------------
+{
+    $| = 1;
+    print "\nChallenge 156, Task #1: Pernicious Numbers (Perl)\n\n";
+}
+
+#==============================================================================
+MAIN:
+#==============================================================================
+{
+    my $target = parse_command_line();
+
+    print "The first $target Pernicious Numbers:\n";
+
+    my @pernicious;
+
+    for (my $n = 1; scalar @pernicious < $target; ++$n)
+    {
+        my $bin  = sprintf '%b', $n;            # Convert to binary
+        my $ones = $bin =~ tr/1//;              # Count the ones
+
+        push @pernicious, $n if is_prime( $ones );
+    }
+
+    printf "%s\n", join ', ', @pernicious;
+}
+
+#------------------------------------------------------------------------------
+sub parse_command_line
+#------------------------------------------------------------------------------
+{
+    my   $args = scalar @ARGV;
+    0 <= $args <= 1 or error( 'Expected no more than 1 command line ' .
+                              "argument, found $args" );
+
+    my $target = $args == 0 ? $TARGET : $ARGV[ 0 ];
+
+       $target =~ / ^ $RE{num}{int} $ /x
+                    or error( qq["$target" is not a valid integer] );
+
+       $target > 0  or error( 'Target must be greater than 0' );
+
+    return $target;
+}
+
+#------------------------------------------------------------------------------
+sub error
+#------------------------------------------------------------------------------
+{
+    my ($message) = @_;
+
+    die "ERROR: $message\n$USAGE";
+}
+
+###############################################################################
diff --git a/challenge-156/athanasius/perl/ch-2.pl b/challenge-156/athanasius/perl/ch-2.pl
new file mode 100644
index 0000000000..0e316974da
--- /dev/null
+++ b/challenge-156/athanasius/perl/ch-2.pl
@@ -0,0 +1,253 @@
+#!perl
+
+###############################################################################
+=comment
+
+Perl Weekly Challenge 156
+=========================
+
+TASK #2
+-------
+*Weird Number*
+
+Submitted by: Mohammad S Anwar
+
+You are given number, $n > 0.
+
+Write a script to find out if the given number is a Weird Number.
+
+According to [ https://en.wikipedia.org/wiki/Weird_number |Wikipedia], it is
+defined as:
+
+    The sum of the proper divisors (divisors including 1 but not itself) of the
+    number is greater than the number, but no subset of those divisors sums to
+    the number itself.
+
+Example 1:
+
+  Input: $n = 12
+  Output: 0
+
+  Since the proper divisors of 12 are 1, 2, 3, 4, and 6, which sum to 16; but
+  2 + 4 + 6 = 12.
+
+Example 2:
+
+  Input: $n = 70
+  Output: 1
+
+  As the proper divisors of 70 are 1, 2, 5, 7, 10, 14, and 35; these sum to 74,
+  but no subset of these sums to 70.
+
+=cut
+###############################################################################
+
+#--------------------------------------#
+# Copyright © 2022 PerlMonk Athanasius #
+#--------------------------------------#
+
+#==============================================================================
+=comment
+
+Interface
+---------
+If the constant $VERBOSE is set to a true value (the default), the output is
+followed by an explanation of why the given n is or is not a weird number.
+
+Table
+-----
+The first 100 Weird Numbers [1], [2]:
+   70,   836,  4030,  5830,  7192,  7912,  9272, 10430, 10570, 10792,
+10990, 11410, 11690, 12110, 12530, 12670, 13370, 13510, 13790, 13930,
+14770, 15610, 15890, 16030, 16310, 16730, 16870, 17272, 17570, 17990,
+18410, 18830, 18970, 19390, 19670, 19810, 20510, 21490, 21770, 21910,
+22190, 23170, 23590, 24290, 24430, 24710, 25130, 25690, 26110, 26530,
+26810, 27230, 27790, 28070, 28630, 29330, 29470, 30170, 30310, 30730,
+31010, 31430, 31990, 32270, 32410, 32690, 33530, 34090, 34370, 34930,
+35210, 35630, 36470, 36610, 37870, 38290, 38990, 39410, 39830, 39970,
+40390, 41090, 41510, 41930, 42070, 42490, 42910, 43190, 43330, 44170,
+44870, 45010, 45290, 45356, 45710, 46130, 46270, 47110, 47390, 47810
+
+Algorithm
+---------
+1. To determine whether n is an abundant number, its proper factors are first
+   generated using the divisors() subroutine from the CPAN Module ntheory
+   (a.k.a. Math::Prime::Util). divisors() returns all the divisors, so the last
+   divisor (viz., n itself) must be removed. The proper divisors are then
+   summed, and the sum compared to n.
+
+2. To determine whether n is a semiperfect number, subsets of n's proper
+   factors are summed and the results compared with n. Subsets are generated by
+   the combinations() subroutine from the CPAN module Algorithm::Combinatorics,
+   which takes 2 arguments: the set from which the subsets are to be drawn, and
+   k, the number of elements in the required subsets.
+
+   Let the set of proper factors be F. We note that the required values of k
+   begin at 3 and end at |F| - 1, because:
+   - for any proper divisor d of n, d < n, so if k = 1, sum = d, which is < n;
+   - the largest possible proper divisor d0 of n is n/2, and the next largest,
+     d1, is < d0, so for k = 2 any sum = (d0 + d1) must be less than n;
+   - n is already known to be abundant, so if k = |F| then the sum > n.
+   
+References
+----------
+[1] "A006037  Weird numbers: abundant (A005101) but not pseudoperfect
+    (A005835).", The On-Line Encyclopedia of Integer Sequences,
+     https://oeis.org/A006037
+[2]  Amiram Eldar, "Table of n, a(n) for n = 1..10000",
+     https://oeis.org/A006037/b006037.txt
+[3] "Weird number", Wikipedia, https://en.wikipedia.org/wiki/Weird_number
+
+=cut
+#==============================================================================
+
+use strict;
+use warnings;
+use Algorithm::Combinatorics qw( combinations );
+use Const::Fast;
+use ntheory                  qw( divisors );
+use Regexp::Common           qw( number );
+
+const my $VERBOSE => 1;
+const my $USAGE   =>
+"Usage:
+  perl $0 <n>
+
+    <n>    A natural number\n";
+
+#------------------------------------------------------------------------------
+BEGIN
+#------------------------------------------------------------------------------
+{
+    $| = 1;
+    print "\nChallenge 156, Task #2: Weird Number (Perl)\n\n";
+}
+
+#==============================================================================
+MAIN:
+#==============================================================================
+{
+    my $n = parse_command_line();
+
+    print "Input:  \$n = $n\n";
+
+    my  @divisors = divisors( $n );
+    pop @divisors;                  # Remove $n to leave only *proper* divisors
+
+    my $sum  = 0;
+       $sum += $_ for @divisors;
+
+    if ($sum <= $n)                 # n is not an abundant number
+    {
+        print "Output: 0\n";
+        explain_failure_deficient( $n, \@divisors, $sum )          if $VERBOSE;
+    }
+    else                            # n is an abundant number
+    {
+        my $subset = find_subset(  $n, \@divisors);
+
+        if (scalar @$subset > 0)    # n is a semiperfect number
+        {
+            print "Output: 0\n";
+            explain_failure_semi(  $n, \@divisors, $sum, $subset ) if $VERBOSE;
+        }
+        else                        # n is not a semiperfect number
+        {
+            print "Output: 1\n";
+            explain_success(       $n, \@divisors, $sum )          if $VERBOSE;
+        }
+    }
+}
+
+#------------------------------------------------------------------------------
+sub find_subset
+#------------------------------------------------------------------------------
+{
+    my ($n, $divisors) = @_;
+    my  @subset;
+
+    L_OUTER:
+    for my $k (3 .. $#$divisors)
+    {
+        my $iter = combinations( $divisors, $k );
+
+        while (my $comb = $iter->next)
+        {
+            my $sum  = 0;
+               $sum += $_ for @$comb;
+
+            if ($sum == $n)
+            {
+                @subset = @$comb;
+                last L_OUTER;
+            }
+        }
+    }
+
+    return \@subset;
+}
+
+#------------------------------------------------------------------------------
+sub explain_failure_deficient             # Not weird because not abundant
+#------------------------------------------------------------------------------
+{
+    my ($n, $divisors, $sum) = @_;
+
+    printf "\nExplanation:\nThe proper divisors of %d (%s) sum to %d," .
+           "\ntherefore %d is not weird because it is not abundant\n",
+            $n, join( ', ', @$divisors ), $sum, $n;
+}
+
+#------------------------------------------------------------------------------
+sub explain_failure_semi                  # Not weird: abundant but semiperfect
+#------------------------------------------------------------------------------
+{
+    my ($n, $divisors, $sum, $subset) = @_;
+
+    printf "\nExplanation:\nThe proper divisors of %d (%s) sum to %d,"  .
+           "\nbut the subset (%s) of these proper divisors sums to %d," .
+           "\ntherefore %d is not weird because, although abundant, "   .
+           "it is also semiperfect\n", 
+            $n, join( ', ', @$divisors ), $sum, join( ', ', @$subset ), $n, $n;
+}
+
+#------------------------------------------------------------------------------
+sub explain_success                       # Weird: abundant and not semiperfect
+#------------------------------------------------------------------------------
+{
+    my ($n, $divisors, $sum) = @_;
+
+    printf "\nExplanation:\nThe proper divisors of %d (%s) sum to %d," .
+           "\nand no subset of these proper divisors sums to %d,"      .
+           "\ntherefore %d is weird because it is abundant but not "   .
+           "semiperfect\n",
+            $n, join( ', ', @$divisors ), $sum, $n, $n;
+}
+
+#------------------------------------------------------------------------------
+sub parse_command_line
+#------------------------------------------------------------------------------
+{
+    my $args = scalar @ARGV;
+       $args == 1 or error( "Expected 1 command line argument, found $args" );
+
+    my $n = $ARGV[ 0 ];
+
+       $n =~ / ^ $RE{num}{int} $ /x
+                  or error( qq["$n" is not a valid integer] );
+
+       $n > 0     or error( 'n must be greater than 0' );
+
+    return $n;
+}
+
+#------------------------------------------------------------------------------
+sub error
+#------------------------------------------------------------------------------
+{
+    my ($message) = @_;
+
+    die "ERROR: $message\n$USAGE";
+}
+
+###############################################################################
diff --git a/challenge-156/athanasius/raku/ch-1.raku b/challenge-156/athanasius/raku/ch-1.raku
new file mode 100644
index 0000000000..d71f4c6237
--- /dev/null
+++ b/challenge-156/athanasius/raku/ch-1.raku
@@ -0,0 +1,122 @@
+use v6d;
+
+###############################################################################
+=begin comment
+
+Perl Weekly Challenge 156
+=========================
+
+TASK #1
+-------
+*Pernicious Numbers*
+
+Submitted by: Mohammad S Anwar
+
+Write a script to permute first 10 Pernicious Numbers.
+
+    A pernicious number is a positive integer which has prime number of ones in
+    its binary representation.
+
+The first pernicious number is 3 since binary representation of 3 = (11) and
+1 + 1 = 2, which is a prime.
+
+Expected Output
+
+  3, 5, 6, 7, 9, 10, 11, 12, 13, 14
+
+=end comment
+###############################################################################
+
+#--------------------------------------#
+# Copyright © 2022 PerlMonk Athanasius #
+#--------------------------------------#
+
+#==============================================================================
+=begin comment
+
+Interface
+---------
+Although the Task specifies a target of 10, I have extended the solution to
+accept any target integer value greater than 0; but if no argument is supplied
+on the command line, the target defaults to 10.
+
+Table
+-----
+The first 100 Pernicious Numbers [1, 2]:
+
+      3,   5,   6,   7,   9,  10,  11,  12,  13,  14,
+     17,  18,  19,  20,  21,  22,  24,  25,  26,  28,
+     31,  33,  34,  35,  36,  37,  38,  40,  41,  42,
+     44,  47,  48,  49,  50,  52,  55,  56,  59,  61,
+     62,  65,  66,  67,  68,  69,  70,  72,  73,  74,
+     76,  79,  80,  81,  82,  84,  87,  88,  91,  93,
+     94,  96,  97,  98, 100, 103, 104, 107, 109, 110,
+    112, 115, 117, 118, 121, 122, 124, 127, 129, 130,
+    131, 132, 133, 134, 136, 137, 138, 140, 143, 144,
+    145, 146, 148, 151, 152, 155, 157, 158, 160, 161
+
+Algorithm
+---------
+The natural numbers, in ascending order, are filtered as follows:
+ - each natural number n is converted to its binary representation b;
+ - the 1-digits in b are counted;
+ - if the count is a primary number, n is recorded as a pernicious number.
+ - the filtering process continues until the number of pernicious numbers found
+   is equal to the given target.
+
+References
+----------
+[1] "A052294  Pernicious numbers: numbers with a prime number of 1's in their
+     binary expansion.", The On-Line Encyclopedia of Integer Sequences,
+     https://oeis.org/A052294
+[2]  Iain Fox, "Table of n, a(n) for n = 1..10000",
+     https://oeis.org/A052294/b052294.txt
+[3] "Pernicious number", Wikipedia,
+     https://en.wikipedia.org/wiki/Pernicious_number
+
+=end comment
+#==============================================================================
+
+my UInt constant $TARGET = 10;
+
+#------------------------------------------------------------------------------
+BEGIN
+#------------------------------------------------------------------------------
+{
+    "\nChallenge 156, Task #1: Pernicious Numbers (Raku)\n".put;
+}
+
+#==============================================================================
+sub MAIN
+(
+    UInt:D $target where * > 0 = $TARGET            #= The required output size
+)
+#==============================================================================
+{
+    "The first $target Pernicious Numbers:".put;
+
+    my UInt @pernicious;
+
+    loop (my UInt $n = 1; +@pernicious < $target; ++$n)
+    {
+        my Str  $bin  = '%b'.sprintf: $n;           # Convert to binary
+        my UInt $ones = +$bin.comb: '1';            # Count the ones
+
+        @pernicious.push: $n if $ones.is-prime;
+    }
+
+    "%s\n".printf: @pernicious.join: ', ';
+}
+
+#------------------------------------------------------------------------------
+sub USAGE()
+#------------------------------------------------------------------------------
+{
+    my Str $usage = $*USAGE;
+
+    $usage ~~ s/ ($*PROGRAM-NAME) /raku $0/;
+
+    $usage.put;
+}
+
+##############################################################################
diff --git a/challenge-156/athanasius/raku/ch-2.raku b/challenge-156/athanasius/raku/ch-2.raku
new file mode 100644
index 0000000000..aade096465
--- /dev/null
+++ b/challenge-156/athanasius/raku/ch-2.raku
@@ -0,0 +1,254 @@
+use v6d;
+
+###############################################################################
+=begin comment
+
+Perl Weekly Challenge 156
+=========================
+
+TASK #2
+-------
+*Weird Number*
+
+Submitted by: Mohammad S Anwar
+
+You are given number, $n > 0.
+
+Write a script to find out if the given number is a Weird Number.
+
+According to [ https://en.wikipedia.org/wiki/Weird_number |Wikipedia], it is
+defined as:
+
+    The sum of the proper divisors (divisors including 1 but not itself) of the
+    number is greater than the number, but no subset of those divisors sums to
+    the number itself.
+
+Example 1:
+
+  Input: $n = 12
+  Output: 0
+
+  Since the proper divisors of 12 are 1, 2, 3, 4, and 6, which sum to 16; but
+  2 + 4 + 6 = 12.
+
+Example 2:
+
+  Input: $n = 70
+  Output: 1
+
+  As the proper divisors of 70 are 1, 2, 5, 7, 10, 14, and 35; these sum to 74,
+  but no subset of these sums to 70.
+
+=end comment
+###############################################################################
+
+#--------------------------------------#
+# Copyright © 2022 PerlMonk Athanasius #
+#--------------------------------------#
+
+#==============================================================================
+=begin comment
+
+Interface
+---------
+If the constant $VERBOSE is set to True, (the default), the output is followed
+by an explanation of why the given n is or is not a weird number.
+
+Table
+-----
+The first 100 Weird Numbers [1], [2]:
+   70,   836,  4030,  5830,  7192,  7912,  9272, 10430, 10570, 10792,
+10990, 11410, 11690, 12110, 12530, 12670, 13370, 13510, 13790, 13930,
+14770, 15610, 15890, 16030, 16310, 16730, 16870, 17272, 17570, 17990,
+18410, 18830, 18970, 19390, 19670, 19810, 20510, 21490, 21770, 21910,
+22190, 23170, 23590, 24290, 24430, 24710, 25130, 25690, 26110, 26530,
+26810, 27230, 27790, 28070, 28630, 29330, 29470, 30170, 30310, 30730,
+31010, 31430, 31990, 32270, 32410, 32690, 33530, 34090, 34370, 34930,
+35210, 35630, 36470, 36610, 37870, 38290, 38990, 39410, 39830, 39970,
+40390, 41090, 41510, 41930, 42070, 42490, 42910, 43190, 43330, 44170,
+44870, 45010, 45290, 45356, 45710, 46130, 46270, 47110, 47390, 47810
+
+Algorithm
+---------
+1. To determine whether n is an abundant number, its proper factors are first
+   generated by filtering integers in the range 1 to ⌊$n / 2⌋ using Raku's
+   built-in divisibility operator, "%%".
+
+2. To determine whether n is a semiperfect number, subsets of n's proper
+   factors are summed and the results compared with n. Subsets are generated by
+   Raku's built-in combinations() method. The argument k to this method
+   specifies the number of elements in the required subsets.
+
+   Let the set of proper factors be F. We note that the required values of k
+   begin at 3 and end at |F| - 1, because:
+   - for any proper divisor d of n, d < n, so if k = 1, sum = d, which is < n;
+   - the largest possible proper divisor d0 of n is n/2, and the next largest,
+     d1, is < d0, so for k = 2 any sum = (d0 + d1) must be less than n;
+   - n is already known to be abundant, so if k = |F| then the sum > n.
+   
+References
+----------
+[1] "A006037  Weird numbers: abundant (A005101) but not pseudoperfect
+    (A005835).", The On-Line Encyclopedia of Integer Sequences,
+     https://oeis.org/A006037
+[2]  Amiram Eldar, "Table of n, a(n) for n = 1..10000",
+     https://oeis.org/A006037/b006037.txt
+[3] "Weird number", Wikipedia, https://en.wikipedia.org/wiki/Weird_number
+
+=end comment
+#==============================================================================
+
+my Bool constant $VERBOSE = True;
+
+#------------------------------------------------------------------------------
+BEGIN
+#------------------------------------------------------------------------------
+{
+    "\nChallenge 156, Task #2: Weird Number (Raku)\n".put;
+}
+
+#==============================================================================
+sub MAIN
+(
+    UInt:D $n where * > 0           #= A natural number
+)
+#==============================================================================
+{
+    "Input:  \$n = $n".put;
+
+    my UInt @divisors = proper-divisors( $n );
+    my UInt $sum      = [+] @divisors;
+
+    if $sum <= $n                   # n is not an abundant number
+    {
+        'Output: 0'.put;
+         explain-failure-deficient( $n, @divisors, $sum )          if $VERBOSE;
+    }
+    else                            # n is an abundant number
+    {
+        my $subset = find-subset(  $n, @divisors);
+
+        if +$subset > 0             # n is a semiperfect number
+        {
+            'Output: 0'.put;
+             explain-failure-semi(  $n, @divisors, $sum, $subset ) if $VERBOSE;
+        }
+        else                        # n is not a semiperfect number
+        {
+            'Output: 1'.put;
+             explain-success(       $n, @divisors, $sum )          if $VERBOSE;
+        }
+    }
+}
+
+#------------------------------------------------------------------------------
+sub find-subset
+(
+            UInt:D  $n where * > 0,          #= A natural number
+    Array:D[UInt:D] $divisors                #= The proper divisors of n
+--> Array:D[UInt:D]                          #= A subset (if any) of the proper
+                                             #=   divisors that sums to n
+)
+#------------------------------------------------------------------------------
+{
+    my UInt @subset;
+
+    # start = 3: max proper divisor of n is n/2, next lower is < n/2, so sum of
+    #            any 2 divisors must be < n
+    # end:       sum of all divisors is known to be > n, so end is |n| - 1
+
+    L-OUTER:
+    for 3 ..^ +$divisors -> UInt $k
+    {
+        for $divisors.combinations: $k -> List $comb
+        {
+            my UInt $sum = [+] $comb;
+
+            if $sum == $n
+            {
+                @subset = @$comb;
+                last L-OUTER;
+            }
+        }
+    }
+
+    return @subset;
+}
+
+#------------------------------------------------------------------------------
+sub proper-divisors
+(
+    UInt:D $n where * > 0                    #= A natural number
+--> List:D[UInt:D]                           #= The proper divisors of n
+)
+#------------------------------------------------------------------------------
+{
+    my UInt @divisors;
+
+    for 1 .. ($n / 2).floor -> UInt $d
+    {
+        @divisors.push: $d if $n %% $d;
+    }
+
+    return @divisors;
+}
+
+#------------------------------------------------------------------------------
+sub explain-failure-deficient             # Not weird because not abundant
+(
+            UInt:D  $n where * > 0,          #= A natural number
+    Array:D[UInt:D] $divisors,               #= The proper divisors of n
+            UInt:D  $sum                     #= The sum of the proper divisors
+)
+#------------------------------------------------------------------------------
+{
+    ("\nExplanation:\nThe proper divisors of %d (%s) sum to %d," ~
+     "\ntherefore %d is not weird because it is not abundant\n").printf:
+      $n, $divisors.join( ', ' ), $sum, $n;
+}
+
+#------------------------------------------------------------------------------
+sub explain-failure-semi                  # Not weird: abundant but semiperfect
+(
+            UInt:D  $n where * > 0,          #= A natural number
+    Array:D[UInt:D] $divisors,               #= The proper divisors of n
+            UInt:D  $sum,                    #= The sum of the proper divisors
+    Array:D[UInt:D] $subset                  #= A subset of the proper divisors
+                                             #=   that sums to n
+)
+#------------------------------------------------------------------------------
+{
+    ("\nExplanation:\nThe proper divisors of %d (%s) sum to %d,"  ~
+     "\nbut the subset (%s) of these proper divisors sums to %d," ~
+     "\ntherefore %d is not weird because, although abundant, "   ~
+     "it is also semiperfect\n").printf:
+      $n, $divisors.join( ', ' ), $sum, $subset.join( ', ' ), $n, $n;
+}
+
+#------------------------------------------------------------------------------
+sub explain-success                       # Weird: abundant and not semiperfect
+(
+            UInt:D  $n where * > 0,          #= A natural number
+    Array:D[UInt:D] $divisors,               #= The proper divisors of n
+            UInt:D  $sum,                    #= The sum of the proper divisors
+)
+#------------------------------------------------------------------------------
+{
+    ("\nExplanation:\nThe proper divisors of %d (%s) sum to %d," ~
+     "\nand no subset of these proper divisors sums to %d,"      ~
+     "\ntherefore %d is weird because it is abundant but not "   ~
+     "semiperfect\n").printf: $n, $divisors.join( ', ' ), $sum, $n, $n;
+}
+
+#------------------------------------------------------------------------------
+sub USAGE()
+#------------------------------------------------------------------------------
+{
+    my Str $usage = $*USAGE;
+
+    $usage ~~ s/ ($*PROGRAM-NAME) /raku $0/;
+
+    $usage.put;
+}
+
+##############################################################################