my @ordered_result_list = sort keys %results;
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That's wrong. You're sorting lexically, so 10 comes before 9.

print sort 1..10;  # 1 10 2 3 4 5 6 7 8 9
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The above is equivalent to

print sort { $a cmp $b } 1..10;  # 1 10 2 3 4 5 6 7 8 9
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You want to sort numerically.

print sort { $a <=> $b } 1..10;  # 1 2 3 4 5 6 7 8 9 10
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Of course, there's no reason to sort the result if you just want the highest.

use List::Util qw( max );

print max 1..10;  # 10
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---

my %results = map { $_ => 1 if ( $low_watermark < $_ && $_ < $high_wat
+ermark ) } @all_numbers;
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That's wrong. You're incorrectly assuming the expression in the map returns nothing when the condition is false.

$ perl -wle'my %h = map { $_ => 1 if $_ > 5; } 1..3; print 0+keys(%h);
+'
Odd number of elements in hash assignment at -e line 1.
1
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You wanted:

my %results = map { if ( $low_watermark < $_ && $_ < $high_watermark )
+ { $_ => 1 } else { () } } @all_numbers;
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Or:

my %results = map { ( $low_watermark < $_ && $_ < $high_watermark ) ? 
+$_ => 1 : () } @all_numbers;
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But why is a hash involved at all?

my @results = grep { $low_watermark < $_ && $_ < $high_watermark } @al
+l_numbers;

print max(@results), "\n";
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