*This post is part of a series on Mohammad Anwar’s excellent Perl Weekly Challenge, where Perl and Raku hackers submit solutions to two different challenges every week. (It’s a lot of fun, if you’re into that sort of thing.)*

Task #2 this week is described as follows:

*You are given a list, @L, of three or more random integers between 1 and 50. A Noble Integer is an integer N in @L, such that there are exactly N integers greater than N in @L. Output any Noble Integer found in @L, or an empty list if none were found.*

*An interesting question is whether or not there can be multiple Noble Integers in a list.*

*For example,* s*uppose we have list of 4 integers [2, 6, 1, 3].*

*Here we have 2 in the above list, known as Noble Integer, since there are exactly 2 integers in the list i.e. 3 and 6, which are greater than 2.*

*Therefore the script would print 2.*

While Mohammad gave me credit for submitting this problem, I only suggested some wording changes right before it was published, so I didn’t have any sort of advantage going in.

The algorithm I came up with for finding Noble Integers is fairly simple and seems obvious: simply sort the array, and then for each array index, `$i`

, `@L.end - $i`

is the number of elements that come after. `@L.end`

in Raku is `$#L`

in Perl: the last index in the array.

To find a Noble Integer then, we just need to know if `@L[$i] == @L.end - $i`

.

## Perl

```
my @L = sort { $a <=> $b } @_;
map { $L[$_] == $#L - $_ ? $L[$_] : () } 0..$#L;
```

I’m using `map`

instead of `grep`

because I’m looping over the indicies, but I want the value as the result. Another option is to use `map { $L[$_] } grep { ... } 0..$#L`

:

```
my @L = sort { $a <=> $b } @_;
map { $L[$_] } grep { $L[$_] == $#L - $_ } 0..$#L;
```

That’s probably just a bit clearer. Not a huge difference, in my opinion.

## Raku

```
@L.sort.pairs.grep({ @L.end - .key == .value })».value;
```

What else do you need! `pairs`

is nice. To be fair, Perl does have `each`

, which I did use in an earlier iteration, but it is more cumbersome to use in cases like this.

## There can be only one

The question of whether there can be more than one Noble Integer in a given list seems easy to answer: **no.**

Need more convincing? Here’s a quick and very informal proof by contradiction:

Hypothesis: there can be more than one Noble Integer in a list. Sort the list. Let *n* be a Noble Integer in list *L, *and suppose it is the smallest Noble Integer in the list. By definition, there are *n* more integers in the list after *L.*

Let *x* be a Noble Integer in *L,* greater than *n*. For *x* to exist, there would have to be at least *n* + 1 integers greater than *x.* Since the list is sorted, and *x* > *n,* there is no way we could have *n* + 1 integers greater than *x,* as that would mean there would be at least *n *+ 2 integers greater than *n,* meaning *n* would not be a Noble Integer. Contradiction. Therefore, we reject our original hypothesis, meaning it is impossible for there to be more than one Noble Integer in a list.