# ETOOBUSY đźš€ minimal blogging for the impatient

# Count Possible Paths

**TL;DR**

What TASK #2 from the Perl Weekly Challenge #117 could (wellâ€¦ SHOULD) have beenâ€¦

Fellow participants to the Perl Weekly Challenge, I have discovered a shocking secret.

We were all tricked. By none other thanâ€¦ well, *you know*.

Conspiracy theory circles knew this since ages: the Find Possible
Paths challenge was supposed to require us *count* how many
different ways to go from the top to the bottom-right, not to
*enumerate* them! Alas, nobody listened to them.

I guess that, were the original challenge published instead:

- I would have lost the occasion to inflict to my blogâ€™s readers a very long post on the solution, namely PWC117 - Find Possible Paths. You canâ€™t reclaim your time back now!
- Most would have probably run into the SchrĂ¶der number and taken advantage of the Recurrence relation (thanks to Some explicit and recursive formulas of the large and little SchrĂ¶der numbers):

This can be (*could have been?*) coded in Raku like this:

```
#!/usr/bin/env raku
use v6;
sub sn (Int:D $N where * > 0) {
state $sns = [1, 2];
while $N > $sns.end {
my $n = $sns.elems;
$sns.push: [+] 3 * $sns[*-1],
(1 .. $n - 2).map({$sns[$_] * $sns[$n - $_ - 1]}).Slip;
}
return $sns[$N];
}
put $_, ' -> ', sn($_) for 1 .. 20;
```

I start to get the gist of itâ€¦ *except* for `flat`

and when to use
`Slip`

, which still trick me almost every time đź™„

Wellâ€¦ there we are at the end. **Now you know!**

*Comments? Octodon, Twitter, GitHub, Reddit, or drop me a line!*