# Challenge 160 Task #1 - No way around four

## Task #1 - Four is magic

### Description

Submitted by: *Mohammad S Anwar*

You are given a positive number, `$n < 10`

.

Write a script to generate english text sequence starting with the English cardinal representation of the given number, the word ‘is’ and then the English cardinal representation of the count of characters that made up the first word, followed by a comma. Continue until you reach four.

Example 1:

```
Input: $n = 5
Output: Five is four, four is magic.
```

Example 2:

```
Input: $n = 7
Output: Seven is five, five is four, four is magic.
```

Example 3:

```
Input: $n = 6
Output: Six is three, three is five, five is four, four is magic.
```

### Solution

After a little break from the weekly challenges and only submitting just the code to my solutions in Challlenge-158, this week I’m back to blogging about it.

We can easily verify all numbers below ten will eventually end up at four when following the process described above.

There are two numbers in the set with four characters - the `5`

and the `9`

. So
they will immediately end up at `4`

in one step and be done. `3`

, `7`

and `8`

all have five characters. They will reach `4`

in two steps by going to `5`

first. Then there are three numbers with three characters left: `1`

, `2`

, and
`6`

. They take three steps `3 -> 5 -> 4`

. So for any number below ten we need a
maximum of three steps to reach `4`

. This will actually work for any number -
there is always fewer characters in a number’s cardinal representation than its
value.

My solution for this challenge expects a positive single digit number as its first argument.

This number will be passed to a `four_is_magic`

routine, which is a tiny wrapper
around the core logic in `_four_is_magic`

. The purpose of this wrapper is to
properly capitalize the resulting sentence.

The core of the solution is a mapping of the expected inputs to their English cardinal representations. This mapping is then used in a recursive process:

- If the input is 4 we are done and return ’four is magic.`
- Convert the input into its cardinal representation
- Take the length of the cardinal representation
- Convert the length into its cardinal representation
- Build the current part of the sentence from both cardinal representation
- Repeat with the length from step 3 and join everything together with a
`,`

**Code:**

```
sub run() {
my ($N) = @ARGV;
die "Expect a single digit positive number!\n" unless $N and $N =~ m/^\d$/;
say four_is_magic($N);
}
sub four_is_magic($n) {
ucfirst _four_is_magic($n);
}
sub _four_is_magic($n) {
my %cardinal_representations = (
1 => 'one',
2 => 'two',
3 => 'three',
4 => 'four',
5 => 'five',
6 => 'six',
7 => 'seven',
8 => 'eight',
9 => 'nine',
);
if ( $n == 4 ) {
return 'four is magic.';
}
my $cardinal = $cardinal_representations{$n};
my $length = length $cardinal;
return join( ', ',
join( ' ', $cardinal, 'is', $cardinal_representations{$length} ),
$length) );
_four_is_magic( }
```

**Output:**

```
One is three, three is five, five is four, four is magic.
Two is three, three is five, five is four, four is magic.
Three is five, five is four, four is magic.
Four is magic.
Five is four, four is magic.
Six is three, three is five, five is four, four is magic.
Seven is five, five is four, four is magic.
Eight is five, five is four, four is magic.
Nine is four, four is magic.
```

My native language being German I went ahead and gave it a try in German as
well. It seems there’s really no way around the four. There is just a
difference in the amount of steps required to reach `4`

. In German, we need an
average of `1.375`

steps for any of the other 8 numbers to reach 4 and `2.125`

steps in English.

```
Eins ist vier, vier ist magisch.
Zwei ist vier, vier ist magisch.
Drei ist vier, vier ist magisch.
Vier ist magisch.
Fünf ist vier, vier ist magisch.
Sechs ist fünf, fünf ist vier, vier ist magisch.
Sieben ist sechs, sechs ist fünf, fünf ist vier, vier ist magisch.
Acht ist vier, vier ist magisch.
Neun ist vier, vier ist magisch.
```

There is no comment section on this site. For questions, suggestions or errors in my post or solution, please create an issue over here or drop me a mail:

` ````
my $mail = join('@', 'pwc', join('.', 'pankoff', 'net'));
```