[Purdue-pm] Perl Weekly Challenge - 004

[Ward, Mark Daniel]

Dear Mark,

Many thanks for sharing!  These are interesting.

If you plan to share at large with the world, I see 3 tiny corrections 
to what you sent.

1.  In your email, you mentioned the link:

https://perlweeklychallenge.org/blog/perl-weekly-challenge-005/f

but I think the "f" at the end of the URL should be removed.

2.  In this pdf file:

https://engineering.purdue.edu/~mark/pwc-004.pdf

you have this formula for Pi:

$$\pi = 4\sum_{k >= 0} -1^{k}\frac{1}{2k+1}$$

but the $-1^{k}$ looks strange.  By order of operations, we should put 
$-1$ into parenthesis, so that it looks like this:

$$\pi = 4\sum_{k >= 0} (-1)^{k}\frac{1}{2k+1}$$

3.  In the summation of the formula above, the sum looks more natural if 
you write $\sum_{k=0}^{\infty}$ or if you write $\sum_{k\geq 0}$.  
Either way would look better than $\sum_{k >= 0}$.  Just FYI.

I hope that those are helpful early-morning comments!

Again, thank you very much for sharing..... just wanted you to know that 
we are reading what you are sending!

Best wishes,

Mark


On 4/22/19 1:14 AM, Mark Senn wrote:
> (See my blog entry at
>      https://engineering.purdue.edu/~mark/pwc-004.pdf
> for the details of the following challenges.)
>
>
> Challenge #1:
> Write a script to output the same number of PI digits as the size of
> your script.  Say, if your script size is 10, it should print
> 3.141592653.
>
> Perl 6 Solution Highlights:
> Find a rapidly converging series for pi and use FatRat (fat rationals)
> for "infinite precision integer fractions".  I checked my code was
> working by comparing it with the first 1000 digits of pi that
> the Wolfram Language (Mathematica) uses.
>
>
> Challenge #2
> You are given a file containing a list of words (case insensitive 1 word
> per line) and a list of letters.  Print each word from the file than can
> be made using only letters from the list.  You can use each letter only
> once (though there can be duplicates and you can use each of them once),
> you don't have to use all the letters. (Disclaimer: The challenge was
> proposed by Scimon Proctor).
>
> Perl 6 Solution Highlights:
> Use the Perl 6 bag data structure.  A bag is a set of which elements
> occur and how many times they occur.  There is a commplete set of
> bag operators.  "$word (<=) $letters" is true if all elements,
> including counts, of word are in letters.
>
>
> Next week's challenges are at
>      https://perlweeklychallenge.org/blog/perl-weekly-challenge-005/f
> I find these to be good exercises.
>
> -mark
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