Word capitalization with Haskell

We have this problem, given a string of words, capitalize just the first letter, but the main trouble here is the lack of a common pattern to distinguish between one and another, for example:

"helloanyonethere" -> "HelloAnyoneThere"
"himartin" -> "HiMartin"
"hellorange" -> "HelloRange"
"thereach" -> "TheReach"

Well, the trouble can be addressed using Haskell, list and the always opportune recursion. The input information would be a dictionary that contains all possible words and the string to analyze; the output should be an string with the capitalized letters.

Pentagonal Numbers in Haskell

As part of my refresh on algorithms, data structures and programming, I found this interesting mathematic problem:

Pentagonal numbers are generated by the formula, P_n=n(3n1)/2. The first ten pentagonal numbers are:

1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...

It can be seen that P₄ + P₇ = 22 + 70 = 92 = P₈. However, their difference, 70  22 = 48, is not pentagonal.

Find the pair of pentagonal numbers, P_j and P_k, for which their sum and difference are pentagonal and D = |P_k  P_j| is minimised; what is the value of D?

Then, I decided to elaborate a program in Haskell that would find the number D. Of course, you can find the code in Github.

Unbalanced Balances...

Once again, I found a challenge in a very common webpage that said the following:

You have a room-full of balances and weights. Each balance weighs ten pounds and is considered perfectly balanced when the sum of weights on its left and right sides are exactly the same. You have placed some weights on some of the balances, and you have placed some of the balances on other balances. Given a description of how the balances are arranged and how much additional weight is on each balance, determine how to add weight to the balances so that they are all perfectly balanced.

There may be more than one way to balance everything, but always choose the way that places additional weight on the lowest balances.

The input file will begin with a single integer, N, specifying how many balances there are.
Balance 0 is specified by lines 1 and 2, balance 1 is specified by lines 3 and 4, etc...
Each pair of lines is formatted as follows:

WL &lt balances &gt
WR &lt balances &gt

WL and WR indicate the weight added to the left and right sides, respectively. &lt balances &gt is a space-delimited list of the other balance that are on that side of this balance. &lt balances &gt may contain zero or more elements.

First Haskell Published Program: Arithmetic Progression

I find Haskell a challenging language, one that let you express yourself in different ways as procedural or object oriented programming allows you to do it. I knew about it quite a few months ago, but I have never had the time to concentrate to develop any example using it. As I found in the Facebook challenge example, I considered was a good opportunity to create a program with the current knowledge of Haskell (minimal) and still learn a lot using what I take for granted in other languages (C++ or Objective C).

At first, it is really a change of paradigm to start thinking about functions instead of variables that you declare at the beginning and use them as the program executes. Here those do not exist in the same way, as it does for loops (while or for) and the list are fundamental for data manipulation, you will notice my tries to force the language to behave as a procedural language, which I am aware it is not the best practice, but for the first steps I consider it is ok.

The statement of the test is the following: