Brevity is the soul of Wit

I'm trying to enter competitions. It is a challenge I'm setting myself that if I want to be successful as a writer I need to write. Many competitions out there aren't really competitions, but serve other useful purposes.
For example, competitions that offer a critique of your work if you pay a larger entrance fee are not really competitions. Although there is a prize, and at least having a chance to recoup the loss is probably worth the risk, these competitions are almost certainly a way for writing consultants and agents to drum up business.
So, what do I do instead?

Have you ever seen a competition for a 100-word story? There are a few. Jeffrey Archer ran such a competition last year, with much fanfare in the Daily Mail, as though this were somehow a new and striking idea from a great, British talent. These competitions have been around for some time in reality, and present a unique challenge to the writer.

Home Away from Home

A short story is the essence of an idea. It must be distilled to the core, presented in a way that allows the reader to feel the fulfilment of having read a complete story, without the extraneous details. Flash Fiction tests this ideal even futher, with a limit of 1000 words (or 500) in which to present, expound and realise a story. Now, think how hard it would be to do this in 100 words.
This is why I'm entering 100 words story competitions. I don't expect to win, but I want to distill my talent down to its core. Can I create a character in such a short frame? Can I make you, the reader, care about them? Can I make their fulfilment mean something to you, and their denouement matter in a handful of pocket-paragraphs?
And how far can or should I push this? Well, last week I entered a story competition. The prize is a simple one: a writing class with the company running the competition.
It is said that Ernest Hemingway was challenged to write a complete story in 10 words or less. He rather famously came up with this:

For Sale. Baby Shoes. Never Worn.

The pathos in this story is palpable. We have to only remember that Hemingway lived through the Great Depression to imagine that this may not only be a perfect story from a man famous for his succinct style, but it could also be a true story.
I read a few examples from previous iterations of the competition and convinced myself it was impossible. Then a thought hit me, and I had my story. I won't write it here (yet), for fear of prejudicing the competition, but once I had the thought, I only had to refine the cadence of the 10 words and my story was written.
Yes, I just used the word "cadence" to describe my writing. Yes, I am painfully aware of how conceited that sounds. Yes, it is the only word that describes what I'm trying to say.
I remember being told that writing involves getting words down on paper and then deleting half of them. As you can probably tell from this, I'm prone to verbosity, so entering these competitions gives me a chance to challenge my ability, evaluate my style and consider that the weight of every word is carried by the reader. My writing needs to be such that every word matters. If I'm filling up pages with redundancy, I'm not writing, I'm creating a word count. Does my story need to be over 120,000 words? Is it really just a short story? Does every paragraph serve to expose my character, my plot, my theme or my tone? If not, it needs to go. In these competitions, I've found a way to practice that. Every word, must move the story forward, or it must be excised.