As a matter of fact, it already exists: http://www.kittysplit.com/ This is a free webapp developed by some people I know. Also, probably prior art or something.

So only 1/3 of fourth graders were able to find the experimental setup to find the best fertilizer level out of nine, when you are only allowed to try six out of them.

The correct strategy consists in going in two steps, first trying out interspaced levels e.g. 2-4-6-8 then "refining" with the two remaining tries around the approximate minimum. This necessitates to model implicitly/intuitively the plant growth as a unimodal (increasing, then decreasing) function of the fertilizer level, thinking ahead with the limited tries constraint, and mentally planning different outcomes of the two steps.

I'd go contrary to the flow and say that 33% of 4rth graders solving an assignment of this difficulty is pretty darn awesome.

There is a difference between randomly sprinkling a paper with references in a superficial effort to make it look "serious" and conform to the usual academic mold; and actively researching, citing and discussing earlier relevant references in comparison to your own work in a balanced way. The latter is how good quality academic writing should be done. The former tends to give rise to papers with pointless laundry lists of citations. I hope your friends were suggesting the latter way. Even if they were not able to point to specific references because they are not specialists of the issue you are addressing, they probably know by experience that it is quite unusual that no previous relevant references exist on a given academic issue. The fact is, nothing annoys a reviewer or an editor more than someone reinventing the wheel and giving the impression of ignoring previous work out of intellectual laziness.

Where there is a clear problem is when an editor or reviewers imposes an obviously irrelevant citation for self-serving reasons.

I found the most fascinating part of TFA to be a link to a post by the Nexicon CTO himself in the comments of the initial article. It's 500 words of frantic, badly spelled gibberish whithout a single grammatically correct sentence and devoid of any substantial argument. You can literally see the poor man going litteraly nuts with rage while the sky is falling on his head.

Try it, it'll do you good. Seriously, I had not experienced such a powerful rush of pure, unaltered, sweet schadenfreude on the internets for a long time.