For (2), you can say "we competed against **the** children from other schools in the same town", or you can remove **the**. Either way it is understandable and the meaning doesn't change. But for (1) you need the article. Otherwise it sounds weird. Although, you could also say "There I had the chance to hone my skills against older pupils." (removing "some of the") Надеюсь, это не вызовет путаницы! Xaxaxa.

If the noun is singular, you must use an article. If the noun is plural or noncountable, the rules are more complicated. Generally, we do not use an article with plurals and noncountables unless they are specific (the). There are also a long list of rules for using "the", for example with general categories of things like "The elephant is the largest land mammal." Or unique things like the planets, the stars, the atmosphere, etc. CORRECTIONS: - ... to hone my skills against some of (1) THE older pupils ... we competed against (2) the children from other schools in the same town. Here, the rule is similar to using "the" with the superlative because you are talking about one or some out of the entire group. THE strongest man in the world, some of THE older pupils, one of THE best people I know. "The" is appropriate in sentence (2) because you are referring to specific children.