В коробке лежат n шариков трёх цветов: красного, синего и зелёного. Если достать из неё любые 61 шарик, то среди них обязательно окажется по крайней мере 15 синих и хотя бы по 7 красных и зелёных. При каком наибольшем n такое возможно?
Is the phrase "любые шестьдесят один шарик" an example of good Russian, i.e. is it correct grammatically? If somehow it's wrong, then how would you change it in order to make it right (and preserve the original meaning)?
I would say that the phrase indeed sounds rather clumsy. However, this is mathematics. In mathematics, precision and unambiguity are preferred over grammatical correctness and fluency. In any language, mathematical jargon often sounds clumsy and difficult to understand (as well as legalese and any other jargon that attempts to achieve exactness and precision). So there is no better way to phrase it.
Also I'll point out that your example written word for word. Ideally, 61 should be written as a numeral, not spelled out. This will make it look better, plus, realistically, you don't often read mathematical problems aloud.
