I was curios about "карандаша"'s origins... Some further digging didn't let me disappointed.
Карандашей is pencils in the genitive case.
Source: http://www.alphadictionary.com/rusgrammar/genplur.html (#3, stem ends on hush (Ш))
This is absolutely inconsistent and should be fixed. It does not accept "A boy has no pencil" and "A boy does not have a pencil". It insists it must be "The boy does not have a pencil". There is no context enforcing "The" and it must accept negation of a noun (not only negation of a verb) - because it's grammatically correct and it accepts it in other exercises.