Sherlock Holmes again!
(Ichi wo kiite juu wo shiru; “Hearing one; knowing ten”)
Having great powers of reasoning and understanding. Learning one part and understanding the whole. Hearing just a little bit about something is enough for the person so described to realize quite a bit more. “A word to the wise is sufficient.”
This sentence comprises a pair of parallel verb phrases in sequence. Each has a number (grammatically, a noun) and a verb, and connects them with the particle を (wo), marking the number as the object of the verb. In the first phrase, the noun is 一 (ichi), “one,” and in the second, it’s 十 (juu), “ten.” What one does to “one” is 聞く (kiku); “to hear,” in conjunctive form. What one does to “ten” is 知る (shiru), “to learn about,” “to be(come) aware of,” “to know,” etc.
Some versions of this kotowaza replace 知る with 悟る (satoru), a related term with connotations of Buddhist enlightenment. Others attach the counter 事 (koto), “(abstract) thing,” to the lone numbers 一 and 十 and make 一事 and 十事.
This saying comes from the Analects of Confucius. It’s based on a longer passage in which Zi Gong is questioned and praises fellow disciple Yan Hui (apparently considered Confucius’ favorite and best disciple), saying “He hears one thing and understands ten, while I hear one thing and only understand two.” It is included in the Osaka iroha karuta set.
(Ichi wo kiite juu wo shiru kurai ni rikairyoku ga aru senpai ni akogarete, mainichi benkyou ni kotsukotsu hagemu koto wo ketsui shita Jirou de atta.)
[Wanting to be like his senior, whose powers of reasoning allowed him to take one fact and deduce ten others, Jirou resolved to study hard every day.]