According to George K. Zipf, more frequent words have more senses. We have tested this law using corpora and wordnets of English, Spanish, Portuguese, French, Polish, Japanese, Indonesian and Chinese. We have proved that the law works pretty well for all of these languages if we take - as Zipf did - mean values of meaning count and averaged ranks. On the other hand, the law disastrously fails in predicting the number of senses for a single lemma. We have also provided the evidence that slope coefficients of Zipfian log-log linear model may vary from language to language.