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MathNet 2019-part-02 — 184 problems (EN–VI) Question 23

Math Olympiad Vault · MathNet 2019-part-02 — 184 problems (EN–VI)

Question 23

In the Jovian Calendar, the months are Julius, Uranius, Plutônius, Ílius, Terrius, Eráclitus and Raley. The months that begin with consonants have 17 days and the months that begin with vowels have 19 days. The year begins in Julius and follows the sequence above, ending in Raley. As in our calendar, the Jovian calendar has a week of 7 days (Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday). Diógenes, a Jovian boy, was born on 11 Plutônius 1999, which was a Sunday.

a) On what day will Diógenes complete 100 days of life?

b) On what day of the week will Diógenes turn 20 years old?