On the planet Euclid, there are 10 days in each month and 18 months in each year. Once every seven years, however, there is a leap year and one day is added to the third month. Each week contains five days which are (in order) ArchimedesDay, BernoulliDay, CavalieriDay, DesCartesDay, and EulerDay.

Question

On the planet Euclid, there are 10 days in each month and 18 months in each year.  Once every seven years, however, there is a leap year and one day is added to the third month.  Each week contains five days which are (in order) ArchimedesDay, BernoulliDay, CavalieriDay, DesCartesDay, and EulerDay.

Fermet was born on a DescartesDay on the first day of the fourth month in a leap year.  On what day of the week will Fermet’s 25th birthday fall?

oobleck · Answer

The year's length is a multiple of 5 days, so the day of the week will advance by one every 7 years.
25 years is 7*3 + 4, so he will have lived through 3 leap years.
That means that in years 21-27 his birthday will be on Dday+3=Bday (4+3 mod 5)