Track / Stage 4 / 308 of 340 #568 of 1964

Problem 568

AMC 12 late, AIME early

Combinatorics Difficulty 5.0 Find the answer

9) Antonio was born on the $1^{\circ}$ March of a year that had 53 Saturdays and 53 Sundays. On which day of the week was he born?

(A) Monday (B) Wednesday $(\mathbf{C})$ Friday

(D) on a different day from the above (E) it cannot be determined with certainty.

Your answer

Multiple choice: answer with the letter of the option you want.

Official solution

9) The answer is (B).

Indeed, the year Antonio was born was a leap year, as a non-leap year has 52 weeks plus one day, and therefore has only one day of the week that repeats 53 times. In a leap year, the days that repeat 53 times are necessarily the first and second day of the year. So January 1st was a Saturday, and counting that January had 31 days and February had 29, March 1st was a Wednesday.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.