Problem:
A unit of blood expires after 10!=10⋅9⋅8⋯1 seconds. Yasin donates a unit of blood at noon on January 1. On what day does his unit of blood expire?
Answer Choices:
A. January 2
B. January 12
C. January 22
D. February 11
E. February 12
Solution:
Converting 10! seconds to days gives
60⋅60⋅2410!=60⋅120⋅1210⋅9⋅8⋅7⋅6⋅120=129⋅8⋅7=42
Because 30 days after January 1 is January 31, 42 days after January 1 is (E)February 12.
The problems on this page are the property of the MAA's American Mathematics Competitions