2021 JMC 10 Problems/Problem 4
Problem
A day in the format is called binary if all of the digits are either
s or
s with leading zeros allowed. How many days in a year are binary?
Solution
The month and date
cannot be of the form
. Each digit
and
can be either
or
but we must subtract the undesired case of
So,
only has
possibilities, and
also has
possibilities. In total, there are
binary days in a year.