A number is said to be made up of non-decreasing digits if all the digits to the left of any digit is less than or equal to that digit.
For example, the four-digit number $1234$ is composed of digits that are non-decreasing. Some other four-digit numbers that are composed of non-decreasing digits are $0011$, $1111$, $1112$, $1122$, $2223$.
Notice that leading zeroes are required: $0000$, $0001$, $0002$ are all valid four-digit numbers with non-decreasing digits.
The question is
How many four-digit numbers are non-decreasing?