Question 159
Let $n$ three-digit numbers satisfy the following properties:
(1) No number contains the digit $0$.
(2) The sum of the digits of each number is $9$.
(3) The units digits of any two numbers are different.
(4) The tens digits of any two numbers are different.
(5) The hundreds digits of any two numbers are different.
Find the largest possible value of $n$.
(1) No number contains the digit $0$.
(2) The sum of the digits of each number is $9$.
(3) The units digits of any two numbers are different.
(4) The tens digits of any two numbers are different.
(5) The hundreds digits of any two numbers are different.
Find the largest possible value of $n$.