Jordan dropped their phone, and now the touchscreen is badly damaged. The left and centre columns of the number pad are completely unresponsive. Only the right-hand column, containing the digits \(3\), \(6\), and \(9\), is still functioning. Jordan wants to set a new \(4\)-digit lock screen PIN using only the working numbers. Jordan sets two rules for the PIN:
A single digit can occur at most three times in the PIN (for example, \(9999\) is not allowed).
The \(4\)-digit PIN must be divisible by \(9\).
How many different \(4\)-digit PINs can Jordan create?
Did You Know?
If the sum of the digits of a number is divisible by \(9\), then the number is divisible by \(9\). If the sum of the digits of a number is not divisible by \(9\), then the number is not divisible by \(9\).
For example, the number \(10\,278\) is divisible by \(9\) since the sum of the digits is \(1+0+2+7+8= 18\), which is divisible by \(9\). However, since the sum of the digits of the number \(12\,345\) is \(15\) and \(15\) is not divisible by \(9\), then the number \(12\,345\) is not divisible by \(9\).