There is a six-digit number, where each digit is either a 1, 2, or 3. If no two consecutive digits are 1, how many of these six-digit numbers are there?
Hint: Use complementary counting! What is the total number of possibilities – the ones that have two consecutive digits of one?
Hint 2: There are \(3^6=729\) total possibilities. What do you need to subtract?
Hope this helps!