This is a question I saw and solved a long time ago, it involves some maths.
There is a keypad
1 2 3
4 5 6
7 8 9
A certain password starts with a 3. Each digit is adjacent (horizontally or vertically) on the keypad to either of the previous two digits of the password. The password length is 10. How many possibilities are there?
For example, 1247879685 is valid but 1234565985 is not (4 is not adjacent to 2 or 3).
Although a complicated combinatorics solution or a program would also work, I'm looking for one that any common person can understand.