combination lock has a numeric keypad with $\{1,2,3,4,5\}$ keys on it$.$ It unlocks when a certain code $($i$.$e$.,$

sequence of digits$)$ is applied to it by pressing the keys on the keypad. The unlocking mechanism reads the input

digits and accepts the input sequence of digits when the last $4$ pressed keys match some predefined pattern. In

this question, the lock opens when the last $4$ digits of input sequences match one of the two patterns in $\{1121,$

$2112\}.$