information, I = k ln (n_before / n_after), where k = 1/ln(2) to give answer in bits.
n_before:= total number of possible states before message is received (108 possible states per key)
n_after:= total number of possible states after message received ( in this case 1, since once you press a key you get 1 response)
So I per key = ln(n_before / n_after )
= 1/ln(2) (108 / 1) = 6.8bits / key
if n_before is 16
= 1/ln(2) (16/1) = 4 bits / key