'''There's a difference between: adding an <math>n^{th}</math> unknown digit after n-1 known digits, and adding n-2 unknown digits before one known digit in the <math>n-1</math> possition.
'''We apply the first one when expressing f(n)- that is, if the n-1 positions are know and the n-1 position is odd, then indeed you have 10 ways to fill the <math>n^{th}</math> position.
adding the <math>n^{th}</math> digit '''after''' n-1 digits (that is, '''you know We apply the first n-1''' digits, and the '''second one when expressing <math>nf^{th(odd)}</math> is unknown''')י, and adding n-2 digits '''before''' the <math>n-1</math> digit (that is, '''you only know the <math>n-1)</math> position''', and the '''previous <math>n-2</math> digits are unknown''')י. In the first case, if the n-1 position that is odd then indeed you have 10 ways to feel the '''<math>n^{th}</math> position'''. In the second case, if the n-1 position is known and odd then you have f(n-2) ways of feeling fill in the '''n-2 previous positions'''.
'''Adi