SOLUTION: Determine the ONES digit of 23 to the power 85

The ones digits of consecutive powers of the number 23 form this sequence


n                1    2    3    4    5    6    7    8    9    10

The last digit   3    9    7    1    3    9    7    1    3     9



The sequence of the last digits is periodical.  The period starts from n = 1  and has the length of 4.


85 = 4*21 + 1.


Therefore, the last digit of the number    is equal to 1 :  the first number of the period.    ANSWER