5) Simone writes the number 3 on the blackboard, then erases it and replaces it with its square, 9, then erases the 9 and replaces it with its square, 81. She repeats this operation a total of 2006 times: each time she replaces the written number with its square. What is the unit digit of the last number written?
(A) 1 ,
(B) $3, \quad$ (C) 5 ,
(D) $7, \quad$ (E) 9 .
5. The answer is (A).

The first three terms of the sequence being constructed are 3, 9, 81. We have reached a term whose units digit is 1, so every time we replace the number with its square, the units digit will not change anymore: $1 \times 1=1$. All terms from the third onward will have 1 as the units digit.