IMC 2009 Q14
14. Catherine's computer correctly calculates \(\dfrac{66^{66}}{2}\). What is the units digit of its answer?
- A 1
- B 2
- C 3
- D 6
- E 8
Intermediate Mathematical Challenge 2009, Question 14. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 8
If \(n\) is a positive integer then the units digit of 66\(n\) is 6. So when a power of 66 is divided by 2, the units digit of the quotient is either 3 or 8. Now 6666 is clearly a multiple of 4, so \(\tfrac{1}{2}\)(6666) is even and therefore has units digit 8 rather than 3.
Solution © UK Mathematics Trust, from the IMC 2009 solutions.