Super computer
What is the units digit of the given expression?
Age
14 to 16
Challenge level
Problem
Catherine's computer correctly calculates $$\frac{66^{66}}{2}$$What is the units digit of the answer?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 8
$6^1 = 6$
$6^2 = 36$
$6^3 = 216$
$6^4 = ...6$ since the last digit comes from multipying the previous last digit by $6$
Last digit of $66^{66}$ is $6$
Divide by $2$: Last digit will be $3$ or $8$
$66^{66}$ will be a multiple of $ 4$ (because $66$ and $66^{65}$ are both even) so $66^{66}\div2$ is even so the last digit must be $8$, not $3$.