Carl computes the number

$$
N=5^{555}+6^{666}+7^{777}
$$

and writes it in decimal notation. What is the last digit of $N$ that Carl writes?
We look at the last digit of each term.

- The last digit of $5^{\bullet}$ is always 5 .
- The last digit of $6^{\bullet}$ is always 6 .
- The last digit of $7^{\bullet}$ cycles $7,9,3,1,7,9,3, \ldots$.

So the last digits are $5,6,7$ in that order. Since $5+6+7=18$, the answer is 8 .