What is the remainder when the sum $1^2 + 2^2 + 3^2 + \dots + 10^2$ is divided by 11?
I recall that there is a formula for the sum of the first n squares, which is $\frac{n(n+1)(2n+1)}{6}$. I wonder if I can use this formula to simplify the calculation of the sum. I plug in n = 10 into the formula and get $\frac{10(11)(21)}{6}$. This simplifies to $385$. Now I need to find the remainder when I divide $385$ by $11$. I could try to do long division, but I also notice that $385 = 11 \times 35 + 0$. This means that the remainder is $0$, and I don't need to do any more calculations. 