Tessellate S.T.E.M.S. (2019) - Computer Science - School - Set 2 - Objective Problem 2

For brevity, I will write $\oplus$ for the bitwise XOR.

Note that for any natural $k,$ $(4k) \oplus (4k+1) \oplus (4k+2) \oplus (4k+3) = 0$ and that $10^{100}$ and $10^{1000}$ are integral multiples of $4,$ so $\begin{aligned} \bigoplus_{n=10^{100}}^{10^{1000}} n &= 10^{1000} \oplus \bigoplus_{k=\frac{10^{100}}{4}}^{\frac{10^{1000}}{4}-1} \left((4k) \oplus (4k+1) \oplus (4k+2) \oplus (4k+3)\right) \\ &= 10^{1000} \oplus \bigoplus_{k=\frac{10^{100}}{4}}^{\frac{10^{1000}}{4}-1} 0 \\ &= \boxed{10^{1000}} \end{aligned}$