https://cs.stackexchange.com/a/139329/114966
Seems like lists and equations are not friendly with each other.
https://cs.stackexchange.com/a/139329/114966
Seems like lists and equations are not friendly with each other.
I seem to have fixed it, now all the indentations are in line and they all say N.
rather than N)
:
\begin{align} v_1 + v_2 + v_3 \qquad = 1\\ \qquad v_2 + v_3 + v_4 = 1\\ v_1 \qquad + v_3 + v_4 = 1\\ v_1 + v_2 \qquad + v_4 = 1\\ \end{align} It's easy to check that $v_1=v_2=v_3=v_4=\frac 13$ is the unique solution.
Consider $v_5 + v_6 + v_7 + v_8 + 0 \cdot v_9 = 1$ and, similarly to the above case, all cyclic shifts of $(v_5, \ldots, v_9)$. Again, the unique solution is $v_5 = v_6 = v_7 = v_8 = v_9 = \frac 14$.
The last equation is $$v_1 + v_2 \qquad + v_5 \qquad + v_{10} = 1$$ Then $v_{10} = 1 - 2 \cdot \frac 13 - \frac 14 = \frac 1 {12}$.