Problem 2

Each letter represents a non-zero digit. What is the value of t?

$\begin{array}{|rrcll|} \hline (1): & c+o-u &=& 0\\ (2): & u+n-t &=& 0\\ (3): & t+c-s &=& 0\\ \hline (1)+(2)-(3): & ( c+o-u ) + ( u+n-t ) - ( t+c-s ) &=& 0+0 -0 \\ & \not \! c +o~ - \not \! u + \not \! u+n-t - t~ - \not \!c+s &=& 0 \\ & o +n+s -2t &=& 0 \\ & o +n+s &=& 2t \\ & 2t &=& o +n+s \quad | \quad o +n+s = 12 \\ & 2t &=& 12 \quad | \quad : 2 \\ & \mathbf{t} & \mathbf{=} & \mathbf{6} \\ \hline \end{array}$