Grid shading that forces a crowded row

A grid of white unit squares has $r$ rows and $c$ columns. In every column exactly $s$ squares are coloured black. Find the smallest $c$, as a function $f(r,t,s)$, that guarantees some row contains at least $t$ black squares, and evaluate $f(30,21,14)$.

43. If every row had at most $t-1$ black squares the total would be at most $r(t-1)$, while the total is $cs$; and a cyclic shading spreads squares evenly so that $cs\le r(t-1)$ is achievable. Hence $f=\lfloor r(t-1)/s\rfloor+1=\lfloor 600/14\rfloor+1=43$.