5E. Stick Division

We can make at most $1$ cut. If we don't make any cuts, the sticks are $\{3, 4, 5\}$ and the difference between the longest and shortest piece is $5 - 3 = 2$. Even if we use our $1$ cut (for example, cutting the stick of length $5$ into $2$ and $3$), the new pieces would be $\{2, 3, 3, 4\}$, resulting in a difference of $4 - 2 = 2$. Thus, the minimum possible difference is $2$.

Since $k=0$, no cuts are allowed. We simply calculate the difference between the longest and shortest initial sticks, which is $10 - 2 = 8$.

All sticks are already the same length (all are $5$). Without making any cuts, the difference between the longest and shortest piece is $5 - 5 = 0$.

There is only one stick. We don't even need to use our available cut; since there is only a single piece, both the longest and shortest pieces are the exact same stick, making the difference $9 - 9 = 0$.

The initial lengths are $\{7, 8, 9\}$, giving an initial difference of $9 - 7 = 2$. Even with $2$ available cuts, there is no way to divide the sticks such that the difference between the maximum and minimum resulting pieces becomes strictly less than $2$. The minimum possible difference remains $2$.