Hi,
For the first one (the grid), you want to find the lower right-hand square, so try to focus on the right column first. For example, what about the upper-right hand (top right) square? What numbers is it already in a row with? What number is already in it's column? There is actually only one number left for it to be!
The other word problem is a little tricky. Suppose there are $N$ students. Consider what each arrangement of the students tells us about $N$.
- If the students are standing in rows of $15$, we definitely know that $15$ is a factor of $N$.
- One long row doesn't tell us much, but we can think of as $N$ is a factor of $N$.
- Rows of one student each can be thought of as saying $1$ is a factor of $N$.
- Rows of $6$ students in each row says $6$ is a factor of $N$.
So far, we know that $6$ and $15$ are factors of $N$, so $N$ is divisible by $2$, $3$, and $5$. The actual key piece of information is that after June 12th there are NO new ways the students can stand in a row. How many factors does $N$ need to have?
Hope this helps!