4. What is the minimum number of stars we must draw in a $4 \times 4$ table so that after erasing any 2 columns and any 2 rows, at least 1 star remains in the table?

Solve the problems independently. You have $3 \frac{1}{2} \mathrm{~h}$ for solving.

The use of notes, literature, or a pocket calculator is not allowed.

46th Mathematical Competition

for high school students in Slovenia

Škofja Loka, April 20, 2002

## PROBLEMS FOR 2nd GRADE
I/4. The image shows that 7 stars suffice. Let's prove that 6 stars do not suffice. In this case, at least in 2 columns there is at most 1 star. If we delete the remaining 2 columns, only 2 stars will be left, which we can delete by emptying the rows in which they lie.

![](https://cdn.mathpix.com/cropped/2024_06_07_e98280e53ded58fe5f86g-6.jpg?height=211&width=214&top_left_y=2096&top_left_x=1663)