5. What is the minimum number of chips that need to be taken so that in any arrangement of them on the cells of a chessboard, there would necessarily be 4 chips standing in a row horizontally?
Solution. Consider one row. To ensure that there are 4 chips in it, there must be no less than 7 chips (6 chips can be placed in two groups of 3 chips). If there are a total of $6 \cdot 8+1=49$ chips, then by the pigeonhole principle, there will definitely be a row with no fewer than 7 chips. On the other hand, it is impossible to get by with fewer chips: 48 chips can be placed in groups of 6 in each row so that the condition is not met. Answer: 49.

Comment. Only the correct answer - 1 point. It is shown that 49 chips are always sufficient - no less than 4 points.