4. Two very small fleas are jumping on a large sheet of paper. The first jump of the fleas is along a straight line towards each other (their jumps may have different lengths). The first flea first jumps to the right, then up, then to the left, then down, then to the right again, and so on. Each jump is 1 cm longer than the previous one. The second flea first jumps to the left, then up, then to the right, then down, then to the left again, and so on. Each subsequent jump is also 1 cm longer than the previous one. After 100 jumps, the fleas are 3 meters apart. How far apart were the fleas initially?
4. Answer: 2 meters. Solution: Let's observe the first four jumps of the first flea: 2 cm more to the left than to the right, and 2 cm more down than up. That is, after four jumps, the first flea moves 2 cm to the left and 2 cm down. Therefore, after 100 jumps, it will move 50 cm to the left and 50 cm down. Similarly, the second flea will move 50 cm to the right and 50 cm down after 100 jumps. Since both fleas have moved down the same amount, the distance between them has increased by $50 \mathrm{~cm} + 50 \mathrm{~cm} = 100 \mathrm{~cm} = 1$ m. Therefore, the initial distance between them was 2 m. Criteria: correct solution - 7 points. Correct reasoning but with an arithmetic error - 5 points. Correct conclusion about the change in position of the flea after a series of four jumps, but no further progress - 2 points. In all other cases, 0 points.