Question

Кузнечик-информатик прыгает вдоль числовой оси. Пока он маленький, он умеет прыгать только вперед на 4 единицы, либо назад на 3. Совершив некоторое количество прыжков, кузнечик понял, что находится на расстоянии не более чем 5 единиц от начала пути. Тут кузнечик вспомнил, что количество разных прыжков отличалось на 3, и каких-то из них было 5. Если кузнечик начал движение в точке с координатами 20, то где он его закончил?

Answer 1

20
-4-3+5-3+5=20
проверьте еще у кого нибудь

Answer 2

Problem Analysis

The problem states that a computerized grasshopper is jumping along a number line. It can jump forward by 4 units or backward by 3 units. The grasshopper realizes that it is within a distance of 5 units from the starting point. Additionally, the grasshopper remembers that the number of different jumps it made differed by 3, and some of them occurred 5 times. The grasshopper started its movement at point 20, and we need to determine where it ended up.

Solution

To solve this problem, we need to analyze the given information and determine the possible positions where the grasshopper could have ended up.

Let's start by considering the possible jumps the grasshopper can make. It can either jump forward by 4 units or backward by 3 units. We can represent these jumps as positive and negative numbers, respectively.

Based on the given information, we know that the grasshopper made a certain number of jumps, and the number of different jumps differed by 3, with some of them occurring 5 times. This means that the grasshopper made a total of 8 jumps (5 + 3) and that there are 5 jumps of one type and 3 jumps of the other type.

To determine the possible positions where the grasshopper could have ended up, we can consider the different combinations of jumps it made. Let's analyze each case:

1. If the grasshopper made 5 jumps forward (4 units each) and 3 jumps backward (3 units each), the total distance covered would be: - (5 * 4) - (3 * 3) = 20 - 9 = 11 units

2. If the grasshopper made 5 jumps backward (3 units each) and 3 jumps forward (4 units each), the total distance covered would be: - (3 * 3) - (5 * 4) = 9 - 20 = -11 units

Since the grasshopper started at point 20 and the maximum distance it can cover is 5 units, it is not possible for the grasshopper to end up at a position that is 11 units away from the starting point. Therefore, the grasshopper cannot end up at a position that is 11 units away from 20.

Based on this analysis, we can conclude that the grasshopper must have made 5 jumps forward and 3 jumps backward. Therefore, the total distance covered is 11 units in the positive direction. Adding this distance to the starting point of 20, we can determine the final position of the grasshopper:

The grasshopper ends up at position 31 on the number line.

Conclusion

The grasshopper, which started at position 20 on the number line, made 5 jumps forward (4 units each) and 3 jumps backward (3 units each). As a result, it ended up at position 31.