Question

Кузнечик может прыгнуть вдоль координатного луча либо на 5 единиц вправо , либо на 3 единицы влево. Он начинает прыгать из начала координат, и хочет оказаться в точке с координатой 61. Какое наименьшее число прыжков ему понабиться сделать? Пожалуйста пишите ответ с решением.

Answer 1

14х5 вправо, окажется в точке 70 и 3х3 влево, окажемся в 61 (17 шагов)

Answer 2

Problem Analysis

A grasshopper can jump either 5 units to the right or 3 units to the left. The grasshopper starts at the origin (0) and wants to reach a point with a coordinate of 61. We need to determine the minimum number of jumps the grasshopper needs to make to reach this point.

Solution

To solve this problem, we can use a simple algorithm. We start at the origin (0) and keep track of the current position of the grasshopper. We continue jumping until we reach or pass the target coordinate of 61.

1. Initialize the current position of the grasshopper to 0. 2. Initialize a counter variable to keep track of the number of jumps made. 3. While the current position is less than the target coordinate (61): - If the current position plus 5 is less than or equal to the target coordinate, jump 5 units to the right and update the current position. - Otherwise, if the current position minus 3 is greater than or equal to the target coordinate, jump 3 units to the left and update the current position. - Increment the counter variable by 1. 4. Print the final value of the counter variable, which represents the minimum number of jumps required to reach the target coordinate.

Let's apply this algorithm step by step:

1. Initialize the current position to 0 and the counter variable to 0. 2. The current position is 0, which is less than the target coordinate of 61. 3. Since the current position plus 5 (0 + 5 = 5) is less than the target coordinate, we jump 5 units to the right and update the current position to 5. Increment the counter variable to 1. 4. The current position is now 5, which is still less than the target coordinate of 61. 5. Since the current position plus 5 (5 + 5 = 10) is less than the target coordinate, we jump 5 units to the right and update the current position to 10. Increment the counter variable to 2. 6. The current position is now 10, which is still less than the target coordinate of 61. 7. Since the current position plus 5 (10 + 5 = 15) is less than the target coordinate, we jump 5 units to the right and update the current position to 15. Increment the counter variable to 3. 8. The current position is now 15, which is still less than the target coordinate of 61. 9. Since the current position plus 5 (15 + 5 = 20) is less than the target coordinate, we jump 5 units to the right and update the current position to 20. Increment the counter variable to 4. 10. The current position is now 20, which is still less than the target coordinate of 61. 11. Since the current position plus 5 (20 + 5 = 25) is less than the target coordinate, we jump 5 units to the right and update the current position to 25. Increment the counter variable to 5. 12. The current position is now 25, which is still less than the target coordinate of 61. 13. Since the current position plus 5 (25 + 5 = 30) is less than the target coordinate, we jump 5 units to the right and update the current position to 30. Increment the counter variable to 6. 14. The current position is now 30, which is still less than the target coordinate of 61. 15. Since the current position plus 5 (30 + 5 = 35) is less than the target coordinate, we jump 5 units to the right and update the current position to 35. Increment the counter variable to 7. 16. The current position is now 35, which is still less than the target coordinate of 61. 17. Since the current position plus 5 (35 + 5 = 40) is less than the target coordinate, we jump 5 units to the right and update the current position to 40. Increment the counter variable to 8. 18. The current position is now 40, which is still less than the target coordinate of 61. 19. Since the current position plus 5 (40 + 5 = 45) is less than the target coordinate, we jump 5 units to the right and update the current position to 45. Increment the counter variable to 9. 20. The current position is now 45, which is still less than the target coordinate of 61. 21. Since the current position plus 5 (45 + 5 = 50) is less than the target coordinate, we jump 5 units to the right and update the current position to 50. Increment the counter variable to 10. 22. The current position is now 50, which is still less than the target coordinate of 61. 23. Since the current position plus 5 (50 + 5 = 55) is less than the target coordinate, we jump 5 units to the right and update the current position to 55. Increment the counter variable to 11. 24. The current position is now 55, which is still less than the target coordinate of 61. 25. Since the current position plus 5 (55 + 5 = 60) is less than the target coordinate, we jump 5 units to the right and update the current position to 60. Increment the counter variable to 12. 26. The current position is now 60, which is still less than the target coordinate of 61. 27. Since the current position plus 5 (60 + 5 = 65) is greater than the target coordinate, we cannot jump 5 units to the right. However, the current position minus 3 (60 - 3 = 57) is greater than or equal to the target coordinate. So, we jump 3 units to the left and update the current position to 57. Increment the counter variable to 13. 28. The current position is now 57, which is still less than the target coordinate of 61. 29. Since the current position plus 5 (57 + 5 = 62) is greater than the target coordinate, we cannot jump 5 units to the right. However, the current position minus 3 (57 - 3 = 54) is greater than or equal to the target coordinate. So, we jump 3 units to the left and update the current position to 54. Increment the counter variable to 14. 30. The current position is now 54, which is still less than the target coordinate of 61. 31. Since the current position plus 5 (54 + 5 = 59) is less than the target coordinate, we cannot jump 5 units to the right. However, the current position minus 3 (54 - 3 = 51) is greater than or equal to the target coordinate. So, we jump 3 units to the left and update the current position to 51. Increment the counter variable to 15. 32. The current position is now 51, which is still less than the target coordinate of 61. 33. Since the current position plus 5 (51 + 5 = 56) is less than the target coordinate, we cannot jump 5 units to the right. However, the current position minus 3 (51 - 3 = 48) is greater than or equal to the target coordinate. So, we jump 3 units to the left and update the current position to 48. Increment the counter variable to 16. 34. The current position is now 48, which is still less than the target coordinate of 61. 35. Since the current position plus 5 (48 + 5 = 53) is less than the target coordinate, we cannot jump 5 units to the right. However, the current position minus 3 (48 - 3 = 45) is greater than or equal to the target coordinate. So, we jump 3 units to the left and update the current position to 45. Increment the counter variable to 17. 36. The current position is now 45, which is still less than the target coordinate of 61. 37. Since the current position plus 5 (45 + 5 = 50) is less than the target coordinate, we cannot jump 5 units to the right. However, the current position minus 3 (45 - 3 = 42) is greater than or equal to the target coordinate. So, we jump 3 units to the left and update the current position to 42. Increment the counter variable to 18. 38. The current position is now 42, which is still less than the target coordinate of 61. 39. Since the current position plus 5 (42 + 5 = 47) is less than the target coordinate, we cannot jump 5 units to the right. However, the current position minus 3 (42 - 3 = 39) is greater than or equal to the target coordinate. So, we jump 3 units to the left and update the current position to 39. Increment the counter variable to 19. 40. The current position is now 39, which is still less than the target coordinate of 61. 41. Since the current position plus 5 (39 + 5 = 44) is less than the target coordinate, we cannot jump 5 units to the right. However, the current position minus 3 (39 - 3 = 36) is greater than or equal to the target coordinate. So, we jump 3 units to the left and update the current position to 36. Increment the counter variable to 20. 42. The current