Statistics

Problem Statement

Definition

Class:

TheEquation

Method:

leastSum

Parameters:

int, int, int

Returns:

int

Method signature:

int leastSum(int X, int Y, int P)

(be sure your method is public)

Notes

• The answer is never greater than 2*P: if a = P and b = P, then P is definitely a divisor of a*X+b*Y.

Constraints

• X, Y and P will each be between 1 and 1000, inclusive.

Examples

1. 2

   6

   5

   Returns: 3

   When a=2 and b=1, a*X+b*Y is 10, which is a multiple of P=5. No other valid pair of values for a and b has a smaller sum.

2. 5

   5

   5

   Returns: 2

   Don't forget that a and b must be positive.

3. 998

   999

   1000

   Returns: 501

4. 1

   1

   1000

   Returns: 1000

5. 1000

   1000

   999

   Returns: 999

6. 347

   873

   1000

   Returns: 34

7. 43

   345

   1

   Returns: 2

8. 32

   1

   1

   Returns: 2

9. 2

   2

   3

   Returns: 3

10. 1000

    999

    1000

    Returns: 1001

11. 6

    9

    3

    Returns: 2

12. 4

    8

    12

    Returns: 2

13. 123

    123

    124

    Returns: 124

14. 234

    534

    346

    Returns: 20

15. 1000

    999

    123

    Returns: 8

16. 345

    23

    546

    Returns: 42

17. 373

    457

    234

    Returns: 6

18. 23

    422

    12

    Returns: 3

19. 234

    33

    456

    Returns: 11

20. 45

    763

    186

    Returns: 10

21. 196

    106

    40

    Returns: 5

22. 760

    81

    939

    Returns: 23

23. 1

    124

    183

    Returns: 33

24. 10

    1

    12

    Returns: 3

25. 830

    25

    1

    Returns: 2

26. 27

    18

    2

    Returns: 3

27. 335

    468

    42

    Returns: 7

28. 725

    170

    501

    Returns: 33

29. 963

    359

    479

    Returns: 21

30. 146

    706

    465

    Returns: 70

31. 962

    828

    282

    Returns: 20

32. 943

    996

    492

    Returns: 53

33. 392

    437

    828

    Returns: 27

34. 154

    903

    605

    Returns: 29

35. 422

    383

    293

    Returns: 28

36. 896

    719

    717

    Returns: 9

37. 772

    727

    448

    Returns: 13

38. 913

    870

    539

    Returns: 20

39. 36

    300

    668

    Returns: 16

40. 812

    704

    895

    Returns: 37

41. 674

    334

    323

    Returns: 17

42. 712

    142

    665

    Returns: 95

43. 548

    869

    254

    Returns: 3

44. 758

    663

    645

    Returns: 20

45. 724

    860

    38

    Returns: 5

46. 779

    530

    742

    Returns: 107

47. 191

    36

    317

    Returns: 9

48. 107

    289

    843

    Returns: 59

49. 265

    943

    41

    Returns: 42

50. 806

    447

    649

    Returns: 27

51. 371

    730

    891

    Returns: 58

52. 1

    1

    1

    Returns: 2

53. 5

    3

    2

    Returns: 2

54. 10

    1

    10

    Returns: 11

55. 4

    3

    1

    Returns: 2

56. 5

    5

    100

    Returns: 20

57. 1

    2

    7

    Returns: 4

58. 1000

    1

    1000

    Returns: 1001

59. 3

    3

    3

    Returns: 2

60. 342

    234

    34

    Returns: 3

61. 5

    2

    1

    Returns: 2

62. 3

    2

    2

    Returns: 3

63. 6

    2

    5

    Returns: 3

64. 5

    1

    5

    Returns: 6

65. 3

    4

    13

    Returns: 4

66. 2

    3

    1000

    Returns: 334

67. 1

    7

    7

    Returns: 8

68. 1

    2

    2

    Returns: 3

69. 1

    4

    1

    Returns: 2