TopCoder Statistics - Problem Statement

Problem Statement

Choose a number between 1 and 9, inclusive. Multiply it by 3. Add 3 to it. Multiply it again by 3. Sum its digits. You got 9, right?

Elly was intrigued by this "magic trick" (that is actually just pure number theory). She now wants to generalize it. In her version you should initially choose a number between 1 and N, inclusive, then you should multiply it by X, add Y, multiply that result by Z, and finally sum the digits of the number you got. If all choices of the initial number lead to the same final result, the girl is satisfied by the triplet (X, Y, Z).

Elly will only consider X, Y, and Z which are positive integers between 1 and 50, inclusive - otherwise the calculations become too difficult for her taste. There is no restriction on whether X, Y, and Z should be equal or not. In the example above X = Y = Z = 3, but (X = 9, Y = 9, Z = 5), (X = 10, Y = 1, Z = 9), or (X = 42, Y = 48, Z = 33) also work for N = 9.

Let's consider the last example in more detail. You may choose any starting value between 1 and 9, inclusive. Suppose you chose the starting value 3. First you multiply it by 42, which gives you 126. Then you add 48, which gives you 174. In the third step you multiply that by 33, getting 5742. Your final answer is the sum of digits of 5742, which is 5+7+4+2 = 18. Starting from the value 1 gives us 1*42 = 42, 42+48 = 90, 90*33 = 2970, and 2+9+7+0 = 18. Similarly, each of the seven other possible starting values produces the final answer 18.

Given the int N, return the number of triplets of positive integers (X, Y, Z) having 1 â¤ X, Y, Z â¤ 50, for which all initial numbers between 1 and N yield the same final answer after the sequence of operations described above.

Definition

Class:: EllysWhatDidYouGet
Method:: getCount
Parameters:: int
Returns:: int
Method signature:: int getCount(int N)
(be sure your method is public)

Constraints

N will be an integer between 1 and 100, inclusive.

Examples

9

Returns: 952
5

Returns: 3515
13

Returns: 456
42

Returns: 149
1

Returns: 125000
2

Returns: 15486
3

Returns: 8941
4

Returns: 5582
6

Returns: 2339
7

Returns: 1683
8

Returns: 1246
10

Returns: 682
11

Returns: 514
12

Returns: 482
14

Returns: 431
15

Returns: 404
16

Returns: 377
17

Returns: 359
18

Returns: 336
19

Returns: 324
20

Returns: 303
21

Returns: 296
22

Returns: 286
23

Returns: 279
24

Returns: 271
25

Returns: 256
26

Returns: 248
27

Returns: 238
28

Returns: 231
29

Returns: 228
30

Returns: 222
31

Returns: 220
32

Returns: 215
33

Returns: 203
34

Returns: 194
35

Returns: 185
36

Returns: 176
37

Returns: 175
38

Returns: 173
39

Returns: 164
40

Returns: 151
41

Returns: 150
43

Returns: 146
44

Returns: 142
45

Returns: 135
46

Returns: 133
47

Returns: 131
48

Returns: 126
49

Returns: 115
50

Returns: 101
51

Returns: 96
52

Returns: 88
53

Returns: 88
54

Returns: 88
55

Returns: 88
56

Returns: 88
57

Returns: 88
58

Returns: 87
59

Returns: 84
60

Returns: 78
61

Returns: 78
62

Returns: 78
63

Returns: 78
64

Returns: 78
65

Returns: 78
66

Returns: 78
67

Returns: 78
68

Returns: 78
69

Returns: 78
70

Returns: 75
71

Returns: 75
72

Returns: 75
73

Returns: 75
74

Returns: 75
75

Returns: 75
76

Returns: 75
77

Returns: 75
78

Returns: 74
79

Returns: 73
80

Returns: 69
81

Returns: 69
82

Returns: 69
83

Returns: 69
84

Returns: 69
85

Returns: 68
86

Returns: 67
87

Returns: 66
88

Returns: 65
89

Returns: 63
90

Returns: 60
91

Returns: 59
92

Returns: 58
93

Returns: 56
94

Returns: 54
95

Returns: 52
96

Returns: 48
97

Returns: 41
98

Returns: 33
99

Returns: 22
100

Returns: 2

Statistics

Problem Statement for "EllysWhatDidYouGet"

Problem Statement

Definition

Constraints

Examples