# Thread: Number sequence driving me crazy!

1. ## Number sequence driving me crazy!

Hello,
I have a sequence of 99 numbers, which I cant determine the pattern for. Are you able to work it out? The numbers are actually the experience points required for a certain level in a computer game. I have been given the numbers to reach level 99 but I need to work out the XP required for the levels up to 200.

Can anyone work out the formula please?

The numbers are:

Quote:
1 10
2 22
3 38
4 61
5 95
6 147
7 227
8 349
9 499
10 667
11 846
12 1032
13 1225
14 1425
15 1632
16 1846
17 2067
18 2295
19 2531
20 2775
21 3027
22 3287
23 3555
24 3831
25 4115
26 4407
27 4707
28 5015
29 5332
30 5658
31 5993
32 6337
33 6690
34 7052
35 7423
36 7803
37 8192
38 8590
39 8998
40 9416
41 9844
42 10282
43 10730
44 11188
45 11656
46 12134
47 12622
48 13120
49 13631
50 14155
51 14692
52 15242
53 15805
54 16381
55 16970
56 17572
57 18187
58 18815
59 19456
60 20110
61 20777
62 21457
63 22150
64 22856
65 23575
66 24307
67 25052
68 25810
69 26581
70 27365
71 28162
72 28972
73 29795
74 30631
75 31480
76 32342
77 33217
78 34105
79 35006
80 35920
81 36847
82 37787
83 38740
84 39706
85 40685
86 41677
87 42682
88 43700
89 44731
90 45775
91 46832
92 47902
93 48985
94 50081
95 51190
96 52312
97 53447
98 54595
99 55762
Many thanks!
TB.

2. Originally Posted by TomBowyer
Hello,
I have a sequence of 99 numbers, which I cant determine the pattern for. Are you able to work it out? The numbers are actually the experience points required for a certain level in a computer game. I have been given the numbers to reach level 99 but I need to work out the XP required for the levels up to 200.

Can anyone work out the formula please?

The numbers are:

Quote:
1 10
2 22
3 38
4 61
5 95
6 147
7 227
8 349
9 499
10 667
Many thanks!
TB.
I did a quick cubic regression analysis on the first 15 elements and came up with

$y=-.2232x^3+14.9565x^2-70.5702x+94.1392$

with a correlation coefficient (R^2) of .9988.

I don't know if that's helpful at all.

3. Hi Masters,
Firstly, thankyou for taking the time to help.

Secondly, im afraid I am not very good at math (GCSE was good, but that was a loooong time ago).

Can anyone explain how I would put your formular to practical use in my application of solving the number sequence?

Edit: Is Y the "experience points", x the level (1 to 99)?

Thankyou,
Tom.

4. Originally Posted by TomBowyer
Hi Masters,
Firstly, thankyou for taking the time to help.

Secondly, im afraid I am not very good at math (GCSE was good, but that was a loooong time ago).

Can anyone explain how I would put your formular to practical use in my application of solving the number sequence?

Edit: Is Y the "experience points", x the level (1 to 99)? Yes

Thankyou,
Tom.
There was an error in my initial function. The coefficient of x^3 should be -.2232. I have edited it so it is now correct.

However, this function does not work for large values of x because the function is cubic has a max value around x=42. If you test x=16, you get 1879 which is close to your value, but not exact.

At 17, y=2120
At 18, y=2367
At 19, y=2621
At 20, y=2879

Bottom line, This doesn't work for you. You'll have to keep looking.

5. Originally Posted by TomBowyer
Hello,
I have a sequence of 99 numbers, which I cant determine the pattern for. Are you able to work it out? The numbers are actually the experience points required for a certain level in a computer game. I have been given the numbers to reach level 99 but I need to work out the XP required for the levels up to 200.

Can anyone work out the formula please?

The numbers are:

Quote:
1 10
2 22
3 38
4 61
5 95
6 147
7 227
8 349
9 499
10 667
11 846
12 1032
13 1225
14 1425
15 1632
16 1846
17 2067
...
96 52312
97 53447
98 54595
99 55762
The numbers are not uniformly spread. It appears as if they are generated with separate functions:

1 thru 11

12 -- 18

19 -- 28

29 -- 38

39 -- 48

49 -- 98

99 -- 198
from 99 to 198 it appears as if this should work.

Starting at 99.
Whatever level you are looking for, LEVEL is the number, and the POINTS will be the result.

k = LEVEL - 99

Subtract 99 from the level with which you are working.

$POINTS = 9.5 k^2 + 1176.5 k + 55762$

Hope that helps.
There is not enough data to guess the next incrementing step beyond level 198.

.