Please can someone help me create a formula for the following data inputs and outputs

[noelmodarres]

Hey all,

Please can someone help me with this.

Input	Output
8​	0​
9​	7​
10​	6​
11​	5​
12​	4​
13​	3​
14​	2​
15​	1​
16​	0​
17​	15​
18​	14​
19​	13​
20​	12​
21​	11​
22​	10​
23​	9​
24​	8​
25​	7​
26​	6​
27​	5​
28​	4​
29​	3​
30​	2​
31​	1​
32​	0​
33​	31​
34​	30​
35​	29​
36​	28​
37​	27​
38​	26​
39​	25​
40​	24​
41​	23​
42​	22​
43​	21​
44​	20​
45​	19​
46​	18​
47​	17​
48​	16​
49​	15​
50​	14​
51​	13​
52​	12​
53​	11​
54​	10​
55​	9​
56​	8​
57​	7​
58​	6​
59​	5​
60​	4​
61​	3​
62​	2​
63​	1​
64​	0​

Thanks

Noel

 

[mmm4444bot]

Hello. The pattern appears to be piecewise linear. What have you done or thought about so far? Is this part of a larger assignment? Please share some context. Thank you.

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[Harry_the_cat]

It could really help if you plotted the points on an x-y axis.

 

[JeffM]

Here is a clue that may lead nowhere.

[math]f(8) = 8 - \left \lfloor \dfrac{8}{8} \right \rfloor = 0.\\ f(9) = 8 - \left \lfloor \dfrac{9}{8} \right \rfloor = 1.\\[/math]
You have to try things to see patterns. Pattern recognition is an art. This clue may be idiotic, but it is something to try.

 

[blamocur]

Here is the graph in yellow with continuation in blue:

 

[Cubist]

I've found a formula. It uses the floor function (like in JeffM's post but in a different context). Please respond so that we can guide you. Have you spotted anything about the points where the output jumps?

 

[blamocur]

I've found a formula. It uses the floor function (like in JeffM's post but in a different context). Please respond so that we can guide you. Have you spotted anything about the points where the output jumps?

Me too, but I used the ceiling function.

 

[Cubist]

Me too, but I used the ceiling function.

From floor to ceiling, but let's avoid ascending as high as the roof again. Before you know it you'll be writing another cool web based solution . (Your graph does look a bit like the roof of the Sydney Opera House.)