What the relation (Equation) between these numbers (X, Y, Z)?
Your answer will be highly appreciated.
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$z=11(x-1)$ and $y=(x+2)\text{mod}10$. – Raskolnikov Aug 17 '14 at 12:15
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1@Raskolnikov: That's not true for $x=8$ and $z=78$ for example. – Frunobulax Aug 17 '14 at 12:17
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not exactly correct, for X >= 8, you need and extra 1, and after X >= 18 yet another one, so it would be Z = 11 * (X-1) + (X-8) div 10 – Pieter21 Aug 17 '14 at 12:18
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I'm unconvinced by your arguments without further information about the origin of the data and possible noise on them. – Raskolnikov Aug 17 '14 at 12:25
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@Raskolnikov: sorry for that, It is a homework. As you I don't have more info :( – Kumar Aug 17 '14 at 12:27
2 Answers
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Well this works:
$$Z - Y = 10X + 11\left\lfloor\frac{X-8}{10}\right\rfloor -2$$
PARI-GP Script:
for(x = 1, 20, printf("X = %d, Z - Y = %d\n", x, 10 * x - 2 + 11 * floor((x - 8) / 10)))
Output:
X = 1, Z - Y = -3
X = 2, Z - Y = 7
X = 3, Z - Y = 17
X = 4, Z - Y = 27
X = 5, Z - Y = 37
X = 6, Z - Y = 47
X = 7, Z - Y = 57
X = 8, Z - Y = 78
X = 9, Z - Y = 88
X = 10, Z - Y = 98
X = 11, Z - Y = 108
X = 12, Z - Y = 118
X = 13, Z - Y = 128
X = 14, Z - Y = 138
X = 15, Z - Y = 148
X = 16, Z - Y = 158
X = 17, Z - Y = 168
X = 18, Z - Y = 189
X = 19, Z - Y = 199
X = 20, Z - Y = 209
Yiyuan Lee
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Did you take into account the floor function part? I'll run a script and edit my answer with the results. – Yiyuan Lee Aug 17 '14 at 12:44
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$\lfloor x \rfloor$ refers to the greatest integer that is not more than $x$. – Yiyuan Lee Aug 17 '14 at 12:51
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Glad I could help. I subtracted $Y$ from $Z$ to get $Z - Y$ and the result suggests some linear sort of pattern with $X$. – Yiyuan Lee Aug 17 '14 at 12:55
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I notice that X * 11 is equal to the value under the corresponding value of the Z axis within a slight discrepancy. Eg 16 * 11 = 176. The corresponding value on the Z axis is 166. Under it is 177 which is close to 176. I think the discrepancy has something to do with Y axis
Sincerely,
WeedWizard420
mahtaht
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