What's The Secret Behind Leveling Up Your Erratic Pokemon?
Pokemon is a video game owned by Nintendo, in which you train a “Pocket Monster” who levels up when it has gained enough experience points from defeating the enemies. The amount of experience
E
X
P
E
r
r
a
t
i
c
(
L
)
that an Erratic Pokemon needs to reach L is given in the table below.
Level 1 2 3 4 5 6 7 8 9 1 0 EXP 2 1 6 5 2 1 2 3 2 3 8 4 0 6 6 3 8 9 4 2 1 3 2 7 1 8 0 0 L e v e l 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 E X P 2 3 6 9 3 0 4 1 3 8 2 3 4 7 2 0 5 7 3 8 6 8 8 1 8 1 5 6 9 5 6 4 1 1 1 1 2 1 2 8 0 0
Which of the following functions is the best approximation of E X P E r r a t i c ( L ) in the range 1 ≤ L ≤ 2 0 ?
Image credit: Bulbagarden
Details and assumptions
If you are interested in Pokemon levels, you might want to look at: The math behind Pokemon levels
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2 solutions
Well, a fool proof solution would be to find the sum of errors(as in (value predicted by a formula) - (actual value)) associated with each formula. Then the formula with the least error is the better one.
I found an absolute error of 1.62 for (-L^4 + 100 * L ^ 3) / 50, which was the least when compared to the other error sums.
But 1 or 2 doesn't satisfy the equation. Why is it so?
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It's not meant to satisfy. It's meant to be very close. That's why it's better to plug in larger numbers, because then if it's 1 or 2 off, that's only a tiny percent off of what it should be. If it's 1 or 2 off of 3, then that could be 33 to 50 percent faulty.
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You are right!
It asks only for an approximate formula. Oh! Why didn't I read it carefully before!!!
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@Maharnab Mitra – Very good tip: Before you start even touching a problem, read the problem 10 times. Great AMC tip, unless it's an easy question. That way you figure out a way to do the problem efficiently rather than immediately jumping to a much harder way of solving it. You also won't make mistakes, like that one.
by option b 20 Fits well........ 8 x 8000/5 = 12800
CASIO Fx570ES PLUS Rules!!!!!!!
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I used a CASIO 96SG PLUS to conduct random checks at weights 1, 3, 5, 7, 9, 12, 14, 15, 19, and 20.
but the expression is wrong at lower levels of the game
ERROR IN PROBLEM: The data for L=10 is repeated, and is omitted for L=12.
Started by taking the 1st through 3rd differences. 3rd diffs were all small (0 - 13), but with slight downward trend, suggesting a cubic polynomial, plus maybe a small negative quartic term. This made the fourth choice seem likeliest.
Then mostly, just evaluated each choice at 1, 2, 5, 10, 20; this eliminated the 3rd choice right away.
The 1st and 2nd choices were pretty good, but the 4th choice was much closer to the data; so it was a clear winner. It seems to be always the nearest integer to that expression. - - - Based on this, I'd say the figure for L=12 should be 3041.
what if it is the way to make us confuse????
Very similar to what I did...cool
You should submit a clarification request / dispute for the error, and I could have corrected it. Will fix that now.
Let's try plugging in things. From intuition, we know that for approximating functions, it's best to choose larger numbers and plug them in. Let's try 6. We plug 6 into all equations -L to the 4th plus 100 times L to the 3rd over 50 is remarkably close. Plugging in seven also works very well. Therefore, -L to the 4th plus 100 times L to the third over 50 is our answer. P.S. Calvin, would you mind resharing one of my notes? I'm doing an exponential growth demonstration and I kind of need to kickstart the process. It'll be pretty cool to see the result. Thanks!