Re^2: Reverse engineering a formula...

I can argue that, given more precise question, a sort of tasks about sequences like "1,2,3,4,5,?" makes perfect sence.
If you're referring to set of functions such that

f(1) = 1
f(2) = 2
f(3) = 3
f(4) = 4
f(5) = 5
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and then calculate f(6) then indeed there surely exists infinite number of different f's conforming these conditions and yet f(6) equals to -7 x phi.

But when you limit answers to functions having only natural numbers, of special kind (let that be polynoms with integral coefficients, with the largest power *no* more than three, then one and only one function fulfills the condition, and this is f(x)=x, and the correct answer is 6.)

Like everywhere else in mathematics, very many things depend on exact phrasing.

addition but I agree that OP has very badly phrased task

update 2+1 small typos

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Re^3: Reverse engineering a formula... by Moron (Curate) on Jun 13, 2006 at 14:21 UTC
Consider the case of y = x + rcos(pix) where r is any real, which produces a sine wiggle around a straight line, where the deviation from the straight line is maximum for half-values of y, but for integer values produces the illusion of y=x. Update oic, you want to limit the types of functions - but without the business knowledge how can you do that? We know it's leasing, but without knowing the business, how do you know it doesn't have a risk component linked to a normal distribution based on the customer's age? That wouldn't be polynomial. More update: yes fletch is right, s/cos/sin/ - my brain did the equivalent of a double negative when I was imagining this. -M Free your mind	[reply]
Re^4: Reverse engineering a formula... by Fletch (Bishop) on Jun 13, 2006 at 15:20 UTC
ITYM `sin` not `cos`; the former intersects `y=x` for integers, while the later intersects for multiples of 0.5. And the extremums would be at `n + (-1)ⁿ sin^-1( 1 / rπ )/π` (for integer `n`). </pedant> :) Update: Gah, I had `2π` rather than `rπ` because I used that as the constant when I checked things.	[reply]
Re^4: Reverse engineering a formula... by vkon (Curate) on Jun 13, 2006 at 16:00 UTC
I think you understand my point (sorry for unperfect English) - sometimes tasks for finding a next number in some sequence of numbers are not useless, and such tasks help training ones brains. OP has many flaws, and this is not really the sequence problem, and "Reverse engineering a formula" is a bad description of the problem As a different note, our teacher said to us that the PI number contains, for example, encoded in it entire "War and Peace" by L.Tolstoy, starting from some position... you only need to find that N and enjoy the reading :) While this is theoretically true, how can you benefit from this knowledge? :) :)	[reply]
Re^5: Reverse engineering a formula... by Moron (Curate) on Jun 14, 2006 at 11:19 UTC
The pusillanimous goal of practising simple logical thinking (e.g. picking the easy option given a number sequence) pales to too little as compared with the value of using more comprehensive thinking to explore a subject, this being undermined by reaching an answer too superficially or habitually, because that in turn psychologically blocks further opportunity to see the bigger picture. In this case, the OP needs at least to gather more information rather than find a logical substitute. See Six Thinking Hats by Edward de Bono for a more precise and comprehensive evaluation of what missed opportunities are at stake. -M Free your mind	[reply]