Ok, this is one I have had in mind for a while. Given the sequence:

733
2583
47336
935569

can you tell which of the following belongs to it?

a) 6243682
b) 7534448
c) 2668765

Hint: you don't need a calculator for this!

I know you are looking for a specific answer but I can prove to you that any number I name is equally good.
You can always create a polynomial that passes through a finite number of points.
Sorry for this lousy answer.

Nir

I guess one could always use finite differences and "reverse engineer" the polynomial that generates the sequence, and this could be quite funny actually! BUT... you would definitely need a calculator!

Here is a second hint: you don't need a calculator, but there is another VERY COMMON object that would be quite handy to solve this.

That's not such a lousy answer, Nir, quite thought provoking. Is it actually proven that there is always a polynomial for a finite number of random numbers?

Anyhow, I wouldn't be able to work backwards to find it even with a calculator.

Is the common object a calendar?

Are the numbers just numbers or do they represent something else?

Magicgeorge,
The object is not a calendar and, as you suspected, the numbers do represent something else!

4 84465 48 47 2

This is exactly why I've stopped showing number sequence puzzles to Looy Simonoff. Any time I do, he always gives me this same answer.

Me: "Looy, what's new?"
Looy: "Kinematic viscosity. What's mu?"

Congratulations to eggshell, who gave the correct answer, and obvious did not guess!

eggshell, do you want to explain your answer?

Yes,

It’s a brilliant idea by the way, Alessandro.

They are the numbers you need to key on a mobile phone using predictive texting and they spell out different colors.

Of course I won't mention the fact that I sat here for hours trying to break the code with by allocating different numbers to different letters of the alphabet. The strange thing is I really can't remember how or what suddenly clicked to give me the answer, perhaps it was one of those Uri Geller moments!!!

MagicGeorge,

If you are interested the simplest way to create such a polynomial is the Lagrange polynomial. If you have a high school math education you can understand it. There are many links on the web.
Of course there are other ways to do it.

Nir