This one is for every riddle fan! Craven, Blaine, etc.

What's next in the following sequence?

3, 5, 7, 9, ___

Scroll down for the answer



















































Yes, you already figured there is something tricky about it.
Actually, the sequence can be practically anything! Just as an example,
I will take the number 66 as being next in the ___. Yes, I know
you're going "Huh? I thought it is 11!" Well, it is, but it's also 66
and any other number you can think of! Here's why:

Let's say we have a function a(x), b(x), c(x), d(x), and e(x).

a(x) = (x-2)(x-3)(x-4)(x-5)/((1-2)(1-3)(1-4)(1-5))
As you can see, a(1) = 1, a(2) = 0, a(3) = 0, a(4) = 0, a(5) = 0

We proceed like this with b(x)-e(x), but replace 1 with 2-5:

b(x) = (x-1)(x-3)(x-4)(x-5)/((2-1)(2-3)(2-4)(2-5))
c(x) = (x-1)(x-2)(x-4)(x-5)/((3-1)(3-2)(3-4)(3-5))
d(x) = (x-1)(x-2)(x-3)(x-5)/((4-1)(4-2)(4-3)(4-5))
e(x) = (x-1)(x-2)(x-3)(x-4)/((5-1)(5-2)(5-3)(5-4))

Now the polynomial y(x) is going to go like this:

y(1) = 3, y(2) = 5, y(3) = 7, y(4) = 9, y(5) = 66

And here is how we do it:

y(x) = 3(a(x))+5(b(x))+7(c(x))+9(d(x))+66(e(x))

When this polynomial is simplified, we simply get:

y(x) = 55/24*x^4 - 275/12*x^3 + 1925/24*x^2 - 1351/12*x + 56

Try entering 1, 2, 3, 4, and 5 as x into this polynomial and
gape at the unexpected results!