6

16

1116

3116

?

132116

1113122116

311311222116

13211321322116

The next term is pretty clearly 7.

:dubious: How?

Just start plugging natural numbers into the expression

(-5819n^4 + 57430n^3 - 186025n^2 + 243590n - 109032)/24.

You get 6, 16, 1116, 3116, 7, -20039, etc.

Pretty obvious, really.

Hoopy Frood is correct.

So are the people who came after me, since they continued the sequence.

And **Lubricious Integument** is right as well. (Thank you google calculator.)

Yes, everyone’s correct but I think **Lubricious Integument** wins the thread.

I just want to know how long that took him (her?) and what method he used to figure that out. Because I can’t see anyone bothering to figure that out by hand.

Yup 132116.

How about…

What’s the next line:

1

1 7

1 7 6

1 7 6 3

5 1 7 6 3

5 9 1 7 6 3

5 9 1 7 6 3 0

5 9 1 7 6 3 2 0

5 4 9 1 7 6 3 2 0

I don’t know the technique, but I’m guessing it was slightly tongue-in-cheek, making the point that these types of numerical sequence puzzles inherently have many solutions. An infinite number of solutions, I imagine.

You can always learn something here in dope!

http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html

I used to give problems on this to my beginning algebra class… didn’t go well.