Sequences

[geodave]

Put up a sequence of numbers, letters, words...whatever. Responders must fill in the next item in the sequence WITH AN EXPLANATION. For example, if I post:

1, 2, 3, 4, 5, __

You could post "6" and say the rule is +1.

However, you could also post "126" and say the rule is:

(n-1)(n-2)(n-3)(n-4)(n-5) + n

[it works -- try it]

[KeyboardWielder]

8 - alternate between odd numbers and powers of 2.

CC1, CCLP2, CCLP3, ___

[geodave]

Nice.

CCLP1 of course!!! Rule is when official levelsets were released chronologically.



[There are other answers. I expect CCLP2DX to be released before CCLP1.]

[geodave]

1, 2, 4, 8, 16, __

3, 1, 4, __, __

a, e, i, u, __

Μ, A, Γ, N, Υ, __

[Markus]

1, 2, 4, 8, 16, __

3, 1, 4, __, __

a, e, i, u, __

Μ, A, Γ, N, Υ, __

32 - Powers of 2

1, 5 - Digits of pi

Not sure about the others.

[geodave]

Good, although both of those have other answers I was looking for.....

[BitBuster]

I'm not sure if the 3, 1, 4 one has enough digits to be a real "sequence." You could say that the next number is two (subtract two, add three, repeat), or you could say that it's 1.3333 (divide by three, multiply by four, repeat). Etc.

[geodave]

The point is that there is more than one answer.

My personal favorite is 3,1,4,2,8

Also 1,2,4,8,16, 31

[Flareon350]

How do you get 31 from that sequence?

A, B, C, D, __

[geodave]

One of my favorite explanations of why the next number can always have more than one answer.

Take a circle. Put a point on it. Now draw all the lines between all the points. (In this case, 0 lines.) Now count how many regions the circle is broken up into (1). Now add a second point, draw all the lines (1) and count the sections (2). Now add a third point, draw all lines between all points that don't already exist (for a total of three lines) and count the sections (4). So you have 1,2,4....

If you repeat this process up to 6, and MAXIMIZE the number of sections (no intersections are of more than two lines), the sequence is 1,2,4,8,16,31,.... I don't know who discovered this, but it's mostly used just to prove this point.

[in this discussion, but "line" I mean "chord or diameter" line segment.]

Also 3,1,4,2,8 are the first five digits of 22/7, a common approximation for pi (derived, I believe from the continued fraction.)

This is where my math-geekiness kills a thread.

A, B, C, D, A -- All Big Cats Dine on Antelope.