[Guest]

Here is a lovely little little brain teaser which I first encountered almost 20 years ago. Goes like this:

Here's a sequence. give me the next number. 0, 1, 2, ?

3

OK, I assume you know it isn't the obvious answer. But, what is the answer?

I will post this without giving a spoiler yet. As soon as i see at least one unobvious answer, with some kind of logical explanation for your choice I will post a spoiler giving the answer I know. There might be more than one, so be prepared to support your reasoning!

Hope you all find this one interesting.

P. O'T

[Guest]

Newbie responding to newbie!

4

As in the sequence goes 0, 1, 2, ?, 4

[Guest]

Another newbie's attempt

5

(n-1)²+1=n

0²=0 so n=1

1²=1 so n=2

2²=4 so n=5

[Izzy]

x^n + 1 works, where x is the number, n is the term in the sequence, and +1 is there because I said so. Here's what I mean:

0^1 = 0 + 1 = 1

1^2 = 1 + 1 = 2

2^3 = 8 + 1 = 9.

It might not be the answer you're looking for, but it works.

[Guest]

OK! Fast reply and nicely reasoned. I especially like "because I said so", Izzy.

Here is the next term in the series

720! (720 factorial)

So the sequence so far is 0, 1, 2, 720!

How do you like me, now?

[Guest]

4!!!!

Clever, I like it.

[Guest]

OK! That was fast! You guys are good. MaestroOD got it in one. Maestro, would you care to give the rest of the guys some insight into your reasoning process?

P O'T

PS This is from a book by Douglas Hofstadter called "Fluid Concepts and Creative Analogies". It's got a lot of great stuff on analogical reasoning, which is just what you need for certain problems on the site. He also wrote "Godel, Escher, Bach", which, if you haven't read it, is one of the most remarkable books written. The topics include thinking, computers, music, self-reference and many others.

[Guest]

4 2x1=2 that takes care of 1 and 2, then 2x2=4 that to me is the logical answer

[Guest]

Newbie I like it, you almost fooled me at first because

0! is 1, not zero. but then i realized the pattern is

0 (no !), 1! (because the factorial starts here, not at 0), 2!!, 3!!!, 4!!!!, 5!!!!!

tricky tricky!!!!!!

[Guest]

I would say

it is adding the last two numbers and adding one to that sum

0+0=0+1=1

0+1=1+1=2

1+2=3+1=4

so I would say 4

[Guest]

Thanks, people for the quick responses. I am a lover of these kinds of puzzles/problems, but not much of a hand at inventing them. I will search for more to post. I love this site!

P O'T