W AH, that's s freaky! In maths club today, I offered that decreasing bases puzzle. They got it with a little (read: lots of) help from me... but then my teacher just came out with 1, 11, 21, ... - that exact same puzzle! I still didn't figure it out without help...
Anyway, here's a little program to churn them out... (my maths teacher thought, if anyone could do it, I could... )
code:
#include <conio.h>
#include <stdio.h>
char str1i[256] = "1";
char str2i[256];
char *str1 = str1i;
char *str2 = str2i;
int main() {
puts(str1);
while (getch() != 27) {
char *p1 = str1;
char *p2 = str2;
char n, c;
while (*p1) {
c = *p1;
n = 0;
while (*p1 == c) {n++; p1++;}
p2[0] = '0' + n;
p2[1] = c;
p2 += 2;
if (p2 - str2 >= 256) {puts("Too long."); return 0;}
}
*p2 = 0;
puts(str2);
(int)str1 ^= (int)str2;
(int)str2 ^= (int)str1;
(int)str1 ^= (int)str2;
}
return 0;
}
Anyway, they thought my puzzle was too hard. Someone offered this puzzle. See if you can get it...
1, 2, 6, ?
This is a set of only four numbers. What is the last number?

Man, I feel so stupid when someone goes into math theory mode like that. I understand it, but I couldn't have come up with it to save my miserable life.

bdavis:
let's see
1,2,6,??
that could be 24(row of x!)
that could be 42(next=previous + sqr(previous)
hell i don't know.
quote: quote:
--------------------------------------------------------------------------------
(there also would be an infinite number of prime numbers ,and i heart a rumor somewhere that there aren't any more prime numbers beond 10^10^10^10^10^10 or so,just a rumor,i should ask one of the mathematicians)
--------------------------------------------------------------------------------
Someone like me?
no i meant someone of the mathematicians in my class who went to all courses of philosophy and still remember
greetz
Shade

Those solutions are all very well, but they don't explain why the number you have to find is the only other number in the set.

Any more suggestions?

Clue: a kid could do this

23yrold3yrold: Don't worry, I didn't come up with that. I just quoted it

Hmm, I like this big grin

Nope. How can you be sure that's the last number in the set?

Hehe, I seem to have you all baffled. And this is S simple! You must think in the way you thought when you were THREE (*wink* wink, that has a triple meaning )

[ May 22, 2001: Message edited by: bdavis ]

Hey! I get it! The last number is 3!

Congratulations, PrimeSlide!
So the three meanings were:
1. Think like a kid;
2. The words are three letters long;
3. I wrote 'THREE' rather than '3' to suggest writing numbers out.
I had no idea the threefoldness of the meanings would incite Goodbytes to guess 3. I really feel like Commander Data now, with all these conspicuous references to the number 3...

Heh, I would never have guessed that one.
1 Een
2 Twee
6 Zes
10 Tien

and another one...
Ones upon a time there was a city ,surrounded by a big wall and with only one gate.To enter this city you have to tell the guard the secret number.So to find out what the secret number is you hide yourself in the bushes and listen to what the people and the guard say:
G:5
P1:4
when the next person arives
G:7
P2:5
and the next
G:11
P3:6
and now it's your turn
G:12
YOU:???

and for those of you who can thing multidimensional:How many ribs has a 4-dimensional cube(3D has 12 ribs(ribs=lines between the points of the object,i'm not sure what the actual translation is))?

shade

Lucky guess: 7?

Hmm...
Shade: we just call them 'edges'
Let E(n) be the number of edges and V(n) be the number of vertices in an n-dimensional cube.
For n >= 2, we take two (n-1)D hypercubes and connect each vertex in one to the corresponding vertex in the other to create the nD hypercube.
V(n) = 2 V(n-1)
E(n) = 2 E(n-1) + V(n-1)
For n = 1, we have a line connecting two vertices. Thus we can form the sequence:
V(1) = 2, E(1) = 1
V(2) = 4, E(2) = 4
V(3) = 8, E(3) = 12 (as expected for a cube)
V(4) = 16, E(4) = 32
Thus a 4D hypercube has 32 edges.

X-G: Nope
You were right with the nybbles(it's spelled with a y though I think). You have to convert the numbers into binary, and then separate them into nybbles. The rest should be easy...

Goodbytes: it seems it's optional; you can have 'nibble' or 'nybble' www.dictionary.com/cgi-bin/dict.pl?term=nybble