Somebody at work has stumped the office with this:

What is the next number?
33 36 39 42 52 60 110


Anyone got any ideas? I can't concentrate on my work because I keep thinking of this :) I'm even using Excel to type in mathmatical equations to find the answer :P

Questions like these make no sense. For every number you can think of, I can make a logic equation that will say it's a "logical" next number.

To make an example easy, let's look at sequence 1, 2, 3.
You can say the next number is 4, because you're counting 1,2,3,4... you can also say the next number is 5 and after that 8, because 1+2=3, 2+3=5, 3+5=8.

But you can also say the next number is 40.
Why? If you look at the function
p(x) = -24 + 78 x - (187x^2)/2 + (107x^3)/2 - (29x^4)/2 + (3x^5)/2
and calculate p(1) you will get 1.
p(2)=2
p(3)=3
p(4)=40

But you can also say 70!
Why?
Take a look at h(x) = -54 + 169x - (397x^2)/2 + 111x^3 - (59x^4)/2 + 3x^5
h(1)=1
h(2)=2
h(3)=3
h(4)=70

Basically, for any given number, you can find a "logic" for just THAT number to be the next in line.

Lets say you want to prove you can find a logic for PI to be the next number in sequence.

Just take a look at function
g(x) = 4 - PI - (19*x)/3 + (11*PI*x)/6 + 4x^2 - PI*x^2 - (2x^3)/3 + (PI*x^3)/6
g(1)=1
g(2)=2
g(3)=3
g(4)=PI

Oh... to answer your question. I would say the next number is 460.

Reason is this function:
p(x) = 152 - (579 x)/2 + (11738 x^2)/45 - (905 x^3)/8 + (919 x^4)/36 - (23 x^5)/8 + (23 x^6)/180

p(8) = 460

What's the next number in sequence 3,5,6,10,12,20

3 - 5 - 6 - 10 - 12 - 20 - 24 - 40 - 48 - 80 - 96 - 160 - 192 - 320 - 384.. .

;)

I know this is a really old question, but I do have the answer to the OP's question:


What is the next number?
33 36 39 42 52 60 110


Assuming that the OP accidentally left out one number in the sequence, so it is actually 33 36 39 42 46 52 60 110, this sequence is the number 42 written first in base 14, then base 13, then base 12, etc. The next number after 110 (which is 42 in base 6) is 132.

3 - 5 - 6 - 10 - 12 - 20 - 24 - 40 - 48 - 80 - 96 - 160 - 192 - 320 - 384 . . .

;)

Very good. And then 640, 768, 1280...