if you get this you are smart

[Piz0wn0reD!!!!!!]

1 2 11 33 12 60 21 147 23 253 1112 14456

what are the next 3 numbers in the pattern?

[BZ_Zorro]

Good post, I'm giving this one a crack. Some comments in white (I've left them vague so the cheaters can't get ideas [img]/images/graemlins/wink.gif[/img])
<font color="white">OK, one pattern in there is easy enough to spot. The other pattern has got me stumped. I can't possibly explain the sequence 1 11 12 21 23 1112 by any normal mathematical progression. I'm fiddling around with base conversions...am I way off?
</font>
Anyway if you could answer this question it'd be very helpful: Can this sequence be solved purely with a knowledge of maths (any field), or do you need to know something else?

[gumpzilla]

Answer in white:
<font color="white"> This is the see and say sequence, (1, 11, 21, 1211, etc.) coupled with a strange requirement that you also multiply numbers of the sequence by ascending primes. Thus, 1, followed by 2*1. Then 11, followed by 3*11. Then 12, 5*12, etc. I will comment that I'm not entirely sure how you swing 0 in the see and say sequence, but we want 60 in see and say, so that's probably 1610, multiply it by 17 to get 27370, and then 1211. So, my answer is 1610, 27370, 1211. EDIT: If you aren't already familiar with the sequence 1, 11, 21, 1211, 111221, 312211, etc., I think this is going to be insanely hard.</font>

[evil_twin]

Gumpzilla beat me to it, my solution matches his, although I had to write it out in detail to convince myself of it. Might as well post the solution for those wanting it spelt out (like me!) :

<font color="white">
It's a "look and say" sequence intertwined with some succesive prime number multiplication.

So, if we start at the beginning, we can explain all the terms:

1
We get the next term by multiplying by the first prime (2)
1x2 = 2

Next term from "look and say". The first term is "one one" so it's 11.
11
11x(the next prime) = 11x3 = 33

Next term from look and say again. Second term is "one two" so it's 12.
12
12x(the next prime) = 12x5 = 60

Back to look and say. Third term is "two ones". 21.
21
21x(the next prime) = 21x7 = 147

33 = "two threes" so the next term is 23. Multiply by the next prime (11) and we get 253.

12 = "one one, one two" = 1112. Multiply by 13 to get 14456.

"one six one zero" = 1610. Multiply by 17 = 27370.

"one two one one" = 1211.


Hence the next three terms are 1610, 27370, 1211. Interesting puzzle, it's been a long time since I've seen the "say and see" sequence and that part took by far the longest to figure. The prime number multiplication part should come fairly easily. As Gump says, if you've never seen a "say and see" sequence before you're probably well lost.

</font>

[Piz0wn0reD!!!!!!]

grump and evil twin got it. i thought this would stump people for a while. Ill make a much harder one now.

[Homer]

<font color="white">I got the whole bit about multiplying by prime numbers, but I don't understand where 1, 11, 12, 21, 23 and 1112 came from. Can someone explain?</font>

[Piz0wn0reD!!!!!!]

<font color="white">the other numbers are "see and say" or whatever its called. for example in this puzzle: "1 11 21 1211 111221" the next number is "312211" or three ones, two twos, two ones. the next numbers in the sequence are describing the preivous ones. </font>

[Homer]

Heh, that's cool, thanks. I hadn't heard of it before.

[Piz0wn0reD!!!!!!]

[ QUOTE ]
Heh, that's cool, thanks. I hadn't heard of it before.

[/ QUOTE ]

its very hard if you havent seen one of them before [img]/images/graemlins/smile.gif[/img]

[jason_t]

This one is easy.

answer: <font color="white">1610 27370 1211</font>

The sequence is a mixture of Conway's look and say sequence and multiplying by the nth prime.

The look and say sequence is incredibly famous. I first encounterd it in a freshman computer science course on computer architecture. I never paid attention to lecture and was always trading notes with a friend. He passed me the first five terms of the sequence and told me to find the next. I found it and was quite pleased with myself and became rather obsessed with the sequence. One interesting thing that can be asked about the sequence is how much longer is the nth term than the (n-1)th term? I was never able to answer this question but it turns out that Conway asked this question too and found the answer. In fact, he showed for any look and say sequence (that is, you don't necessarily have to start with the number 1, you could start with any number you like and then do look and say on it) the length of the nth term is approximately C = 1.303577269034296... the length of the (n-1)th term. That number C is the only positive root of a certain degree 71 polynomial.