The Hacker Project - a free online game

The rules:
1.  Each post must contain the solution to the previous pattern, followed by your own new pattern.
2.  The solution to the pattern must be the simplest solution given the data you provide.
3.  If a pattern too confusing, people can request that it be lengthened to give them more hints.

I'll start off simple, with a classic...

1, 1, 2, 3, 5, x, y, z

x = 8
y = 13
z = 21

Tiak, you used Fibonacci(1,1), which is too much of a classic for anyone here to miss.


2, 11, 101, 1009, a, b, c


Have fun. This is a subset of a series I expect all of you to know, if that helps.

a = 10007
b = 100003
c = 1000003

Smallest prime number larger than 10^(n-1)

This is a fun one... it's a bit obscure but I like it.

(5,11), (7,13), (11,17), (a,b), (c,d), (e,f)

Each of those entries is a pair of numbers.

Araeus, you're supposed to do mine first.

But since it's there, my guess:

(13,19), (17,23), (23,29).

Primes separated by 6.

Missed you wrote that.

Yep, you got it.

Sexy primes
http://en.wikipedia.org/wiki/Sexy_primes

Yeah... primes numbers seperated by six... chosen mostly for the name.

I find if you don't start the game off easy, it never gets started. :P

Anyway, just to mix things up, I have a different kind of classic, frequently presented as a puzzle, before I delve into the obscure.

10, 1110, 3110, 132110, x, y, z

I've seen that one before.

So I'll wait a little before I post.

x=1113122110
y=311311222110
z=13211321322110

Reading it out digit by digit helps.  :)

1, 1, 2, 3, 5, 7, 11, x, y, z

This sequence gives me nightmares sometimes, one of the harder classes I took with one of the professors I liked the most.

Ha: Partial answer

Equally legitimate answer is:

13123110
23124110
1413223110



Let me guess:

16
24
35

Zac >> Legitimate answer, but not the one I was looking for either!  :laugh:
Maybe we should have a minimum on the number of terms to give in a sequence.

Expanding for the next three terms...

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, x, y, z

And for a hint, the sequence does not have a recurrence relation to describe it, but does have a generating function.

Ooookay, topic kill... *bump*

So uh, that may have been too obscure? I'll put a new one up, but if Zac would like to post his own since he provided an alternate solution he's free to do so. This one's just for laughs.

8, 6, 7, 5, x, y, z

And no, it's not 6, 4, 5.

Here's one:

1, 1, 9, 6, 3, x, y, z.

crude, and likely to earn a few facepalms, but also likely to keep people guessing.



Moen: 3, 0, 9? (Bad song reference)

You got it! (You got it!) eight-six-seven-five-three-oh-nai-eee-aaaii-nnee.  :laugh:

Hey, any song that inspires people to bad prank calls is okay in my book.

No one in 18 hours...

My guess is 8, 7, 3. Every other number in the decimal expansion of pi.

And I thought it would be harder. Oh well.

Can't stump 'em all the time!

2, 3, 3, 5, 10, 13, 39, 43, 172, 177, x, y, z

Rating this one a 4/10 on the difficulty scale.

685, 691, 4146

+1,*1,+2,*2,...

How about:

1, 2, 3, 1, 5, 2, 7, 2, 3, 2, 11, 2, a, b, c

needed to be a little longer to start

That's a strange one. I'm going to give this a longshot and say

a=13
b=2
c=3

Edit:
Continuing the sequence because I'm bored.

1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 2, 19, 2, 3, 2, 23, 2, 5, 2, 3, 2, 29, 2, 31, 2, 3, 2, 5, 2, 37, 2, 3, 2, 41, 2, 43, 2, 3, 2, 47, 2, 7, 2, 3, 2, 53, 2, 5, 2, 3, 2, 59, 2, 61, 2, 3, 2, 5, 2, 67, 2, 3, 2, 71, 2, 73, 2, 3, 2, 7, 2, 79, 2, 3, 2, 83, 2, 5, 2, 3, 2, 89, 2, 7, 2, 3, 2, 5, 2, 97, 2, 3, 2, 101, 2, 103, 2, 3, 2, 107, 2, 109, 2, 3, 2, 113, 2, 5, 2, 3, 2, 7, 2, 11, etc...

Moen got it, though I'd like to know Neo's logic. My pattern was lowest prime factor

I'd like to know neo's logic as well.

Also, I think you have a small mistake there. I have a feeling it should start 1,2,3,2,5,2,7,...
I was thinking it was lowest prime factor of n > 1, but that one piece of data threw me off.

Edit:

Right, my turn now.

2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, x, y, z

I want your reasoning too!

Double Edit:

Why'd you delete your post neo? No shame in a wrong guess.

Mistyped there. Sorry.

Right, my turn now.

2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, x, y, z
[/quote]

I can't come up with anything: perhaps the next few numbers.

50, 52, 54, 56, 60, x, y, z

Hint: It's the evens with an extra rule. Think in words. Extra hint will appear here in another 12-13 hours.

62, 64, 66?

If thats right, then why is there a gap between (0), 2, 4, 6, and 30, 32, 34?

That's what I've been thinking about. Also: why are the evens ending in 8s left out.

Correct!

Think about it this way. What do ten, twenty, and eight have that two, four, six, thirty, forty, fifty, and sixty don't have?
Also, zero is not part of the sequence.

*groan* Even numbers which do not contain the letter "e" Now that leaves me...  :confused2:

Well then, what's your sequence? :3

Ok then...

This sequence is to show the dangers of the sequence which you posted previously: 

3,6,7,9,13,15,16,17,19,23,x,y,z

This one is a more "normal" sequence which you should be able to deduce  :17:

4,2,5,2,6,0,3,7,6,4,6,9,0,8,x,y,z

Have a good one :drink:

3,6,7,9,13,15,16,17,19,23,x,y,z :

Im guessing the next would be 26,27,29?  :14:


4,2,5,2,6,0,3,7,6,4,6,9,0,8,x,y,z :

X = 0
Y = 4
Z = 3

Had to wiki this one, cant remember all the digits lol  :16:

That is correct. Can you explain why it's not 25, 26, 27 though?



Nothing wrong with Wiki ;-) That one was easy huh... we await your pattern.

What are those patterns?

I can't figure out the first, but it probably has to do with the spellings of the numbers.

The second is each of the digits of pi + 1 (mod 10).

Bingo ;-)

The first in fact is made to show the level of weirdness you introduce when you try to make patterns based on the spelling of numbers. I'll give Moen a hint - it does have to do with the spelling of numbers... but the language used as a reference is not English.

3,6,7,9,13,15,16,17,19,23,x,y,z

You got me there, it's hard to figure out if you don't know the reference language. And I just made a point a couple days ago on the forums that we had a good amount of people who don't write/speak English as a first language.

I tried looking at German, Dutch, French, Spanish and Japanese, but I've had no luck so far.

Well honestly I just guessed the first one, the reason I didnt include the 25 is because in English, fifteen is spelled differently than "five" or "twenty-five". If you split the word twenty-five, its made up of "twenty" and "five;" and because the number "five" is left out in the sequence, so I guessed 25 is not in the sequence either.   :laugh:

Heres my pattern, theres no tricks to it and you dont need to know any languages either.  :16:



2,3,5,5,7,9,8,10,12,14,12,14,x,y,z


and heres another one:

11543
12322
23411
14564
23xyz

My guess is 15,15,17 but I am probably wrong as that 9 in there does not fit into my model very well...

(btw moen - the language was Spanish it just go to show how complicated things get when you have to not only know the language but also find the applicable rule within the language!)

Nop

My hint is to look at how the numbers change ( For example, a lot of numbers have a difference of 2 except a few, why is that? )

Ok now that makes a lot more sense.

16, 18, 20, 17, 19, 21...

Here I am certain of a patten... whether it is the pattern which you foresaw I am not so sure as 16,18,20 is simply a bit easy no?

Thats correct!

I never said its a complex pattern have I?  :13:

That's a weird pattern, but a nice one.

Some might have neglected this little jewel posted earlier:

But as I did give a response lets find another pattern... how about...

2,4,7,8,11,13,14,15,16,17,19,22,23,26,28,29,x,y,z

(nb: A great classic, but with a twist)

Guess: 30 31 32

If that's not right then perhaps put a few more numbers in?  :7:

Bingo  :12:

Congratulations that is exactly the pattern - we used to play this in class in fourth grade or something... thus as I said, a great classic  :laugh:

Heres an easy one.


2,4,16,256,65536,a,b,(and ifyou can) c.

it's X squared

4294967296
281474976710656
18446744073709551616


Hmm, how about:

15, 20, 20, 6, 6, 19, 19, 5, 14, 20, a, b, c

Sry ZacQuicksilver. You almost had it.
4294967296=a
281474976710656=wrong
18446744073709551616=b

Like i said try and get c. But you did get a and b. c I choose cause you cant do it on the calculator.

Could c be;
340282366920938463463374607431768211456

I cant find a single calculator that can take a so long row of numbers.

Ding!!ding!!ding!!ding!!
You are corrected. :first:

But back to.

Must of made a mistake on the calculator. I had the formula right though [Xn=(Xn-1)^2].



That one I posted is going to be fun. Just think about it.

15, 20, 20, 6, 6, 19, 19, 5, 14, 20, a, b, c

a = 5
b = 20
c = 20

1,2,3,4,5,6,7,8,9,10,11,12,13 :)

Hope people are still interested in this  :2:

Nicely done. Care to explain the pattern for everyone else so they understand (and I know you understand)


As for

Counting is kinda lame, so why don't you do a real pattern, since you did get it.

Emm, that was the hint for other people....


11543
12322
23411
14564
23xyz

no one solved this one yet, i think

Can someone post a hint for this one. I've been racking my brain, and it still doesn't make sense

23378? I have no idea at all so Im guessing wildly.

is this it?:

11543
12322
23411
14564
23223

x = 2 y = 2 z = 3