Cuckoo's Egg Series

A forum for good logic/math puzzles.

Moderators: jestingrabbit, Moderators General, Prelates

User avatar
nuggetmonkey
Posts: 45
Joined: Wed Nov 15, 2006 2:52 am UTC

Cuckoo's Egg Series

Postby nuggetmonkey » Wed Nov 15, 2006 3:02 am UTC

#1 What is the next letter?

OTTFFSS_


#2 What comes next in the series

1 11 21 1211 111221 ______


These come from The Cuckoo's Egg: Tracking a Spy Through the Maze of Computer Espionage by Cliff Stoll.

User avatar
hermaj
Posts: 6139
Joined: Sun Oct 15, 2006 10:37 am UTC
Location: Sydney, Australia
Contact:

Re: Cuckoo's Egg Series

Postby hermaj » Wed Nov 15, 2006 3:08 am UTC

I know the first:

E. One two three four five six seven eight


I am lost on the second, but it looks kind of familiar...

User avatar
Gelsamel
Lame and emo
Posts: 8237
Joined: Thu Oct 05, 2006 10:49 am UTC
Location: Melbourne, Victoria, Australia

Re: Cuckoo's Egg Series

Postby Gelsamel » Wed Nov 15, 2006 3:15 am UTC

Spoilz wrote:One, One One, Two Ones, One Two One One, One one one two two ones, three ones two twos one one. Therefore 312211

User avatar
Verysillyman
"Do me! Do me!"
Posts: 1442
Joined: Sat Aug 19, 2006 11:25 am UTC
Location: Drinks Cabinet.
Contact:

Re: Cuckoo's Egg Series

Postby Verysillyman » Wed Nov 15, 2006 3:16 am UTC

312211. each consecutive number describes the one before it. ie, the one before this one had three 1s, two 2s, then one 1


Edit: Beaten to the chase! or soe other phrase that sounds lke that but actually makes some sense.

User avatar
Gelsamel
Lame and emo
Posts: 8237
Joined: Thu Oct 05, 2006 10:49 am UTC
Location: Melbourne, Victoria, Australia

Re: Cuckoo's Egg Series

Postby Gelsamel » Wed Nov 15, 2006 3:30 am UTC

Verysillyman wrote:Edit: Beaten to the chase! or soe other phrase that sounds lke that but actually makes some sense.


Owned :D

User avatar
Pathway
Leon Sumbitches...?
Posts: 647
Joined: Sun Oct 15, 2006 5:59 pm UTC

Postby Pathway » Wed Nov 15, 2006 4:27 am UTC

This one isn't a pure mathematics puzzle. Still a logic problem, also still undeniably ingenious but...

Who's up for some math?

User avatar
yy2bggggs
Posts: 1261
Joined: Tue Oct 17, 2006 6:42 am UTC

Postby yy2bggggs » Wed Nov 15, 2006 7:10 am UTC

Pathway wrote:Who's up for some math?


In a castle where the king now does reign,
Are the bedrooms where seven have lain;
Each were closer to he
Than each other you see
You can see why they weren't very plane.

GreedyAlgorithm
Posts: 286
Joined: Tue Aug 22, 2006 10:35 pm UTC
Contact:

Re: Cuckoo's Egg Series

Postby GreedyAlgorithm » Wed Nov 15, 2006 7:35 am UTC

nuggetmonkey wrote:#2 What comes next in the series

1 11 21 1211 111221 ______

OEIS says there are at least three sensical continuations.
GENERATION 1-i: The first time you see this, copy it into your sig on any forum. Square it, and then add i to the generation.

User avatar
Gelsamel
Lame and emo
Posts: 8237
Joined: Thu Oct 05, 2006 10:49 am UTC
Location: Melbourne, Victoria, Australia

Postby Gelsamel » Wed Nov 15, 2006 7:38 am UTC

I don't see how

"Modified Look-and-Say sequence where 2 is the largest number that may be used."


Is sensical at all.

User avatar
ulnevets
Posts: 186
Joined: Wed Aug 09, 2006 1:45 am UTC
Contact:

Postby ulnevets » Wed Nov 15, 2006 7:44 am UTC

Gelsamel wrote:I don't see how

"Modified Look-and-Say sequence where 2 is the largest number that may be used."


Is sensical at all.

means that instead of three ones, you say two ones one one.

all three seem pretty much the same to me.

User avatar
Gelsamel
Lame and emo
Posts: 8237
Joined: Thu Oct 05, 2006 10:49 am UTC
Location: Melbourne, Victoria, Australia

Postby Gelsamel » Wed Nov 15, 2006 7:55 am UTC

..I didn't say I didn't understand it.

With only a maximum of two the previous number is redundantly described.

Buton
Posts: 83
Joined: Wed Nov 01, 2006 4:38 pm UTC

Postby Buton » Wed Nov 15, 2006 4:48 pm UTC

Okay so these sequences are messed up... no really they are :D

(if you can find the right number for each, you're awesome)
1. 1, 2, 3, 4, ___
2. 1, 4, 9, 16, ___
3. 1, 2, 4, 8, ___
4. 2, 3, 5, 7, ___


Buton

User avatar
Kizyr
Posts: 2070
Joined: Wed Nov 15, 2006 4:16 am UTC
Location: Virginia
Contact:

Re: Cuckoo's Egg Series

Postby Kizyr » Wed Nov 15, 2006 5:11 pm UTC

GreedyAlgorithm wrote:
nuggetmonkey wrote:#2 What comes next in the series
1 11 21 1211 111221 ______

OEIS says there are at least three sensical continuations.


You could modify the series algorithm by saying that the next number in the sequence has to be the shortest (in number of characters) possible. So 312211 would be the only option, since 21112211, 11212211, etc., are all longer. Of course, to know for certain, you'd have to have the next number in the series, and be asked for the one following that.

Buton wrote:1. 1, 2, 3, 4, ___
2. 1, 4, 9, 16, ___
3. 1, 2, 4, 8, ___
4. 2, 3, 5, 7, ___


5 (sequential)
25 (squares)
16 (powers of 2)
11 (prime numbers)
KF
~Kizyr
Image

Buton
Posts: 83
Joined: Wed Nov 01, 2006 4:38 pm UTC

Postby Buton » Wed Nov 15, 2006 5:14 pm UTC

Sorry KF, you got all 4 wrong. I think you may have missed my comment about the series being messed up. Although your answer to #4 is partially right (the justification part... sort of)

Buton

GreedyAlgorithm
Posts: 286
Joined: Tue Aug 22, 2006 10:35 pm UTC
Contact:

Postby GreedyAlgorithm » Wed Nov 15, 2006 6:46 pm UTC

Buton wrote:Okay so these sequences are messed up... no really they are :D

(if you can find the right number for each, you're awesome)
1. 1, 2, 3, 4, ___
2. 1, 4, 9, 16, ___
3. 1, 2, 4, 8, ___
4. 2, 3, 5, 7, ___


Buton

1. 1, 2, 3, 4, 19: ((7/12)*x^4 - (35/6)*x^3 + (245/12)*x^2 - (169/6)*x + 14)
2. 1, 4, 9, 16, 19: ((-1/4)*x^4 + (5/2)*x^3 - (31/4)*x^2 + (25/2)*x - 6)
3. 1, 2, 4, 8, 19: ((1/6)*x^4 - (3/2)*x^3 + (16/3)*x^2 - 7*x + 4)
4. 2, 3, 5, 7, 19: ((11/24)*x^4 - (19/4)*x^3 + (421/24)*x^2 - (101/4)*x + 14)
GENERATION 1-i: The first time you see this, copy it into your sig on any forum. Square it, and then add i to the generation.

User avatar
Kizyr
Posts: 2070
Joined: Wed Nov 15, 2006 4:16 am UTC
Location: Virginia
Contact:

Postby Kizyr » Wed Nov 15, 2006 6:51 pm UTC

Buton wrote:Sorry KF, you got all 4 wrong. I think you may have missed my comment about the series being messed up. Although your answer to #4 is partially right (the justification part... sort of)

Buton


Dangit. I had a feeling it wasn't gonna be that easy. KF
~Kizyr
Image

Buton
Posts: 83
Joined: Wed Nov 01, 2006 4:38 pm UTC

Postby Buton » Wed Nov 15, 2006 7:09 pm UTC

Oh man, greedy, you're on the right track. Although with this type of problem, you can make up a formula to fit nearly any sequence... hrmm

Buton

User avatar
SpitValve
Not a mod.
Posts: 5130
Joined: Tue Sep 26, 2006 9:51 am UTC
Location: Lower pork village

Postby SpitValve » Wed Nov 15, 2006 8:54 pm UTC

Buton wrote:Oh man, greedy, you're on the right track. Although with this type of problem, you can make up a formula to fit nearly any sequence... hrmm


Polynomials will defeat all!

Buton
Posts: 83
Joined: Wed Nov 01, 2006 4:38 pm UTC

Postby Buton » Wed Nov 15, 2006 11:54 pm UTC

Okay, here's the answers I was looking for ;P

1. 29. the sequence is n_i = i^4 - 10i^3 + 35i^2 - 49i + 24
2. 49. The sequence is n_i = i^4 - 10i^3 + 36i^2 - 50i + 24
3. 28. This time the sequence is n_i = 2^(i-1) + (i^4)/2 - 5i^3 + (35i^2)/2 - 25i + 12
4. it's just the primes so the answer is 10. It would have been 11 had I been using base ten, but I'm using base eleven this time.



That's it for my tricks ;P

Buton[/quote]

User avatar
phlip
Restorer of Worlds
Posts: 7572
Joined: Sat Sep 23, 2006 3:56 am UTC
Location: Australia
Contact:

Postby phlip » Thu Nov 16, 2006 12:49 am UTC

Ok, so what comes next in this sequence:

1, ___

Code: Select all

enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}
[he/him/his]

User avatar
no-genius
Seemed like a good idea at the time
Posts: 4221
Joined: Wed May 17, 2006 6:32 pm UTC
Location: UK
Contact:

Postby no-genius » Thu Nov 16, 2006 12:58 am UTC

phlip wrote:Ok, so what comes next in this sequence:

1, ___



5
I don't sing, I just shout. All. On. One. Note.
Official ironmen you are free, champions officially

The Mighty Thesaurus wrote:Why? It does nothing to address dance music's core problem: the fact that it sucks.

User avatar
svk1325
Posts: 139
Joined: Mon Jul 17, 2006 9:10 am UTC
Location: Take a guess...
Contact:

Postby svk1325 » Thu Nov 16, 2006 1:14 am UTC

phlip wrote:Ok, so what comes next in this sequence:

1, ___


1.0707106... + .070106... i

f_n = sqrt((n-1)i) + 1
:D

sqrt(i) = 1/sqrt(2) + 1/sqrt(2) i
In case you didn't know. Check it for yourself if you don't believe me.
Last edited by svk1325 on Thu Nov 16, 2006 2:33 am UTC, edited 1 time in total.
"Insanity in a measured dose is a good thing - the difficulty lies in the measurement."

GreedyAlgorithm
Posts: 286
Joined: Tue Aug 22, 2006 10:35 pm UTC
Contact:

Postby GreedyAlgorithm » Thu Nov 16, 2006 2:05 am UTC

phlip wrote:Ok, so what comes next in this sequence:

1, ___


I know this sequence! It is S(n), where S(k) is chosen such that upon seeing S(1)..S(k-1), you'd think the sequence was some recognized sequence X, but after seeing S(k), you'd revise your opinion to think it was the next most recognized sequence. For the purposes of the sequence 1,1,1,1,1,1,1... is defined as more recognized than 1,2,3,4,5,6,7...

Therefore the next number is 2.
GENERATION 1-i: The first time you see this, copy it into your sig on any forum. Square it, and then add i to the generation.

User avatar
Verysillyman
"Do me! Do me!"
Posts: 1442
Joined: Sat Aug 19, 2006 11:25 am UTC
Location: Drinks Cabinet.
Contact:

Postby Verysillyman » Fri Nov 17, 2006 11:18 am UTC

I think the second series is
27, you're adding consecutive primes?

User avatar
no-genius
Seemed like a good idea at the time
Posts: 4221
Joined: Wed May 17, 2006 6:32 pm UTC
Location: UK
Contact:

Postby no-genius » Fri Nov 17, 2006 2:23 pm UTC

GreedyAlgorithm wrote:
phlip wrote:Ok, so what comes next in this sequence:

1, ___


I know this sequence! It is S(n), where S(k) is chosen such that upon seeing S(1)..S(k-1), you'd think the sequence was some recognized sequence X, but after seeing S(k), you'd revise your opinion to think it was the next most recognized sequence. For the purposes of the sequence 1,1,1,1,1,1,1... is defined as more recognized than 1,2,3,4,5,6,7...

Therefore the next number is 2.



:? But surely that makes 2 the most likely next number? So it must be 5
I don't sing, I just shout. All. On. One. Note.
Official ironmen you are free, champions officially

The Mighty Thesaurus wrote:Why? It does nothing to address dance music's core problem: the fact that it sucks.

planck
Posts: 8
Joined: Thu Nov 16, 2006 9:45 am UTC

Postby planck » Fri Nov 17, 2006 11:37 pm UTC

GreedyAlgorithm wrote:I know this sequence! It is S(n), where S(k) is chosen such that upon seeing S(1)..S(k-1), you'd think the sequence was some recognized sequence X, but after seeing S(k), you'd revise your opinion to think it was the next most recognized sequence.
Now that you've posted it, it is a recognised sequence. Call it the K'th most recognised sequence. As you generate terms, you reach some N for which you have eliminated all the more recognised sequences.

What is S(N)?

arecanut0
Posts: 40
Joined: Sat Nov 04, 2006 5:40 pm UTC
Location: MA

Postby arecanut0 » Sat Nov 18, 2006 12:36 am UTC

Buton wrote:Okay so these sequences are messed up... no really they are :D

(if you can find the right number for each, you're awesome)
1. 1, 2, 3, 4, ___
2. 1, 4, 9, 16, ___
3. 1, 2, 4, 8, ___
4. 2, 3, 5, 7, ___


Buton


Why not 1, 2, 3, 4, 1, 2, 3, 4, ... for the first one, for example? :?
"To me, love is a game... like Starcraft." -on some Korean drama/soap

GreedyAlgorithm
Posts: 286
Joined: Tue Aug 22, 2006 10:35 pm UTC
Contact:

Postby GreedyAlgorithm » Mon Nov 27, 2006 9:31 pm UTC

planck wrote:
GreedyAlgorithm wrote:I know this sequence! It is S(n), where S(k) is chosen such that upon seeing S(1)..S(k-1), you'd think the sequence was some recognized sequence X, but after seeing S(k), you'd revise your opinion to think it was the next most recognized sequence.
Now that you've posted it, it is a recognised sequence. Call it the K'th most recognised sequence. As you generate terms, you reach some N for which you have eliminated all the more recognised sequences.

What is S(N)?

You've discovered the hidden beauty of S: it's necessarily of finite length.
GENERATION 1-i: The first time you see this, copy it into your sig on any forum. Square it, and then add i to the generation.


Return to “Logic Puzzles”

Who is online

Users browsing this forum: No registered users and 6 guests