## Cuckoo's Egg Series

A forum for good logic/math puzzles.

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nuggetmonkey
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### Cuckoo's Egg Series

#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.

hermaj
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### Re: Cuckoo's Egg Series

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...

Gelsamel
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### Re: Cuckoo's Egg Series

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

Verysillyman
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### Re: Cuckoo's Egg Series

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.

Gelsamel
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### Re: Cuckoo's Egg Series

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

Owned

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

Who's up for some math?

yy2bggggs
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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
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### Re: Cuckoo's Egg Series

nuggetmonkey wrote:#2 What comes next in the series

1 11 21 1211 111221 ______

OEIS says there are at least three sensical continuations.
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Gelsamel
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I don't see how

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

Is sensical at all.

ulnevets
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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.

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

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

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

(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

Kizyr
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### Re: Cuckoo's Egg Series

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

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

(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.

Kizyr
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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

Buton
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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

SpitValve
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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
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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]

phlip
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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]

no-genius
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phlip wrote:Ok, so what comes next in this sequence:

1, ___

5
I don't sing, I just shout. All. On. One. Note.
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The Mighty Thesaurus wrote:Why? It does nothing to address dance music's core problem: the fact that it sucks.

svk1325
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phlip wrote:Ok, so what comes next in this sequence:

1, ___

1.0707106... + .070106... i

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

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.
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GreedyAlgorithm
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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.

Verysillyman
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I think the second series is

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

(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
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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.