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20 Questions Type Puzzel

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20 Questions Type Puzzel
Sejanus Offline
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#51
RE: 20 Questions Type Puzzel
January 22, 2015 at 12:56 am
1, 2, 1, 2, 4, 7, 12, -3...
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GrandizerII Offline
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#52
RE: 20 Questions Type Puzzel
January 22, 2015 at 8:58 am
(January 22, 2015 at 12:18 am)IATIA Wrote: Interesting, but the first 2 does not really fit in.

How so?
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Jenny A Offline
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#53
RE: 20 Questions Type Puzzel
January 22, 2015 at 11:44 am
(January 22, 2015 at 8:58 am)Irrational Wrote:
(January 22, 2015 at 12:18 am)IATIA Wrote: Interesting, but the first 2 does not really fit in.

How so?

Yes, how so?

The intervals between the numbers are ascending primes times alternating ascending powers of 2 and 3.

6-2=4=2x2
15-6=9=3x3
35-15=20=5x2x2
77-35=42=7x3x3
165-77=88=11x2x2x2
516-165=351=13x3x3x3

1 is the prime before 2 and any number to the power of zero is one. So the difference between 2 and the number before it would be one. Thus
2-1=1=1* (3 to the zero power). So the number in sequence before 2 would be 1.
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IATIA Offline
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#54
RE: 20 Questions Type Puzzel
January 22, 2015 at 12:03 pm
You are right. I guess technically we have three answers to the sequence, albeit not sequential as was my intent, but not wrong either.
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TheRealJoeFish Offline
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#55
RE: 20 Questions Type Puzzel
January 22, 2015 at 1:05 pm
(January 22, 2015 at 11:44 am)Jenny A Wrote:
(January 22, 2015 at 8:58 am)Irrational Wrote: How so?

Yes, how so?

The intervals between the numbers are ascending primes times alternating ascending powers of 2 and 3.

6-2=4=2x2
15-6=9=3x3
35-15=20=5x2x2
77-35=42=7x3x3
165-77=88=11x2x2x2
516-165=351=13x3x3x3

1 is the prime before 2 and any number to the power of zero is one. So the difference between 2 and the number before it would be one. Thus
2-1=1=1* (3 to the zero power). So the number in sequence before 2 would be 1.

7x3x3 = 63, not 42, so your 4th step doesn't hold. But if we just fix that arithmetic error, we get:
2
2+(2*2*1) = 6
6+(3*3*1) = 15
15+(5*2*2) = 35
35+(7*3*2) = 77
77+(11*2*3) = 143
143+(13*3*3)= 260 (which breaks from the p_(n-1)*p_n pattern).

And then you can go

260+(17*2*4) = 396
396+(19*3*4) = 624.

This sequence would be defined as n_0 = 2, n_i = n_(i-1) + (p_i)*(2.5+(.5*(-1)^i))*(ceiling(i/2))

The point, I think, is that if you give a finite sequence portion of a sequence, there are an infinite number of sequences that can follow, if you're creative!

To bookend, the "other" solution, other than 143, was 165.

2
2*2+2 = 6
6*6+3 = 15
15*2+5 = 35
35*2+7 = 77
77*2+11 = 165

and so on!
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GrandizerII Offline
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#56
RE: 20 Questions Type Puzzel
January 22, 2015 at 1:12 pm
(January 22, 2015 at 1:05 pm)TRJF Wrote: To bookend, the "other" solution, other than 143, was 165.

2
2*2+2 = 6
6*6+3 = 15
15*2+5 = 35
35*2+7 = 77
77*2+11 = 165

and so on!

How does the first term fit the sequence in this case? There is no natural prime number before 2.
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TheRealJoeFish Offline
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#57
RE: 20 Questions Type Puzzel
January 22, 2015 at 1:50 pm
(January 22, 2015 at 1:12 pm)Irrational Wrote:
(January 22, 2015 at 1:05 pm)TRJF Wrote: To bookend, the "other" solution, other than 143, was 165.

2
2*2+2 = 6
6*6+3 = 15
15*2+5 = 35
35*2+7 = 77
77*2+11 = 165

and so on!

How does the first term fit the sequence in this case? There is no natural prime number before 2.

The first term being 2? You just have to define it. Each term in the sequence depends on the number before it, but the first term in the sequence by definition doesn't have a number before it. So you've just got to start somewhere.

For instance, the initial 1, 1 doesn't "fit" the Fibonacci sequence. That's just where you start.
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GrandizerII Offline
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#58
RE: 20 Questions Type Puzzel
January 22, 2015 at 5:52 pm
True. Actually, all sequences are like that. Not sure what I was wondering about.
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IATIA Offline
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#59
RE: 20 Questions Type Puzzel
January 22, 2015 at 9:28 pm
(January 22, 2015 at 1:05 pm)TRJF Wrote: To bookend, the "other" solution, other than 143, was 165.

2
2*2+2 = 6
6*2+3 = 15
15*2+5 = 35
35*2+7 = 77
77*2+11 = 165

and so on!
Minor correction, but that is it.
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God has no place within these walls, just as facts have no place within organized religion.
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-- Ned Flanders

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-- The Rev Lovejoy
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20 Questions Type Puzzel

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