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Topic: Next Number? (Read 854 times) |
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ThudnBlunder
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Next Number?
« on: Oct 15th, 2004, 6:15am » |
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Which number comes next?
10, 9, 60, 90, 70, 66, ?
a) 96
b) 10100
c) Either of the above
d) None of the above
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| « Last Edit: Oct 15th, 2004, 10:56am by ThudnBlunder » |
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DeMark
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Re: Next Number?
« Reply #1 on: Oct 15th, 2004, 10:39am » |
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I'd say a) 96, but I don't know how to read b). Someone to tell me?
If I got it right, then this would work the same way: 2, 4, 50, 20, 16, 61. (With the same answers)
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| « Last Edit: Oct 15th, 2004, 10:43am by DeMark » |
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ThudnBlunder
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Re: Next Number?
« Reply #2 on: Oct 15th, 2004, 10:56am » |
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Quote:but I don't know how to read b). Someone to tell me?
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10100 = 100000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000
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Icarus
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Re: Next Number?
« Reply #3 on: Oct 15th, 2004, 6:13pm » |
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More generally, an means n copies of the number a multiplied together. So we have
101 = 10
102 = 10[times]10 = 100
103 = 10[times]10[times]10 = 1,000
104 = 10[times]10[times]10[times]10 = 10,000
...
10100 = 1000...(100 zeros)...000
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TenaliRaman
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Re: Next Number?
« Reply #4 on: Oct 17th, 2004, 10:45am » |
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Constructing a simple BDT,
10 9 60 90 70 66 | 290
1 -51 -30 20 4 | -224
52 -21 -50 16 | 228
73 29 -66 | -212
44 95 | 146
-51 | -51
extrapolating the next term i get 290
so i choose d 
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Emul P Edmon
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Re: Next Number?
« Reply #5 on: Oct 24th, 2004, 10:36am » |
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I'd say (c) either, but then again I'm not seeing this as a mathematical problem, but rather, that there are two solutions that follow lexically. Why? (Just count the number of letters in each number when spelled-out - ninety-six or one-googol ) 
edited by Icarus to hide the solution
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| « Last Edit: Oct 25th, 2004, 3:27pm by Icarus » |
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John_Gaughan
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Re: Next Number?
« Reply #6 on: Oct 25th, 2004, 8:35am » |
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Emul, that is an interesting solution. It threw me off too because I always look for mathematical, not linguistical, solutions. I usually get problems such as these wrong for that reason.
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Emul P Edmon
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Re: Next Number?
« Reply #7 on: Oct 25th, 2004, 4:16pm » |
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I'm also guessing that I'm wrong... But I want to hear from THUDandBLUNDER.
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ThudnBlunder
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Re: Next Number?
« Reply #8 on: Oct 25th, 2004, 9:47pm » |
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on Oct 25th, 2004, 4:16pm, Emul P Edmon wrote:| I'm also guessing that I'm wrong... But I want to hear from THUDandBLUNDER. |
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No, you are right - although Sloane gives only a).
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coolnfundu
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Re: Next Number?
« Reply #9 on: Nov 10th, 2004, 10:25pm » |
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ok no linguistics involved I think in this new sequence ...
1, 4, 16, 64, ?
options
a) 512
b) 256
c) 128
d) 75
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| « Last Edit: Nov 10th, 2004, 10:38pm by coolnfundu » |
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Three Hands
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Re: Next Number?
« Reply #10 on: Nov 11th, 2004, 7:06am » |
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I'd opt for b)
:: simple sequence of multiplying the previous number by 4, I believe... ::
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coolnfundu
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Re: Next Number?
« Reply #11 on: Nov 11th, 2004, 7:13am » |
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well according to a series 512 is the answer depending upon some memory thingie in computers 
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ThudnBlunder
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Re: Next Number?
« Reply #12 on: Nov 11th, 2004, 9:32am » |
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Quote:| :: simple sequence of multiplying the previous number by 4, I believe... :: |
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There is no logical reason why one should prefer
xn = 4xn-1
to
xn = xn-1*xn-2
except that it might take up less memory in those computer thingies.
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| « Last Edit: Nov 11th, 2004, 9:49pm by ThudnBlunder » |
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rmsgrey
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Re: Next Number?
« Reply #13 on: Nov 11th, 2004, 11:00am » |
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on Nov 11th, 2004, 9:32am, THUDandBLUNDER wrote:
There is no logical, let alone a philosophical (...snigger), reason why one should prefer
xn = 4xn-1
to
xn = xn-1*xn-2
except that it might take up less memory in those computer thingies.
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And they give two different sequences: 1, 4, 16, 64... and 1, 4, 4, 16, 64...
Oh, and having two initial conditions rather than one feels like a good reason to not prefer the latter. Otherwise, there's no logical reason not to be the sequence xn=SUM (1<=i<=5) (xn-i) with initial conditions 1, 4, 16, 64, x5 where the 5th term can be whatever you want...
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ThudnBlunder
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Re: Next Number?
« Reply #14 on: Nov 11th, 2004, 9:31pm » |
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Quote:| And they give two different sequences: 1, 4, 16, 64... and 1, 4, 4, 16, 64... |
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Yes, I don't know what I was thinking of. 
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Grimbal
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Re: Next Number?
« Reply #15 on: Nov 12th, 2004, 12:16am » |
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Another alternative:
1, 4, 16, 64, 111, 114, 116, 164, 121, 214, ...
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coolnfundu
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Re: Next Number?
« Reply #16 on: Nov 15th, 2004, 10:29pm » |
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ok here is another series
0, 1, 1, -5 ....
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