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abc
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Sequence of Numbers Puzzle
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Sep 25 22:30 UTC 2000 |
[this is circulating at work; have fun!]
What is the missing number in the following sequence: 10, 11, 12, 13, 14,
15, 16, 17, 20, 22, 24, 31, 100, ------, 10000 (Hint: The missing number
is in ternary notation)
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| 65 responses total. |
other
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response 1 of 65:
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Sep 26 03:49 UTC 2000 |
I've never heard of ternary notation, but if you'll enighten me, I'll make
a stab at it.
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gelinas
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response 2 of 65:
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Sep 26 03:59 UTC 2000 |
"Ternary" means "in three elements, parts or divisions; using three as the
base."
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other
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response 3 of 65:
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Sep 26 05:01 UTC 2000 |
Okay, then. Color me clueless...
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janc
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response 4 of 65:
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Sep 26 06:07 UTC 2000 |
121
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janc
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response 5 of 65:
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Sep 26 06:10 UTC 2000 |
View hidden response.
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aruba
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response 6 of 65:
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Sep 26 14:56 UTC 2000 |
Very clever.
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mooncat
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response 7 of 65:
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Sep 26 18:48 UTC 2000 |
tricky...
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other
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response 8 of 65:
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Sep 28 02:02 UTC 2000 |
anyone care to explain it to those of us too burnt to put any real brain into
figuring it out?
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edina
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response 9 of 65:
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Sep 28 02:04 UTC 2000 |
Or for those of us not mathematically gifted?
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mcnally
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response 10 of 65:
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Sep 28 02:34 UTC 2000 |
At the "Respond, pass, forget, quit?" prompt (if using Picospan)
try the following commands:
set noforget
only 5
set forget
That will allow you to see the hidden text in Jan's spoiler in
response #5..
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senna
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response 11 of 65:
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Sep 28 04:58 UTC 2000 |
Hmm. I see. I still dont' get it. Comes from not taking a math class in
four years.
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gelinas
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response 12 of 65:
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Sep 28 05:18 UTC 2000 |
No, it's not math. Look at the relationships in column two.
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mcnally
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response 13 of 65:
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Sep 28 05:29 UTC 2000 |
OK -- a quick introduction to numbers.. The numbers most of us are used to
using are written in base 10 notation -- that means that there's a factor
of ten difference between any two adjoining digits and that within a digit
position there are ten possible values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9..
When we write a whole number in any base, the convention is for the
rightmost digit place to represent the digit times the base raised to
the zeroth power, the next digit to the left is multiplied times the
base to the first power, and so on, with each digit going leftwards
multiplied times the base raised to an increasing power.
The thing is, having each digit represent a power of ten is just a
convention -- there's no reason it has to be ten at all.. It's most
likely ten because that's the number of digits most of us humans have
on our hands, but had we, as a species, had six fingers on each hand
we might well be counting by twelves and not tens.. (In fact, those
who grew up around the same time I did may have fond memories of being
introduced to the concept of alternate bases by a Saturday morning
"Schoolhouse Rock" cartoon dealing with just that idea.
Anyway, let's take the number "128" as an example.
When we write it in base 10, we write it as "129" because it is:
9 times ten to the zeroth power (9 times 1 ), plus
2 times ten to the first power (two times decimal 10 ), plus
1 times ten to the second power (1 times decimal 100)..
We could just as easily write it in any other base.. If we choose to
write it in base 16 (which is called "hexadecimal, and is a base frequently
used by computer programmers) we would write that number as "80" because
it is:
1 times sixteen to the zeroth power (eight times 1), plus
8 times sixteen to the first power (eight times decimal 16)..
If we wanted to write it in base 8 it would be "201":
1 times eight to the zeroth power (1 times 1), plus
0 times eight to the first power (0 times 8), plus
2 times eight to the second power (2 times decimal 64)..
If you recompute the numbers written in different bases, as Jan did in #5,
you'll figure out why the missing number is 121..
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jor
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response 14 of 65:
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Sep 28 20:57 UTC 2000 |
what a strage series that is
is there a name for it
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rcurl
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response 15 of 65:
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Sep 29 16:40 UTC 2000 |
Seems to me it is just an "invention". I don't see how such a type
of series would arise in nature (not that it has to - just an observation),
and it also becomes ill defined for n < 2.
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brighn
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response 16 of 65:
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Sep 29 16:58 UTC 2000 |
For that matter, it's arbitrary that it's restricted to integers. ;}
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mcnally
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response 17 of 65:
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Sep 29 21:15 UTC 2000 |
Also, the "interestingness" of this sequence is mostly related to its
appearance when written in our number system, which is merely a convention.
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lelande
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response 18 of 65:
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Oct 2 02:37 UTC 2000 |
GOLGO13 IS HERE TO FUCK MEN
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bobcat
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response 19 of 65:
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Oct 2 06:08 UTC 2000 |
In base 17 the term would be "G".
What would it be in base 1?
answer follows
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gelinas
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response 20 of 65:
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Oct 2 06:10 UTC 2000 |
I can't count in base 1. :( In base ten, it's 16.
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bobcat
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response 21 of 65:
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Oct 2 06:10 UTC 2000 |
View hidden response.
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brighn
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response 22 of 65:
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Oct 2 14:09 UTC 2000 |
Base 1 is "just a convention" ... then again, all bases are.
But then, base 1 (as you call it) doesn't function the same way that all the
other bases do; "Base 1" (outside of what you call it) is nonsensical... the
rightmost position would represent 1^0, the next would represent 1^1, then
1^2, then 1^3, and so forth... you'd never get above 1.
In base 14.5, it's 11/ (using / to represent ".5" in an integer position).
But then we'd be getting silly. =}
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mcnally
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response 23 of 65:
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Oct 2 17:32 UTC 2000 |
Nah.. You're not getting really silly until you start using imaginary
bases..
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brighn
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response 24 of 65:
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Oct 2 17:42 UTC 2000 |
So how would one depict 16 in base i?
=}
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