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Old 2008-11-19, 21:09   #1
davar55
 
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Default How Many Numbers

Using all ten digits 0 thru 9 exactly once each,
and the operations addition, multiplication, concatenation,
(and parenthesization),
how many different numbers (values) can be formed?

(I left out exponentiation because the values get too large.)
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Old 2008-11-19, 21:45   #2
petrw1
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Quote:
Originally Posted by davar55 View Post
Using all ten digits 0 thru 9 exactly once each,
and the operations addition, multiplication, concatenation,
(and parenthesization),
how many different numbers (values) can be formed?

(I left out exponentiation because the values get too large.)
Did you intentionally leave out Subtraction and Division?
I assume concatenation means, for example: 9876543210
OR 9876 X 543210.
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Old 2008-11-20, 15:24   #3
davar55
 
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I left out subtraction and division to avoid negatives and messy fractions,
which don't concatenate well. By concatenation I just mean the operation
(say, #) that takes two integers (say A=aaaa and B=bbb) and forms the
integer A#B with digits aaaabbb. For this problem, for example,
(1*2+4+(5+6)*3+7)#(8+90) = (46)#(98) = 4698.
(The digits within a multi-digit number are impliciitly concatenated.)
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Old 2008-12-05, 20:39   #4
uigrad
 
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I found a version of this puzzle that is less computational, and may be more fun for the average person:

http://www.stetson.edu/~efriedma/plustimes/
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Old 2008-12-06, 00:33   #5
Orgasmic Troll
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Quote:
Originally Posted by davar55 View Post
Using all ten digits 0 thru 9 exactly once each,
and the operations addition, multiplication, concatenation,
(and parenthesization),
how many different numbers (values) can be formed?

(I left out exponentiation because the values get too large.)
A lot.

There are already 10! - 9! = 3,265,920 just from taking 10 digit numbers

A (x/+) AAAAAAAAA
AA (x/+) AAAAAAAA
AAA (x/+) AAAAAAA
AAAA (x/+) AAAAAA
AAAAA (x/+) AAAAA

gives us 36 * 9! = 26,127,360 different equations

and it'll just get crazier from there.
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Old 2008-12-06, 19:05   #6
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Quote:
Originally Posted by Orgasmic Troll View Post
it'll just get crazier from there.
I certainly agree.
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Old 2008-12-07, 09:18   #7
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Quote:
Originally Posted by davar55 View Post
how many different numbers (values) can be formed?
Using the first L nonnegative integer numbers I've gotten:
Code:
f(1)=1
f(2)=3
f(3)=11
f(4)=70
f(5)=554
f(6)=5322
f(7)=57627
f(8)=712657
f(9)=9162463
So for example L=3 means using 0,1,2 and we can form f(3)=11 different numbers
Is it a good table? If yes I can post my program (I'm unable to compute f(10), so the original problem, because that would require 2GB or more RAM).

Last fiddled with by R. Gerbicz on 2008-12-07 at 09:47
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Old 2009-07-02, 20:21   #8
davar55
 
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Quote:
Originally Posted by 10metreh View Post
I certainly agree.
Depends on what you mean by crazier.

Exponential explosion is kinda crazy-weird, isn't it?
But if P=NP (and if you think about it ...),
doesn't that make things look a bit saner?

And don't say it depends on how you define sane.
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