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 2008-11-19, 21:09 #1 davar55     May 2004 New York City 10000100010112 Posts 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.)
2008-11-19, 21:45   #2
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

12F916 Posts

Quote:
 Originally Posted by davar55 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.

 2008-11-20, 15:24 #3 davar55     May 2004 New York City 5×7×112 Posts 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.)
 2008-12-05, 20:39 #4 uigrad     Aug 2008 2·43 Posts 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/
2008-12-06, 00:33   #5
Orgasmic Troll
Cranksta Rap Ayatollah

Jul 2003

641 Posts

Quote:
 Originally Posted by davar55 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.

2008-12-06, 19:05   #6
10metreh

Nov 2008

1001000100102 Posts

Quote:
 Originally Posted by Orgasmic Troll it'll just get crazier from there.
I certainly agree.

2008-12-07, 09:18   #7
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

151910 Posts

Quote:
 Originally Posted by davar55 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

2009-07-02, 20:21   #8
davar55

May 2004
New York City

5×7×112 Posts

Quote:
 Originally Posted by 10metreh 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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