20081119, 21:09  #1 
May 2004
New York City
1000010001011_{2} 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.) 
20081119, 21:45  #2  
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
12F9_{16} Posts 
Quote:
I assume concatenation means, for example: 9876543210 OR 9876 X 543210. 

20081120, 15:24  #3 
May 2004
New York City
5×7×11^{2} 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 multidigit number are impliciitly concatenated.) 
20081205, 20:39  #4 
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/ 
20081206, 00:33  #5  
Cranksta Rap Ayatollah
Jul 2003
641 Posts 
Quote:
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. 

20081206, 19:05  #6 
Nov 2008
100100010010_{2} Posts 

20081207, 09:18  #7 
"Robert Gerbicz"
Oct 2005
Hungary
1519_{10} Posts 
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 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 20081207 at 09:47 
20090702, 20:21  #8 
May 2004
New York City
5×7×11^{2} Posts 

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