[Date Index]
[Thread Index]
[Author Index]
# Re: A Monte Carlo Simulation with loop structure
In response to Daniel Sanders, I wrote:
>> a 9 seemed to come up less often a 10 supposedly in the experience of
>> gamblers.
>One way to check this is to use ReplaceList:
>
> In[1]:= ReplaceList[Range[6], {___, a_, ___, b_, ___, c_, ___} :>
> {a, b, c} /; a + b + c == 9]
>
> Out[1]= {{2, 3, 4}, {1, 3, 5}, {1, 2, 6}}
>
> In[2]:= ReplaceList[Range[6], {___, a_, ___, b_, ___, c_, ___} :>
> {a, b, c} /; a + b + c == 10]
>
> Out[2]= {{2, 3, 5}, {1, 4, 5}, {1, 3, 6}}
Reading the question properly shows that I have not answered the
question. One method (using an exhaustive search via pattern-matching)
to compute the number of ways that sums of 9 and 10 can arise is as
follows:
In[1]:= ReplaceList[Table[Range[6],{3}],
{{___, a_, ___},{___,b_, ___},{___,c_, ___}} :>
{a, b, c} /; a + b + c == 9]//Length
Out[1]= 25
In[2]:= ReplaceList[Table[Range[6],{3}],
{{___, a_, ___},{___,b_, ___},{___,c_, ___}} :>
{a, b, c} /; a + b + c == 10]//Length
Out[2]= 27
Hence there are two more ways that sum to 10 (because summing to 9
includes the triple {3,3,3}).
An exhaustive search can be avoided as follows: e.g., use Table to
construct all ways with sum 9:
Table[{i,j,9-i-j},{i,6},{j,Max[1,9-i-6],Min[6,9-i-1]}]
Cheers,
Paul
____________________________________________________________________
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia Nedlands WA 6907
mailto:paul@physics.uwa.edu.au AUSTRALIA
http://www.pd.uwa.edu.au/~paul
God IS a weakly left-handed dice player
____________________________________________________________________
Prev by Date:
**Re: Evaluate In Place**
Next by Date:
**Re: A Monte Carlo Simulation with loop structure**
Prev by thread:
**A Monte Carlo Simulation with loop structure**
Next by thread:
**Re: A Monte Carlo Simulation with loop structure**
| |