Function to solve a simple combinatorial maths puzzle from the command line

marbles () { c=''; for i in $(seq $1); do c+='{b,r}'; done; x=$(eval echo $c); p=''; for i in $(seq $2); do p+='b*r'; done; y=$(grep -wo "${p}b*" <<< $x); wc -l <<< "$y"; grep -vc 'rr' <<< "$y"; }
Suppose you have 11 marbles, 4 of which are red, the rest being blue. The marbles are indistinguishable, apart from colour. How many different ways are there to arrange the marbles in a line? And how many ways are there to arrange them so that no two red marbles are adjacent? There are simple mathematical solutions to these questions, but it's also possible to generate and count all possibilities directly on the command line, using little more than brace expansion, grep and wc! The answer to the question posed above is that there are 330 ways of arranging the marbles in a line, 70 of which have no two red marbles adjacent. See the sample output. To follow the call to marbles 11 4: after c=''; for i in $(seq $1); do c+='{b,r}'; done;, $c equals {b,r}{b,r}{b,r}{b,r}{b,r}{b,r}{b,r}{b,r}{b,r}{b,r}{b,r} After x=$(eval echo $c), and brace expansion, $x equals bbbbbbbbbbb bbbbbbbbbbr ... rrrrrrrrrrb rrrrrrrrrrr, which is all 2^11 = 2048 strings of 11 b's and r's. After p=''; for i in $(seq $2); do p+='b*r'; done;, $p equals b*rb*rb*rb*r Next, after y=$(grep -wo "${p}b*" Finally, grep -vc 'rr'
Sample Output
$ marbles 11 4
330
70
$ marbles 15 5
3003
462
marbles 5 2
10
6

-4
By: quintic
2010-08-27 23:04:33

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