find random number between 1-7

Question:
Given a random number generator say r(5) generates number between 1-5 uniformly at random , use it to in r(7) which should generate a random number between 1-7 uniformly at random.


Solution:

int rand7() //random number from 1 - 7
{
    int r = 0;
    do
    {
       int a = rand(5) - 1; //uniformly at random from 0 to 4
       int b = rand(5) - 1;  //uniformly at random from 0 to 4
       r = 5*b + a;  //uniformly at random from 0 to 24
    }
    while (r >= 21); // in this event, we have to roll again
   //postcondition of loop: we have a number uniformly at random between 0 and 20

return r % 7 + 1; 



//there are 3 numbers in [0, 20] for each possible return value

//so each has equal probability.      

} 







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