Suppose you have a function (or a magic ball) that is capable of producing a totally random integer between 1 and 5 (inclusive).
Using this, how would you generate a random number (also an integer) between 1 and 7 (inclusive)? (Note that the for the number to be random, all integers between 1 and 7 must have an equal chance of being generated)
Assume that using your 1-5 generator is pretty time-consuming, so you want to minimize the number of times you are going to use it.
Use RAND5() to generate a binary number like this:
BINARY():
repeat
let B = RAND5()
until B<5
if B=1 or 2, return 0; else, return 1
This BINARY() function does, on the average, 5/4ths calls to RAND5().
You can construct the desired function as
RANDOM_1_TO_7():
return BINARY() + 2*BINARY() + 4*BINARY()
which requires three calls to BINARY(), and thus 15/4ths calls to RAND5().
A binary solution
