Expand a random range from 1–5 to 1–7

Question

Given a function which produces a random integer in the range 1 to 5, write a function which produces a random integer in the range 1 to 7.

1. What is a simple so

Answer 1

The following produces a uniform distribution on {1, 2, 3, 4, 5, 6, 7} using a random number generator producing a uniform distribution on {1, 2, 3, 4, 5}. The code is messy, but the logic is clear.

public static int random_7(Random rg) {
    int returnValue = 0;
    while (returnValue == 0) {
        for (int i = 1; i <= 3; i++) {
            returnValue = (returnValue << 1) + SimulateFairCoin(rg);
        }
    }
    return returnValue;
}

private static int SimulateFairCoin(Random rg) {
    while (true) {
        int flipOne = random_5_mod_2(rg);
        int flipTwo = random_5_mod_2(rg);

        if (flipOne == 0 && flipTwo == 1) {
            return 0;
        }
        else if (flipOne == 1 && flipTwo == 0) {
            return 1;
        }
    }
}

private static int random_5_mod_2(Random rg) {
    return random_5(rg) % 2;
}

private static int random_5(Random rg) {
    return rg.Next(5) + 1;
}