From 5 dice rolls, generate a random number in the range [1 - 100]

Question

I was going through some coding exercises, and had some trouble with this question:

From 5 dice (6-sided) rolls, generate a random number in the range [1 - 100].

I implemented the following method, but the returned number is not random (called the function 1,000,000 times and several numbers never show up in 1 - 100).

public static int generator() {

     Random rand = new Random();
     int dices = 0;

     for(int i = 0; i < 5; i++) {
         dices += rand.nextInt(6) + 1;
     }

     int originalStart = 5;
     int originalEnd = 30;
     int newStart = 1;
     int newEnd = 100;

     double scale = (double) (newEnd - newStart) / (originalEnd - originalStart);
     return (int) (newStart + ((dices - originalStart) * scale));
}

Answer 1

Ok, so 5 dice rolls, each with 6 options. if they are un-ordered you have a range of 5-30 as mentioned above - never sufficient for 1-100.

You need to assume an order, this gives you a scale of 1,1,1,1,1 - 6,6,6,6,6 (base 6) assuming 1 --> 0 value, you have a 5 digit base 6 number generated. As we all know 6^5 = 7776 unique possibilities. ;)

For this I am going to give you a biased random solution.

int total = 0;
int[] diceRolls;
for (int roll : diceRolls) {
    total = total*6 + roll - 1;
}

return total % 100 + 1;

thanks to JosEdu for clarifying bracket requirement

Also if you wanted to un-bias this, you could divide range by the maxval given in my description above, and subsequently multiply by your total (then add offset), but you would still need to determine what rounding rules you used.