Sum of roll of N dice

[Thomas Klemm]

(05-02-2018 07:01 AM)Jim Horn Wrote:  So, just find a random number from 0 to (6^N)-1, convert to base 6, add the sum of its digits plus N (to correct the "subtract 1 from each digit") and there you go: the sum of the six rolled dice with only one random number generation.

We don't really need to convert to base 6 if we only want the sum of the digits.
Here's a small program for the HP-42S:

Code:

6
RCL ST Y
Y↑X
RAN
×
IP
+
0
LASTX
LBL 00
X=0?
GTO 01
6
÷
IP
+
LASTX
GTO 00
LBL 01
R↓
5
×
−

Just enter N and it calculates the sum.

The program works similar to the Base Conversion but instead of multiplying the digits by powers of 10 they are just added.

Let's assume we want to calculate the digits of the number 137₁₀ = 345₆.
So we divide 137 consecutively by 6 and get 22 and then 3.
This allows to represent the digits as:

Code:

5 = 137 - 6 · 22
4 = 22 - 6 · 3
3 = 3

The sum of the digits is then:

Code:

5 + 4 + 3 = 137 - 5 · 22 - 5 · 3 = 137 - 5(22 + 3) = 12

Thus we don't have to calculate the remainder after the division by 6.