Puzzle - RPL and others

[Albert Chan]

(04-28-2021 08:45 PM)Allen Wrote:  I propose a 63 Byte solution for 41c/42s with a slight rube-goldberg look to the code to minimize size, but maintains divisibility throughout.
...
running total starts with -9 for various reasons
...

Hi, Allen

How does the code work ?
I do not see any search, and the loop is basically counting digits.

To understand it, I translate to Lua, trying to simplify as much as possible

Code:

function puzzle() 
    local a, b, c, total = 19, -9, -27, -9
    for x = 3, 9 do
        local y = ((a*x + b)*x + c)*x   -- horner([a,b,c], x)
        total = total * 10
        total = (total - total%x) + y   -- x divides total
        print(x, y, total)
    end
    return total + 18
end

lua> puzzle()
3      351       261
4      964       3572
5      2015     37735
6      3618     380964
7      5887     3815525
8      8936     38164184
9      12879   381654711
381654729

Where does the cubic, 19x³ - 9x² - 27x, comes from ?
Why total start at -9 ? Why total + 18 at the end ?