Puzzle - RPL and others

[Allen]

(04-29-2021 05:16 PM)Albert Chan Wrote:  How does the code work ?

In having fun with different ways to calculate the final SSN, I wanted to play around with as simiple an inner loop as possible.

Here's a more simplified 46-byte solution that's a smaller, faster, and clearer

Code:


00 { 46-Byte Prgm }
01 19
02 STO 01
03 2                   
04 STO 00           initialize varibles
05 STO× 01        ensures first 2 digits are multiple of 2
06 ISG 00
07>LBL 01
08 4
09 RCL 00
10 X!=Y?
11 SIGN
12 SQRT
13 RCL× 00     add digit if not equal 4, else add double the digit
14 RCL 01
15 10              multiply by 10
16 ×
17 ENTER
18 ENTER
19 RCL 00
20 MOD          calculate difference to closest multiple of current digit
21 -                
22 +               add difference to running total
23 STO 01       PRX after this line if you want to see the number being constructed
24 ISG 00
25 X<>Y          NOP
26 RCL 00
27 ×
28 LOG
29 9               terminate with 9 digit number
30 X>Y?
31 GTO 01
32 RCL 01       recall the answer
33 .END.

If you take the central part of this code:

Code:


15 RCL 01
16 10
17 ×
18 ENTER
19 ENTER
20 RCL 00
21 MOD
22 -

it assembles (left to right) a number that is divisible by the numbers 3 through 9. Unfortunately the naive way produces a number that is not pan-digital.

Python Example here:

Code:


m=3
for j in range(2,10):
    m*=10
    m+=j-m%j
    print(m)
    
32
321
3212
32125
321252
3212524
32125248
321252489

With a few small corrections during the process one can trick the calculator to produce correct results using the naive algorithm:

Code:


m=38                             <- start with 38
for j in range(3,10):         <-  start with 3
    m*=10
    m+=j-m%j
    if j==4: m+=j              <-  add 4 if current variable is 4 
    print(m)
    
381
3816
38165
381654
3816547
38165472
381654729

(04-29-2021 05:16 PM)Albert Chan Wrote:  Where does the cubic, 19x³ - 9x² - 27x, comes from ?
Why total start at -9 ? Why total + 18 at the end ?

In my initial larger version, I was looking for a correction factor for the naive approach to make the number pandigital without modifying the actual structure of the program.

381654729 - 321252489 = 60402240

As it turns out, adding the results of the polynomial 19x³ - 9x² - 27x for 2<x<10 was within 18 of the final answer. The rest of the rube-goldberg looking code is byte savings by reusing the constants {-27,-9,19} to either initialize variables, create coefficients, or implement the final offset (+18).