Solving a simple addition / multiplication puzzle.

[deachp]

Hello,
It's an underdetermined system of 4 variables and two equations, therefore it has infinitely many solutions. If the goal is to obtain positive values with two decimal points, one can combine a quadratic equation, divisor calculation, and filtering out negative numbers and rational numbers. Here, I've developed a program for the 50G calculator that could be ported to the HP Prime:

«
711 0 0 0 0 0 0 -> P a b c d ldivis ldivis2
«
4 P * 1000000 * DIVIS 'ldivis' STO
1 ldivis SIZE FOR i
ldivis i GET 'a' STO
4 P * a / DIVIS 'ldivis2' STO

1 ldivis2 SIZE FOR j
ldivis2 j GET 'b' STO

IF '((a+b)-P)^2' ->NUM '4*P*1000000/(a*b)' ->NUM >= THEN

IF '((P-(a+b))+SQRT(((a+b)-P)^2-4*P*1000000/(a*b)))/2' ->NUM DUP FP 0 == THEN

'c' STO
'P-c-a-b' EVAL 'd' STO

IF a 0 > b 0 > AND c 0 > AND d 0 > AND THEN

a I->R 100 / "a" ->TAG
b I->R 100 / "b" ->TAG
c I->R 100 / "c" ->TAG
d I->R 100 / "d" ->TAG

END
ELSE DROP
END
END
NEXT
NEXT
»
»

SQRT: Square root symbol
-> : Arrow

a:1.25
b:3.16
c:1.5
d:1.2

It takes 20 sec., to emulator in "Authentic Calculator Speed" mode, to found the answers. It can be optimized.

-Dante Aroní C.