Solving a simple addition / multiplication puzzle.

[case2001]

(02-18-2024 04:36 AM)Albert Chan Wrote:  Before solving puzzle, I checked if AM ≥ GM

AM(a,b,c,d) = 7.11/4 ≈ 1.78
GM(a,b,c,d) = ⁴√(7.11) ≈ 1.63

AM ≥ GM --> solution is possible.

(02-18-2024 03:49 AM)Johnh Wrote:  What is the significance of your first line?

If we use units of pennies, we are really searching for integer solution.

A + B + C + D = 711
A * B * C * D = 711 * 10^6 = 79 * 9 * 10^6

79 is a prime number, must go in one of the variable, I just put it in A

B + C + D = 711 - 79k
k * B * C * D = (9 * 10^6)

(B, C, D) must be divisors of (9 * 10^6)

Could you explain why 79 must be one of the values? I cannot find the answer.

Thank you

Patrick