Solving a simple addition / multiplication puzzle.

[Albert Chan]

711 = 79 * 9 --> a = 0.79k, for positive integer k

b+c+d = 7.11 - 0.79k
k*b*c*d = 9.

9*10^6, divisors ≥ 100: 100,120,125,144,150,160,180,192,200,225,240,250,288,300, ...

k=1:
b+c+d = 6.32
b*c*d = 9

9 ≈ 3.00 * 1.732 * 1.732 --> sum of factors ≈ 6.46, too high
9 ≈ 2.88 * 1.768 * 1.768 --> sum of factors ≈ 6.42, again too high
9 ≈ 2.50 * 1.897 * 1.897 --> sum of factors ≈ 6.29, possible
9 = 2.50 * 2.00 * 1.80 --> sum of factors = 6.30
9 = 2.50 * 2.25 * 1.60 --> sum of factors = 6.35 --> 2.5 no good
9 ≈ 2.40 * 2.25 * 1.667 --> sum of factors ≈ 6.317
9 ≈ 2.40 * 2.40 * 1.563 --> sum of factors ≈ 6.363 --> 2.4 no good
9 ≈ 2.25 * 2.25 * 1.778 --> sum of factors < 6.317, can't get higher, k=1 no good

We still do sum of factors, even for fractional pennies, so that we know when to stop.

k=4 give the first solution:

3.16 + 1.50 + 1.25 + 1.20 = 7.11
3.16 * 1.50 * 1.25 * 1.20 = 7.11