Au trimis soluţii corecte: Aurel Ionescu, Zoltan Szabo, Ady Nicolae, Simona Popescu, Horia Ciobanu, Cristian Bălănoiu.

Dintre acestea, am reţinut:

1. Ady Nicolae:

Avem relația:

A + (13*B:C) + D + (12*E) – F – 11 + (G*H:I)  - 10 = 66

Facem notațiile:

E1 = 13*B:C;     E2 = 12*E;      E3 = G*H:I

Obținem:

A + D – F = 87 – (E1 + E2 + E3)

 Să analizăm fiecare expresie în parte:

E1 = 13*B:C

13 este număr prim, deci C=1.       E1 = {26, 39, 52, 65, 78, 91, 104, 117}

 E2 = 12*D.                                     E2 = {24, 36, 48, 60, 72, 84, 96, 108}

 E3 = G*H:I

2*6:4=3, 2*8:4=4, 2*9:3=6, 3*4:2=6, 3*4:6=2, 3*6:9=2, 3*6:2=9, 3*8:6=4, 3*8:4=6, 3*8:2=12, 4*5:2=10, 4*6:3=8, 4*6:3=8, 4*9:6=6, 5*6:3=10, 5*8:4=10, 5*8:2=20, 6*8:2=24, 6*8:4=12, 7*8:2=28, 7*9:3=21, 8*9:2=36, 8*9:3=24

                   A + D – F = 87 – (E1 + E2 + E3)

max (A+D-F) = (9+8-2) = 15

Avem următoarele variante posibile:

A + D – F = 87 – (26 + 36 + E3) = 25 – E3

A + D – F = 87 – (26 + 48 + E3) = 13 – E3

A + D – F = 87 – (26 + 60 + E3) = 1 – E3

A + D – F = 87 – (39 + 24 + E3) = 24 – E3

A + D – F = 87 – (39 + 48 + E3) = E3

A + D – F = 87 – (52 + 24 + E3) = 11 – E3

 Singura variantă posibilă este:

A + D – F = 11 – E3

A + D – F = 11 – 3*8:6

A + D – F = 7

9 + 5 – 7 = 7

 Avem:

A = 9, B = 4, C = 1, D = 5, E = 2, F = 7, G = 3, H = 8, I = 6

9 + 13 * 4 : 1 + 5 + 12 * 2 – 7 – 11 + 3 * 8 : 6 – 10 = 66

 

2. ZoltanSzabo:

Am gasit 84 de solutii.

20 de solutii in care rezultatele impartirilor sunt numere intregi:

  1.  3 + 13 * 2 / 1 + 5 + 12 * 4 - 7 - 11 + 8 * 9 / 6 - 10 = 66
  2.  5 + 13 * 2 / 1 + 3 + 12 * 4 - 7 - 11 + 8 * 9 / 6 - 10 = 66
  3.  3 + 13 * 2 / 1 + 5 + 12 * 4 - 7 - 11 + 9 * 8 / 6 - 10 = 66
  4.  5 + 13 * 2 / 1 + 3 + 12 * 4 - 7 - 11 + 9 * 8 / 6 - 10 = 66
  5.  6 + 13 * 3 / 1 + 9 + 12 * 2 - 5 - 11 + 7 * 8 / 4 - 10 = 66 
  6.  9 + 13 * 3 / 1 + 6 + 12 * 2 - 5 - 11 + 7 * 8 / 4 - 10 = 66
  7.  6 + 13 * 3 / 1 + 9 + 12 * 2 - 5 - 11 + 8 * 7 / 4 - 10 = 66 
  8.  9 + 13 * 3 / 1 + 6 + 12 * 2 - 5 - 11 + 8 * 7 / 4 - 10 = 66
  9.  5 + 13 * 3 / 1 + 7 + 12 * 2 - 6 - 11 + 8 * 9 / 4 - 10 = 66
10.  7 + 13 * 3 / 1 + 5 + 12 * 2 - 6 - 11 + 8 * 9 / 4 - 10 = 66
11.  5 + 13 * 3 / 1 + 7 + 12 * 2 - 6 - 11 + 9 * 8 / 4 - 10 = 66
12.  7 + 13 * 3 / 1 + 5 + 12 * 2 - 6 - 11 + 9 * 8 / 4 - 10 = 66
13.  5 + 13 * 4 / 1 + 9 + 12 * 2 - 7 - 11 + 3 * 8 / 6 - 10 = 66
14.  9 + 13 * 4 / 1 + 5 + 12 * 2 - 7 - 11 + 3 * 8 / 6 - 10 = 66
15.  5 + 13 * 4 / 1 + 9 + 12 * 2 - 7 - 11 + 8 * 3 / 6 - 10 = 66
16.  9 + 13 * 4 / 1 + 5 + 12 * 2 - 7 - 11 + 8 * 3 / 6 - 10 = 66
17.  5 + 13 * 9 / 3 + 6 + 12 * 2 - 1 - 11 + 7 * 8 / 4 - 10 = 66
18.  6 + 13 * 9 / 3 + 5 + 12 * 2 - 1 - 11 + 7 * 8 / 4 - 10 = 66
19.  5 + 13 * 9 / 3 + 6 + 12 * 2 - 1 - 11 + 8 * 7 / 4 - 10 = 66
20.  6 + 13 * 9 / 3 + 5 + 12 * 2 - 1 - 11 + 8 * 7 / 4 - 10 = 66

Alte 64 de solutii in care rezultatele impartilrilor nu sunt numere intregi, dar rezultatul final este de asemenea 66:

21.  7 + 13 * 3 / 2 + 8 + 12 * 5 - 9 - 11 + 1 * 6 / 4 - 10 = 66
22.  8 + 13 * 3 / 2 + 7 + 12 * 5 - 9 - 11 + 1 * 6 / 4 - 10 = 66
23.  1 + 13 * 3 / 2 + 9 + 12 * 5 - 6 - 11 + 4 * 7 / 8 - 10 = 66
24.  9 + 13 * 3 / 2 + 1 + 12 * 5 - 6 - 11 + 4 * 7 / 8 - 10 = 66
25.  7 + 13 * 3 / 2 + 8 + 12 * 5 - 9 - 11 + 6 * 1 / 4 - 10 = 66
26.  8 + 13 * 3 / 2 + 7 + 12 * 5 - 9 - 11 + 6 * 1 / 4 - 10 = 66
27.  1 + 13 * 3 / 2 + 9 + 12 * 5 - 6 - 11 + 7 * 4 / 8 - 10 = 66
28.  9 + 13 * 3 / 2 + 1 + 12 * 5 - 6 - 11 + 7 * 4 / 8 - 10 = 66
29.  1 + 13 * 3 / 2 + 4 + 12 * 5 - 8 - 11 + 7 * 9 / 6 - 10 = 66
30.  4 + 13 * 3 / 2 + 1 + 12 * 5 - 8 - 11 + 7 * 9 / 6 - 10 = 66
31.  1 + 13 * 3 / 2 + 4 + 12 * 5 - 8 - 11 + 9 * 7 / 6 - 10 = 66
32.  4 + 13 * 3 / 2 + 1 + 12 * 5 - 8 - 11 + 9 * 7 / 6 - 10 = 66
33.  7 + 13 * 5 / 2 + 8 + 12 * 4 - 9 - 11 + 1 * 3 / 6 - 10 = 66
34.  8 + 13 * 5 / 2 + 7 + 12 * 4 - 9 - 11 + 1 * 3 / 6 - 10 = 66
35.  7 + 13 * 5 / 2 + 8 + 12 * 4 - 9 - 11 + 3 * 1 / 6 - 10 = 66
36.  8 + 13 * 5 / 2 + 7 + 12 * 4 - 9 - 11 + 3 * 1 / 6 - 10 = 66
37.  1 + 13 * 5 / 2 + 8 + 12 * 4 - 7 - 11 + 3 * 9 / 6 - 10 = 66
38.  8 + 13 * 5 / 2 + 1 + 12 * 4 - 7 - 11 + 3 * 9 / 6 - 10 = 66
39.  1 + 13 * 5 / 2 + 3 + 12 * 4 - 8 - 11 + 7 * 9 / 6 - 10 = 66
40.  3 + 13 * 5 / 2 + 1 + 12 * 4 - 8 - 11 + 7 * 9 / 6 - 10 = 66
41.  1 + 13 * 5 / 2 + 8 + 12 * 4 - 7 - 11 + 9 * 3 / 6 - 10 = 66
42.  8 + 13 * 5 / 2 + 1 + 12 * 4 - 7 - 11 + 9 * 3 / 6 - 10 = 66
43.  1 + 13 * 5 / 2 + 3 + 12 * 4 - 8 - 11 + 9 * 7 / 6 - 10 = 66
44.  3 + 13 * 5 / 2 + 1 + 12 * 4 - 8 - 11 + 9 * 7 / 6 - 10 = 66
45.  1 + 13 * 5 / 3 + 9 + 12 * 4 - 2 - 11 + 7 * 8 / 6 - 10 = 66
46.  9 + 13 * 5 / 3 + 1 + 12 * 4 - 2 - 11 + 7 * 8 / 6 - 10 = 66
47.  1 + 13 * 5 / 3 + 9 + 12 * 4 - 2 - 11 + 8 * 7 / 6 - 10 = 66
48.  9 + 13 * 5 / 3 + 1 + 12 * 4 - 2 - 11 + 8 * 7 / 6 - 10 = 66
49.  7 + 13 * 6 / 4 + 8 + 12 * 5 - 9 - 11 + 1 * 3 / 2 - 10 = 66
50.  8 + 13 * 6 / 4 + 7 + 12 * 5 - 9 - 11 + 1 * 3 / 2 - 10 = 66
51.  3 + 13 * 6 / 4 + 9 + 12 * 5 - 8 - 11 + 1 * 7 / 2 - 10 = 66
52.  9 + 13 * 6 / 4 + 3 + 12 * 5 - 8 - 11 + 1 * 7 / 2 - 10 = 66
53.  7 + 13 * 6 / 4 + 8 + 12 * 5 - 9 - 11 + 3 * 1 / 2 - 10 = 66
54.  8 + 13 * 6 / 4 + 7 + 12 * 5 - 9 - 11 + 3 * 1 / 2 - 10 = 66
55.  3 + 13 * 6 / 4 + 9 + 12 * 5 - 8 - 11 + 7 * 1 / 2 - 10 = 66
56.  9 + 13 * 6 / 4 + 3 + 12 * 5 - 8 - 11 + 7 * 1 / 2 - 10 = 66
57.  5 + 13 * 7 / 2 + 8 + 12 * 3 - 9 - 11 + 1 * 6 / 4 - 10 = 66
58.  8 + 13 * 7 / 2 + 5 + 12 * 3 - 9 - 11 + 1 * 6 / 4 - 10 = 66
59.  5 + 13 * 7 / 2 + 8 + 12 * 3 - 9 - 11 + 6 * 1 / 4 - 10 = 66
60.  8 + 13 * 7 / 2 + 5 + 12 * 3 - 9 - 11 + 6 * 1 / 4 - 10 = 66
61.  1 + 13 * 8 / 3 + 7 + 12 * 4 - 5 - 11 + 2 * 6 / 9 - 10 = 66
62.  7 + 13 * 8 / 3 + 1 + 12 * 4 - 5 - 11 + 2 * 6 / 9 - 10 = 66
63.  1 + 13 * 8 / 3 + 7 + 12 * 4 - 5 - 11 + 6 * 2 / 9 - 10 = 66
64.  7