Be-logic - Vizualizare solutie

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

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