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Aviso: Este post sólo tiene sentido si has visto el capítulo 18 de Lost

Como bien dice Hugo “Hurley” Reyes: Los números son chungos (The numbers are bad!).

Voy a demostrar que TODOS los números enteros hasta el 108 son chungos, es decir, que se pueden construir usando 4, 8, 15, 16, 23 y 42, sin repetir ninguno de ellos.

1: 16 - 15 = 1
2: 42 + 23 - 16 - 15 - (8 x 4) = 2
3: 15 - (8 + 4) = 3
4: 42 - 23 - 15 = 4
5: (16 + 4) - 15 = 5
6: ((4 x 42) / 8 ) - 15 = 6
7: 15 - 8 = 7
8: 23 - 15 = 8
9: (4 x 8 ) - 23 = 9
10: (15 + 23 + 42)/8 = 10
11: 15 - 4 = 11
12: 4 + 8 = 12
13: (42 - 16) / (8 / 4) = 13
14: (4 x 8 ) - 15 + 16 + 23 - 42 = 14
15: 23 - 8 = 15
16: 4 - 8 - 15 + 16 - 23 + 42 = 16
17: (4 x 8 ) - 15 = 17
18: (4 x 15) - 42 = 18
19: 23 - 4 = 19
20: (4 x 8 ) - 15 - 16 - 23 + 42 = 20
21: (42 x 4) / 8 = 21
22: 15 - 16 + 23 = 22
23: 8 + 15 = 23
24: 8 + 16 = 24
25: 23 + (8 / 4) = 25
26: 42 - 16 = 26
27: 4 + 23 = 27
28: 4 + 8 + 16 = 28
29: (16 + 42) / (8 / 4) = 29
30: 4 - 8 - 15 - 16 + 23 + 42 = 30
31: 8 + 23 = 31
32: 4 x 8 = 32
33: 42 - 16 + 15 - 8 = 33
34: 42 - 8 = 34
35: 4 + 8 + 23 = 35
36: (4 x 15) - (16 + 8 ) = 36
37: (4 x 15) - 23 = 37
38: 15 + 23 = 38
39: 16 + 23 = 39
40: 42 - (8 / 4) = 40
41: (4 x 16) - 23 = 41
42: 4 + 15 + 23 = 42
43: 4 + (8 x 15) - 16 - 23 - 42 = 43
44: (4 x 8 ) + 15 + 16 + 23 - 42 = 44
45: 42 + 15 - 8 - 4 = 45
46: 4 + 42 = 46
47: 8 + 16 + 23 = 47
48: 42 + 23 - 15 - (8 / 4) = 48
49: (4 x 16) - 15 = 49
50: 42 - 23 - 16 + 15 + (8 x 4) = 50
51: 4 + 8 + 16 + 23 = 51
52: (4 x 8 ) - 15 + 16 - 23 + 42 = 52
53: 42 + 15 - 4 = 53
54: 4 + 8 + 42 = 54
55: (8 x 15) - 42 - 23 = 55
56: (4 x 16) - 8 = 56
57: 15 + 42 = 57
58: 16 + 42 = 58
59: (4 x 15) - (8 + 16) + 23 = 59
60: 4 - 8 + 15 - 16 + 23 + 42 = 60
61: 4 + 15 + 42 = 61
62: 4 + 16 + 42 = 62
63: (4 x 15) - (16 + 23) + 42 = 63
64: 4 x 16 = 64
65: 23 + 42 = 65
66: 42 + 23 - 16 - 15 + (8 x 4) = 66
67: 42 + 23 + (8 / 4) = 67
68: 4 + 15 - 16 + 23 + 42 = 68
69: 4 + 23 + 42 = 69
70: (4 x 8 x 15) - (16 x 23) - 42 = 70
71: 42 + 16 + 15 - (8 / 4) = 71
72: (8 x 15 x 23) - (4 x 16 x 42) = 72
73: 15 + 16 + 42 = 73
74: 8 - 15 + 16 + 23 + 42 = 74
75: 4 + (8 x 15) + 16 - 23 - 42 = 75
76: (4 + 8 + 15 + 23 + 42) - 16 = 76
77: 4 + 8 + 23 + 42 = 77
78: (4 + 8 + 16 + 23 + 42) - 15 = 78
79: 42 + 23 + 16 - (8 / 4) = 79
80: 15 + 23 + 42 = 80
81: 16 + 23 + 42 = 81
82: (16 / 8 ) + 15 + 23 + 42 = 82
83: (8 / 4) + 16 + 23 + 42 = 83
84: (8 + 15 + 23 + 42) - 4 = 84
85: 4 + 16 + 23 + 42 = 85
86: (8 x 16) - 42 = 86
87: (4 x 16) + 23 = 87
88: 8 + 15 + 23 + 42 = 88
89: 4 + (8 x 15) - 16 + 23 - 42 = 89
90: (23 x 4) - (16 / 8 ) = 90
91: ((42 - 23) x 4) + 15 = 91
92: 4 + 8 + 15 + 23 + 42 = 92
93: 4 + 8 + 16 + 23 + 42 = 93
94: (23 x 4) + (16 / 8 ) = 94
95: ((23 - 4) x 8 ) - 42 - 15 = 95
96: (4 x 8 ) + 15 - 16 + 23 + 42 = 96
97: (8 x 15) - 23 = 97
98: (4 x 8 ) - 15 + 16 + 23 + 42 = 98
99: (4 x 15) + 16 + 23 = 99
100: 4 + 15 + 16 + 23 + 42 = 100
101: (8 x 16) - 4 - 23 = 101
102: (4 x 16) + 15 + 23 = 102
103: ((23 - 8 ) x 4) + 42 + 16 - 15 = 103
104: 8 + 15 + 16 + 23 + 42 = 104
105: (8 x 16) - 23 = 105
106: ((42 - 15) x 4) - (16 / 8 ) = 106
107: (4 x 23) + 15 = 107
108: 4 + 8 + 15 + 16 + 23 + 42 = 108

Naturalmente, algunos números se pueden calcular de más de una manera, he tendido a escoger la más sencilla aritméticamente o la que utilize los 6 números.

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