Conforme anunciamos no post " O problema dos Cinco Cincos ", publicamos a seguir a solução completa.
Conforme anunciamos no post "O problema dos Cinco Cincos", publicamos a seguir a solução completa.
Segue a relação das expressões que se utilizam de apenas 5 numerais 5 para resultar nos números de 1 a 100.
[Via BBA]
Segue a relação das expressões que se utilizam de apenas 5 numerais 5 para resultar nos números de 1 a 100.
1
| ( 5 / 5 ) x 55-5 | = 1 |
2
| ( 5 / 5 ) + 55-5 | = 2 |
3
| ( 5 / 5 ) + ( 5+5 ) / 5 | = 3 |
4
| 5 - ( 5 / 5 ) x ( 5 / 5 ) | = 4 |
5
| 55 / 55 x ( 5 ) | = 5 |
6
| 5 + ( 5 / 5 ) x ( 5 / 5 ) | = 6 |
7
| 5 + ( 5 / 5 ) + ( 5 / 5 ) | = 7 |
8
| 5 + 5 – [ ( 5 +5 ) / 5 ] | = 8 |
9
| 5+ 5 – 55-5 | = 9 |
10
| 5+5 x 55-5 | = 10 |
11
| 5 + 5 + 55-5 | = 11 |
12
| 5 + 5 + ( 5 +5 ) / 5 ] | = 12 |
13
| 5? – ( 5 / 5 + 5 / 5 ) | = 13 |
14
| 5? - ( 55 / 55 ) | = 14 |
15
| 5? x ( 55 / 55 ) | = 15 |
16
| 5? + ( 55 / 55 ) | = 16 |
17
| 5? + ( 5 / 5 + 5 / 5 ) | = 17 |
18
| 5? + ( 5 + 5 + 5 ) / 5 ] | = 18 |
19
| 5? +5 – 55-5 | = 19 |
20
| 5? + 5 x 55-5 | = 20 |
21
| ( 5 x 5 ) - [ 5 – ( 5 / 5 ) ] | = 21 |
22
| ( 5? + 5 ) + ( 5+5 ) / 5 | = 22 |
23
| ( 5! - 5 ) / 5 x ( 5 / 5 ) | = 23 |
24
| ( 5? + 5? ) – ( 5 - 5 / 5 ) | = 24 |
25
| ( 5? + 5? ) – ( 5 x 5 / 5 ) | = 25 |
26
| ( 5? + 5? ) – ( 5 – 5 / 5 ) | = 26 |
27
| ( 5! + 5? ) / 5 x ( 5 / 5 ) | = 27 |
28
| ( 5? + 5? ) – [ ( 5+5 ) / 5 ] | = 28 |
29
| ( 5? + 5? ) - 55-5 | = 29 |
30
| ( 5? +5? ) x 55-5 | = 30 |
31
| ( 5? + 5? ) + 55-5 | = 31 |
32
| ( 5? + 5? ) + [ ( 5+5 ) / 5 ] | = 32 |
33
| ( 5! + 5? + 5? +5? ) / 5 | = 33 |
34
| 5? + 5? + [ ( 5 – ( 5 / 5 ) ] | = 34 |
35
| 5? + 5? + [ 5 x ( 5 / 5 ) ] | = 35 |
36
| 5? + 5? + [ 5 + ( 5 / 5 ) ] | = 36 |
37
| ( 5! + 5! – 55 ) / 5 | = 37 |
38
| 5? + 5? +5 + ( 5? / 5 ) | = 38 |
39
| 5! / 5 +5 + 5 +5 | = 39 |
40
| [ ( 5? ) +( 5 x 5 ) ] x ( 5 / 5 ) | = 40 |
41
| ( 5? ) + ( 5 x 5 ) +( 5 / 5 ) | = 41 |
42
| [ ( 5! + 5! ) – ( 5? + 5? ) ] / 5 | = 42 |
43
| [ ( 5! + 5! ) – ( 5 x 5 ) ] / 5 | = 43 |
44
| ( 5? + 5? + 5? ) – ( 5 / 5 ) | = 44 |
45
| ( 5 x 5 ) + ( 5 x 5 ) – 5 | = 45 |
46
| ( 5? + 5? + 5? ) + 5 / 5 | = 46 |
47
| [ ( 5! + 5?) / 5 ] + ( 5? + 5 ) | = 47 |
48
| ( 5? + 5? +5?) + ( 5?/ 5 ) | = 48 |
49
| 5 x ( 5 + 5 ) – ( 5 / 5 ) | = 49 |
50
| 5 x ( 5 + 5 ) x ( 5 / 5 ) | = 50 |
51
| 5 x ( 5 + 5 ) + ( 5 / 5 ) | = 51 |
52
| ( 5? x 5 ) - [ ( 5! – 5 ) / 5 ] | = 52 |
53
| ( 5! / 5 ) + ( 5! / 5 ) + 5 | = 53 |
54
| ( 5! + 5! + 5? + 5?) / 5 | = 54 |
55
| 5? + 5? + 5? + ( 5 + 5 ) | = 55 |
56
| 55 + 55-5 | = 56 |
57
| 55 + [ ( 5+5 ) / 5 ] | = 57 |
58
| [ ( 5! + 5!) / 5 ] + ( 5+5 ) | = 58 |
59
| ( 5? x 5 ) – 5? – ( 5 / 5 ) | = 59 |
60
| ( 5 x 5? ) – 5? x 5 / 5 | = 60 |
61
| ( 5 x 5? ) - 5? + ( 5 / 5 ) | = 61 |
62
| 5! – 55 - 5? / 5 | = 62 |
63
| 5! / 5 +5! / 5 + 5? | = 63 |
64
| ( 5? x 5 ) – 55 / 5 | = 64 |
65
| 5? +5? + 5? + 5? +5 | = 65 |
66
| ( 55 / 5 ) + 55 | = 66 |
67
| ( 5? x 5 ) – 5 - ( 5? / 5 ) | = 67 |
68
| ( 5! + 5!) / 5 + ( 5? + 5 ) | = 68 |
69
| ( 5? + 5? +5?) + ( 5! / 5 ) | = 69 |
70
| ( 55 ) + 5 +5 +5 | = 70 |
71
| ( 5? x 5 ) – ( 5- 5 / 5 ) | = 71 |
72
| 5! – ( 5! / 5 + 5! / 5 ) | = 72 |
73
| 55 + 5? + 5?/ 5 | = 73 |
74
| 5? x 5 – 55-5 | = 74 |
75
| 5? x 5 x 55-5 | = 75 |
76
| 5? x 5 + 55-5 | = 76 |
77
| ( 5? x 5 ) + [ ( 5 + 5 ) / 5 ] | = 77 |
78
| ( 5? x 5 x 5 + 5?) / 5 | = 78 |
79
| 5? x 5 + 5 – ( 5 / 5 ) | = 79 |
80
| 5? x 5 +5 x ( 5 / 5 ) | = 80 |
81
| 5? x 5 +5 + ( 5 / 5 ) | = 81 |
82
| ( 5? x 5 + 5?) - (5! / 5?) | = 82 |
83
| 5? x 5 +5 + ( 5? / 5 ) | = 83 |
84
| ( 5? x 5 ) – 5? + ( 5! / 5 ) | = 84 |
85
| 55 + ( 5 x 5 ) + 5 | = 85 |
86
| 5! – ( 5! / 5 ) – 5? +5 | = 86 |
87
| 5? x 5 + 5? -5?/ 5 | = 87 |
88
| ( 5? x 5 + 5 ) + ( 5! / 5? ) | = 88 |
89
| ( 5? x 5 ) + 5? - ( 5 / 5 ) | = 89 |
90
| 5? x 5 + 5? x ( 5 / 5 ) | = 90 |
91
| 5? x 5 + 5? + ( 5 / 5 ) | = 91 |
92
| 5! - ( 5 x 5 + 5? / 5 ) | = 92 |
93
| 5? x 5 + ( 5? / 5 ) + 5? ) | = 93 |
94
| ( 5? x 5 ) – 5 + ( 5! / 5 ) | = 94 |
95
| ( 5! ) – ( 5! / 5 + 5 / 5 ) | = 95 |
96
| ( 5! +5! +5! + 5! ) / 5 | = 96 |
97
| 5! – ( 5! / 5 ) + 5 / 5 | = 97 |
98
| 5! - [ ( 120 -10) / 5 ] | = 98 |
99
| 5! – ( 5! / 5 ) + 5? / 5 | = 99 |
100
| 5! - ( 5 + 5 + 5 + 5) | = 100 |
[Via BBA]
Posso falar por mim, foi uma grata satisfação achar alguns números. E quem quiser descobrir alguns "inéditos" pode tentar continuar a sequência com o 101, 102, 103 ... e ver até onde vai com isso. :D
ResponderExcluirAgora que eu vi solução possa até pensar em tentar fazer.
ResponderExcluirPede para sair, zero dois.
ResponderExcluirE a saga continua: 101 = (5!-5?)-5+(5/5)
ResponderExcluir102 -> (5!-5?)-[(5+5)/5)]? #soufoda
ResponderExcluir103 = 5! - ( 5?) - (5+5)/5)
ResponderExcluir104 = 5! - (5? + 5 elevado a 5-5) ( vou dar um tempo pois parece que isso não tem fim!)
ResponderExcluir5? significa o q?
ResponderExcluirConforme explicamos em O problema dos cinco cincos - http://blog.brasilacademico.com/2013/10/o-problema-dos-cinco-cincos.html - O operador ? é chamado de "termial", e ele está para o fatorial assim como o somatório estaria para o produtório. Desse modo, 5? = 5 + 4 + 3 + 2 + 1 cuja soma é 15.
ResponderExcluirBom Dia
ResponderExcluirOS OITO OITO
8888-8888= 0
8888/8888= 1
88/88+88/88= 2
88-88+(8+8+8)/8= 3
8/8+8/8+8/8+8/8= 4
(8+8+8+8+8)/8+8-8= 5
8-8/8-8/8+(8-8)/8= 6
(8+8+8+8+8+8+8)/8= 7
8+8/8-8/8+(8-8)/8= 8
8+8/8+8-8+(8-8)/8= 9
88/8-8/8+(8-8)/8= 10
88/8+8-8+(8-8)/8= 11
(8+8+8+8)/8+8+8-8= 12
(8+8+8+8)/8+8+8/8= 13
88/8+8/8+(8+8)/8= 14
8+8-8/8+88-88= 15
8+8+888-888= 16
8+8+8/8+88-88= 17
8+8+8/8+8/8+8-8= 18
8+8+8/8+8/8+8/8= 19
8+8+8-(8+8+8+8)/8= 20
8+8-8/8+8-(8+8)/8= 21
8+8+8-8/8-(8^8-8)= 22
8+8+8-8/8+(8-8)/8= 23
8+8+8+(88-88)/8= 24
8+8+8+(8^88-88)= 25
8+8+8+8/8+(8^8-8)= 26
8+8+8+8/8+(8+8)/8= 27
8+8+8+(8+8+8+8)/8= 28
8+8+8+8-(8+8+8)/8= 29
8+8+8+8-8/8-8/8= 30
8+8+8+8-8/8+8-8= 31
8+8+8+8+8/8-8/8= 32
8+8+8+8+8/8+8-8= 33
8+8+8+8+8/8+8/8= 34
8+8+8+8+(8+8+8)/8= 35
8+8+8+88/8+8/8= 36
(888/8)/((8+8+8)/8)= 37
8+8+8+8+8-(8+8)/8= 38
8+8+8+8+8-(8^8-8)= 39
8+8+8+8+8+(8-8)/8= 40
8+8+8+8+8+(8^8-8)= 41
8+8+8+8+8+(8+8)/8= 42
88/8-8+8+8+8+8=43
8.8-(88/8+8+8/8))=44
8.8-[(8+8)+(8+8+8/8)]= 45
8.8-[(8+8)+(8/8+8/8)]= 46
8+8+8+8-8+8-8/8= 47
8+8+8+8-8+8+8-8= 48
8+8+8+8-8+8+8/8= 49
8.8-[(8+8)-(8/8+8/8)]= 50
88/8+8+8+8+8+8=51
8.8-((88)/8+(8^8-8))=52
8.8-(88/8+(8-8)/8)=53
8.8-(88/8-(8^8-8))=54
88-8-8-8-8-8/8=55
88-8-8-8-8+8-8=56
88-8-8-8-8+8/8=57
8.8-(8-(8+8)/8+8-8)=58
8.8-8+(8+8)/8+8/8)=59
8.8-(8+8)/8+(8+8)/8=60
8.8-(8+8+8)/8+8-8)=61
8.8-(8+8)/8+(8-8)/8)=62
8.8-8/8+8-8+8-8=63
8.8+(8-8)/8+(8-8)/8)=64
8.8+8/8+8-8+8-8=65
8.8+8/8+8/8+8-8=66
8.8+8/8+8/8+8/8=67
8.8+(8+8)/8+(8+8)/8=68
8.8+8-(8+8)/8-8/8=69
8.8+8-(8+8)/8+8-8=70
8.8+8-(8+8)/8+8/8=71
88-8-8+8-8+8-8=72
88-8-8+8/8+8-8=73
88-8-8+8/8+8/8=74
88+(8+8+8)/8-8-8=75
88-(8+8+8+8)/8-8=76
88-8-(8+8)/8-8/8=77
88-8-(8+8)/8+8-8=78
88-8-8/8+(8-8)/8=79
88-8+8-8+(8-8)/8=80
88-8+8/8+(8-8)/8=81
88-8+8-8+(8+8)/8=82
88-8+8/8+(8+8)/8=83
88-8/8-(8+8+8)/8=84
88-8+8-(8+8+8)/8=85
88+8/8-(8+8+8)/8=86
88-8/8+88-88=87
88+88/8-88/8=88
88+8/8+88-88=89
88+8/8+8/8-8+8=90
88+8/8+8/8+8/8=91
88+(8+8)/8+(8+8)/8=92
88+8-(8+8)/8-8/8=93
88+(8.8)/8-(8+8)/8=94
88+(8.8)/8-(8^8-8)=95
88+(8.8)/8+(8-8)/8=96
88+88/8-(8+8)/8=97
88+88/8-(8^8-8)=98
88+88/8+(8-8)/8)=99
88+88/8+(8^8-8)=100
Djeosede.
Bom Dia
ResponderExcluirmais uma pequena sequência.
OS NOVE NOVES
(9999-9999)/9= 0
(9+9)/9-9/9+9-9+9-9= 1
(9+9)/9+(9-9)/9+(9-9)/9= 2
(9+9)/9+9/9+9-9+9-9= 3
(9+9)/9+(9+9)/9+(9-9)/9= 4
9-9/9-9/9-9/9-9/9= 5
9-9/9-9/9-9/9+9-9= 6
9-99/99-99/99= 7
9-9999/9999= 8
9+9999-9999= 9
9+9999/9999= 10
9+99/99+99/99= 11
9+9/9+9/9+9/9+9-9= 12
99/9+(9+9)/9+(9-9)/9= 13
9+9/9+(9+9)/9+(9+9)/9= 14
99/9+(9+9)/9+(9+9)/9= 15
9+9-(9+9)/9+9/9-9/9= 16
9+9-(9+9)/9+9/9+9-9= 17
9+9-(9-9)/9+9-9+9-9= 18
9+9+9/9+(9-9)/9+9-9= 19
9+9+(9+9)/9+9-9+9-9= 20
(99/9)+(99/9)-(9^9-9)= 21
(99/9)+(99/9)-(9-9)/9= 22
(99/9)+(99/9)+(9^9-9)= 23
(99/9)+(99/9)+(9+9)/9= 24
9+9+9-(9+9)/9(9-9)/9= 25
9+9+9-(9/9)+9-9+9-9= 26
9+9+9-(9-9)/9+(9-9)/9= 27
9+9+9+(9/9)+9-9+9-9= 28
9+9+9+(9/9)+(9/9)+9-9= 29
9+9+9+(9/9)+(9/9)+(9/9)= 30
9+9+9+(9+9)/9+(9+9/9)= 31
99/9+99/9+9+9/9= 32
99/9+99/9+99/9= 33
9+9+9+9-(9+9)/9-9+9= 34
9+9+9+9-(9+9)/9+9/9= 35
9+9+9+9+(9-9)/9+9-9= 36
9+9+9+9+(9+9)/9-9/9= 37
9+9+9+9+(9+9)/9-9+9= 38
9+9+9+9+(9+9)/9+9/9= 39
9+9+9+9+(9+9+9+9)/9= 40
(9.9-9/9)/(9+9)/9+9/9= 41
9+9+9+9+9-(9+9+9)/9= 42
9+9+9+9+9-9/9-9/9= 43
9+9+9+9+9-(9/9)+9-9= 44
9+9+9+9+9-(9/9)+9/9= 45
9+9+9+9+9+(9/9)+9-9= 46
9+9+9+9+9+(9/9)+9/9= 47
9+9+9+9+9+(9+9+9)/9= 48
(9.9-(9^9-9)/(9+9)/9(9= 49
(99+9/9)/(9+9)/9+9-9= 50
(99+9/9)/(9+9)/9+9/9= 51
9.9-(9+9+9)-9/9-9/9= 52
9.9-(9+9+9)-99/99= 53
9.9-(9+9+9)-99+99= 54
9.9-(9+9+9)+99/99= 55
9.9-(9+9+9)+9/9+9/9= 56
9.9-(9+9+9)+(9+9+9)/9= 57
[99-(9^9-9)]/(9+9)/9+9= 58
9.9-(9+9)-(9+9+9+9)/9= 59
9.9-(9+9)-(9+9)9-9/9= 60
9.9-(9+9)-(9+9)9-9+9= 61
9.9-(9+9)-(9-9)9-9/9= 62
9.9-(9+9)+(9-9)9-9+9= 63
9.9-(9+9)+(9-9)9+9/9= 64
9.9-(9+9)+(9+9)9+9-9= 65
9.9-(9+9)+(9+9)9+9/9= 66
9.9-(9+9)+(9+9+9+9)/9= 67
9.9-9-(9+9)/9-(9+9)/9= 68
9.9-9-(9+9)/9-(9^9-9)= 69
9.9-9-(9+9)/9-(9-9)/9= 70
9.9-9-(9^9-9)+(9-9)/9= 71
9.9-9+(9-9)/9+(9-9)/9= 72
9.9-9+(9^9-9)+(9-9)/9= 73
9.9-9+(9+9)/9+(9-9)/9= 74
9.9-9+(9+9)/9+(9^9-9)= 75
9.9-9+(9+9)/9+(9+9)/9= 76
9.9-9+(9+9+9+9+9)/9= 77
9.9-9/9-9/9-(9^9-9)= 78
9.9-9/9-9/9-(9-9)/9= 79
9.9-9/9-9+9+(9-9)/9= 80
9.9-9+9-9+9+(9-9)/9= 81
9.9+9/9-9+9+(9-9)/9= 82
9.9+9-9-9+9+(9+9)/9= 83
9.9+9/9-9+9+(9+9)/9= 84
9.9+9/9+9/9+(9+9)/9= 85
99-9/9-99/9-9/9= 86
99-9/9-99/9-9+9= 87
99-99/9+9-9+9-9= 88
99-99/9+9/9+9-9= 89
99-9+99-99+9-9= 90
99-9+9/9+9-9+9-9= 91
99-9+9/9+9/9+9-9= 92
99-9+9/9+9/9+9/9= 93
99-(9+9+9)/9-(9+9)/9= 94
99-(9+9+9)/9-(9^9-9)= 95
99-(9+9+9)/9-(9-9)/9= 96
99-(9+9)/9+9-9+9-9= 97
99-9/9+(9-9)/9+9-9= 98
99+(999-999)/9= 99
99+99/99+(9-9)/9= 100
Djeosede.
Tá inspirado.
ResponderExcluirOS DOIS DOIS
ResponderExcluirFOI USADO O TERMIAL, onde: 2?=3; 2??=6 e 2???=21
2-2=0
2/2=1
2??/2?=2
2??/2=3
2.2=4
2?+2=5
2?+2?=6
2???/2?=7
2^2?=8
2??+2?=9
(2.2)?=10
2????/2???=11
2??+2??=12
2???-2??=15
Djeosede.
Oi, boa tarde.
ResponderExcluirVai aí uma sequência envolvendo adição,subtração,multiplicação, divisão,potenciação,fatorial e termial.Usando os três três.
Com os quatro quatros tenho feito até 800 por enquanto.
OS TRÊS TRÊS
(3-3)/3= 0
3^3-3= 1
3-3/3= 2
3+3-3= 3
3+3/3= 4
3?-3/3= 5
3.3-3= 6
3?+3/3= 7
3?+3?/3= 8
3+3+3= 9
3??/3+3= 10
33/3= 11
3??-3.3= 12
3??/3+3?= 13
3??-3??/3= 14
3?.3-3= 15
3!!/(3.3)?=16
3???/3??+3?=17
3??-(3?-3)=18
3??-3?/3=19
3??-3/3=20
3??+3-3=21
3??+3/3=22
3??+3?/3=23
3^3-3=24
onde: 3?=6; 3??=21; 3???=231
obrigado.
Djeosede.