THE YEAR PUZZLE (program by Heiner Marxen) Version: $Revision: 1.18 $ $Date: 2006/02/01 17:22:10 $ Target signature = 1996 Without permutation of signature digits. Intermediate (de)nominator range = -500000 .. 500000 Result range = 0 .. 200 With standard binary operators: + - * / With standard unary operators: - sqrt With parentheses. With concatenation. With exponentiation (^). With factorial (!). With even/odd factorial (!!). With decimal point. Could not solve 4 of 201 values [2.0%]. 0 = 1*(9-9)*6 1 = 1+(9-9)*6 2 = -1+9/(9-6) 3 = 1*9/(9-6) 4 = 19-9-6 5 = -1+9/9*6 6 = 1*9/9*6 7 = 1+9/9*6 8 = 1+9/9+6 9 = 1*9/sqrt(9)+6 10 = 19-sqrt(9)-6 11 = -1+9+9-6 12 = 1*9+9-6 13 = 1+9+9-6 14 = -1^9+9+6 15 = (1+9)*9/6 16 = 19-9+6 17 = -1+sqrt(9)+9+6 18 = 1*9+sqrt(9)+6 19 = 1+sqrt(9)+9+6 20 = -1+sqrt(9)*9-6 21 = 1*sqrt(9)*9-6 22 = 19+9-6 23 = -1+9+9+6 24 = 1*9+9+6 25 = 1+9+9+6 26 = -1+9*(9-6) 27 = 1*9*(9-6) 28 = 1+9*(9-6) 29 = -1+sqrt(9)+sqrt(sqrt(9)^6) 30 = (1+9)*(9-6) 31 = 1+sqrt(9)+sqrt(sqrt(9)^6) 32 = 1/sqrt(9)*96 33 = 1*sqrt(9)*9+6 34 = 19+9+6 35 = -19+9*6 36 = 1*(9-sqrt(9))*6 37 = 19+sqrt(9)*6 38 = 19/sqrt(9)*6 39 = (1+sqrt(9))!+9+6 40 = 1/(9+9)*6! 41 = -1+sqrt(9)!+sqrt(9)!*6 42 = (1+sqrt(9))*9+6 43 = 1+sqrt(9)!+sqrt(9)!*6 44 = -1-9+9*6 45 = -1*9+9*6 46 = 1-9+9*6 47 = -1+sqrt(9)!*9-6 48 = (1^9-9)*-6 49 = 1+sqrt(9)!*9-6 50 = -1-sqrt(9)+9*6 51 = 19*sqrt(9)-6 52 = 1-sqrt(9)+9*6 53 = -1^9+9*6 54 = 1^9*9*6 55 = 1^9+9*6 56 = -1+sqrt(9)+9*6 57 = 19*(9-6) 58 = 1+sqrt(9)+9*6 59 = -1+sqrt(9)!+9*6 60 = (19-9)*6 61 = 1+sqrt(9)!+9*6 62 = -1+9+9*6 63 = 1*9+9*6 64 = 1+9+9*6 65 = 1+(sqrt(9)!/sqrt(9))^6 66 = (1-9)*-9-6 67 = 1+sqrt(sqrt(9)!*(sqrt(9)!+6!)) 68 = (-1+sqrt(9)!)!/sqrt(9)!+6!! 69 = (1+sqrt(9)!)*9+6 70 = (1+sqrt(9))^sqrt(9)+6 71 = -1+(sqrt(9)+9)*6 72 = 1*(sqrt(9)+9)*6 73 = 19+9*6 74 = -1+9*9-6 75 = 1*9*9-6 76 = 1+9*9-6 77 = -19+96 78 = (1-9)*-9+6 79 = -1/9*(9-6!) 80 = -1+9*(sqrt(9)+6) 81 = 1/9*sqrt(9)^6 82 = 1+9*(sqrt(9)+6) 83 = -1+9!/sqrt(9)!/6! 84 = (1+9)*9-6 85 = 1+9!/sqrt(9)!/6! 86 = -1-9+96 87 = 1*9*9+6 88 = 1-9+96 89 = -1-sqrt(9)!+96 90 = (1+9)*(sqrt(9)+6) 91 = 1-sqrt(9)!+96 92 = -1+99-6 93 = 1*99-6 94 = 1+99-6 95 = -1^9+96 96 = (1+9)*9+6 97 = 1^9+96 98 = -1+sqrt(9)+96 99 = 1*sqrt(9)+96 100 = 1+sqrt(9)+96 101 = -1+sqrt(9)!+96 102 = (1-9-9)*-6 103 = 1+sqrt(9)!+96 104 = -1+9+96 105 = 1*9+96 106 = 1+9+96 107 = -1+(9+9)*6 108 = 1*(9+9)*6 109 = 1+(9+9)*6 110 = -1-9+(sqrt(9)!)!/6 111 = -1*9+(sqrt(9)!)!/6 112 = 1-9+(sqrt(9)!)!/6 113 = -1+(sqrt(9)!)!/sqrt(9)!-6 114 = (1+9+9)*6 115 = 19+96 116 = -1-sqrt(9)+(sqrt(9)!)!/6 117 = (-1+sqrt(9)!)!-9+6 118 = 1-sqrt(9)+(sqrt(9)!)!/6 119 = -1+(-9/9+6)! 120 = (1-9)*(-9-6) 121 = 1+(-9/9+6)! 122 = -1+sqrt(9)+(sqrt(9)!)!/6 123 = (-1+sqrt(9)!)!+9-6 124 = 1+sqrt(9)+(sqrt(9)!)!/6 125 = sqrt((-1+9-sqrt(9))^6) 126 = (-1+9-sqrt(9))!+6 127 = 1+sqrt(9)!+(sqrt(9)!)!/6 128 = -1+9+(sqrt(9)!)!/6 129 = 1*9+(sqrt(9)!)!/6 130 = 1+9+(sqrt(9)!)!/6 131 = (-1+sqrt(9)!)^sqrt(9)+6 132 = (19+sqrt(9))*6 133 = ? 134 = -1+9*(9+6) 135 = 1*9*(9+6) 136 = 1+9*(9+6) 137 = -1-sqrt(9)!+sqrt(9)*6!! 138 = (1+sqrt(9))!*sqrt(9)!-6 139 = 19+(sqrt(9)!)!/6 140 = (1+sqrt(9)!)!/sqrt(9)!/6 141 = -1*sqrt(9)+sqrt(9)*6!! 142 = 1-sqrt(9)+sqrt(9)*6!! 143 = -1+9/sqrt(9)*6!! 144 = (1-9)*-sqrt(9)*6 145 = 1+9/sqrt(9)*6!! 146 = -1+99+6!! 147 = (-1+sqrt(9)!)!+sqrt(sqrt(9)^6) 148 = 1+99+6!! 149 = -1+sqrt(9)!+sqrt(9)*6!! 150 = (1+9)*(9+6) 151 = 199-6!! 152 = -1+9!!/9+6!! 153 = 1*9!!/9+6!! 154 = 1+9!!/9+6!! 155 = -1+(9!!-9)/6 156 = (1-sqrt(9)*9)*-6 157 = 1+(9!!-9)/6 158 = -1+(9!!+9)/6 159 = 1*(9!!+9)/6 160 = (1-sqrt(9))/9*-6! 161 = -1+sqrt(9)*9*6 162 = 1*sqrt(9)*9*6 163 = 1+sqrt(9)*9*6 164 = -1+99/.6 165 = 19*9-6 166 = 1+99/.6 167 = -1+9!/sqrt(9)/6! 168 = (19+9)*6 169 = 1+9!/sqrt(9)/6! 170 = -1+sqrt(9)*(9+6!!) 171 = 19*(sqrt(9)+6) 172 = 1+sqrt(9)*(9+6!!) 173 = (-1+sqrt(9)!)^sqrt(9)+6!! 174 = (-1+sqrt(9)!)!+9*6 175 = ((1+sqrt(9)!)!!+9!!)/6 176 = (-1+9)!!/sqrt(9)+6!! 177 = 19*9+6 178 = 1+9!!-(sqrt(9)!)!!-6! 179 = -1+(sqrt(9)!)!*sqrt(sqrt(9)/6!!) 180 = (1+9)*sqrt(9)*6 181 = 1+(sqrt(9)!)!*sqrt(sqrt(9)/6!!) 182 = ? 183 = (-1+sqrt(9)!)!!*9+6!! 184 = ((-1+9)!!+(sqrt(9)!)!)/6 185 = 1/9*(9!!+6!) 186 = (1+sqrt(9))*(sqrt(9)!)!!-6 187 = ? 188 = (-1+(sqrt(9)!)!!)/sqrt(sqrt(9)/6!!) 189 = (1+sqrt(9)!)*sqrt(sqrt(9)^6) 190 = 19*sqrt(9)!/.6 191 = -1+(sqrt(9)!)!/sqrt(9)-6!! 192 = (1-sqrt(9))*-96 193 = 199-6 194 = ? 195 = (1-sqrt(9)!)*(9-6!!) 196 = (1+(sqrt(9)!)!!)/sqrt(sqrt(9)/6!!) 197 = -19+sqrt(sqrt(9)!^6) 198 = ((1+sqrt(9))!+9)*6 199 = sqrt(1+9!/9-6!) 200 = (-1+9-sqrt(9))!/.6