THE YEAR PUZZLE (program by Heiner Marxen) Version: $Revision: 1.18 $ $Date: 2006/02/01 17:22:10 $ Target signature = 1999 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 5 of 201 values [2.5%]. 0 = 19*(9-9) 1 = 19-9-9 2 = 1*(9+9)/9 3 = 1+(9+9)/9 4 = 1+sqrt(9)*9/9 5 = 1+sqrt(9)+9/9 6 = 1*9-9/sqrt(9) 7 = -1+9-9/9 8 = 1*9-9/9 9 = 1+9-9/9 10 = 1+9*9/9 11 = 1*99/9 12 = 1+99/9 13 = 19+sqrt(9)-9 14 = -1+9+9-sqrt(9) 15 = 1*9+9-sqrt(9) 16 = 19-9/sqrt(9) 17 = -1^9+9+9 18 = 19-9/9 19 = 19*9/9 20 = 19+9/9 21 = 1*9+sqrt(9)+9 22 = 19+9/sqrt(9) 23 = -1+sqrt(9)*9-sqrt(9) 24 = (1-9)*-9/sqrt(9) 25 = 19+9-sqrt(9) 26 = -1+9+9+9 27 = 1*9+9+9 28 = 1+9+9+9 29 = -1+sqrt(9)+sqrt(9)*9 30 = sqrt((1+99)*9) 31 = 19+sqrt(9)+9 32 = -1+99/sqrt(9) 33 = 1*99/sqrt(9) 34 = 1+99/sqrt(9) 35 = -1+9+sqrt(9)*9 36 = 1*9+sqrt(9)*9 37 = 19+9+9 38 = 19*sqrt(9)!/sqrt(9) 39 = (1+9)*sqrt(9)+9 40 = 1*(sqrt(9)!)!/(9+9) 41 = 1+(sqrt(9)!)!/(9+9) 42 = (1+sqrt(9))!+9+9 43 = 1+sqrt(9)!+sqrt(9)!*sqrt(9)! 44 = -1+sqrt(9)!*9-9 45 = (1+sqrt(9))*9+9 46 = 19+sqrt(9)*9 47 = -1+sqrt(9)!*9-sqrt(9)! 48 = 19*sqrt(9)-9 49 = 1+sqrt(9)!*9-sqrt(9)! 50 = -1+sqrt(9)!*9-sqrt(9) 51 = (1-9-9)*-sqrt(9) 52 = 1+sqrt(9)!*9-sqrt(9) 53 = -1+sqrt(9)*(9+9) 54 = 1*sqrt(9)*(9+9) 55 = 1+sqrt(9)*(9+9) 56 = -1+sqrt(9)+sqrt(9)!*9 57 = 19*9/sqrt(9) 58 = 1+sqrt(9)+sqrt(9)!*9 59 = -1+sqrt(9)!+sqrt(9)!*9 60 = 19*sqrt(9)+sqrt(9) 61 = (1+sqrt(9))^sqrt(9)-sqrt(9) 62 = -19+9*9 63 = (1-9)*-9-9 64 = (1+9/sqrt(9))^sqrt(9) 65 = (-1+9)!/(sqrt(9)!)!+9 66 = 19*sqrt(9)+9 67 = (1+sqrt(9))^sqrt(9)+sqrt(9) 68 = (-1+sqrt(9)!)!/sqrt(9)!+(sqrt(9)!)!! 69 = (1-9)*-9-sqrt(9) 70 = -1+(sqrt(9)!)!/9-9 71 = -1+9*9-9 72 = 1*9*9-9 73 = 1+9*9-9 74 = -1+9*9-sqrt(9)! 75 = (1-9)*-9+sqrt(9) 76 = 1+9*9-sqrt(9)! 77 = -1+9*9-sqrt(9) 78 = 1*9*9-sqrt(9) 79 = 1+9*9-sqrt(9) 80 = -19+99 81 = (1+9)*9-9 82 = (1/9+9)*9 83 = -1+sqrt(9)+9*9 84 = 1*sqrt(9)+9*9 85 = 1+sqrt(9)+9*9 86 = -1+sqrt(9)!+9*9 87 = (1+9)*9-sqrt(9) 88 = 1+sqrt(9)!+9*9 89 = -1+99-9 90 = 1*99-9 91 = 1+99-9 92 = -1+99-sqrt(9)! 93 = (1+9)*9+sqrt(9) 94 = 1+99-sqrt(9)! 95 = -1+99-sqrt(9) 96 = 1*99-sqrt(9) 97 = 1+99-sqrt(9) 98 = -1^9+99 99 = (1+9)*9+9 100 = 19+9*9 101 = -1+sqrt(9)+99 102 = 1*sqrt(9)+99 103 = 1+sqrt(9)+99 104 = -1+sqrt(9)!+99 105 = 1*sqrt(9)!+99 106 = 1+sqrt(9)!+99 107 = -1+9+99 108 = 1*9+99 109 = 1+9+99 110 = (-1+sqrt(9)+9)!/9! 111 = 19*sqrt(9)!-sqrt(9) 112 = 1+(sqrt(9)!)!/sqrt(9)!-9 113 = -1+(sqrt(9)!)!/sqrt(9)!-sqrt(9)! 114 = 19*(9-sqrt(9)) 115 = 1+(sqrt(9)!)!/sqrt(9)!-sqrt(9)! 116 = (-1+sqrt(9)!)^sqrt(9)-9 117 = (1+sqrt(9)+9)*9 118 = 19+99 119 = -1+(sqrt(9)!-9/9)! 120 = (1+9)*(sqrt(9)+9) 121 = 1+(sqrt(9)!-9/9)! 122 = (-1+sqrt(9)!)^sqrt(9)-sqrt(9) 123 = 19*sqrt(9)!+9 124 = 1+sqrt(9)+(sqrt(9)!)!/sqrt(9)! 125 = (-1+9-sqrt(9))^sqrt(9) 126 = (1-sqrt(9)!-9)*-9 127 = 1+sqrt(9)!+(sqrt(9)!)!/sqrt(9)! 128 = -1+9+(sqrt(9)!)!/sqrt(9)! 129 = (-1+9-sqrt(9))!+9 130 = 1+9+(sqrt(9)!)!/sqrt(9)! 131 = (-1+sqrt(9)!)^sqrt(9)+sqrt(9)! 132 = (19+sqrt(9))*sqrt(9)! 133 = ? 134 = -1+9*(sqrt(9)!+9) 135 = 1*9*(sqrt(9)!+9) 136 = 1+9*(sqrt(9)!+9) 137 = (-1+9)!!/sqrt(9)+9 138 = (-1+sqrt(9)!)!+9+9 139 = 19+(sqrt(9)!)!/sqrt(9)! 140 = (1+sqrt(9)!)!/sqrt(9)!/sqrt(9)! 141 = (1+sqrt(9))!*sqrt(9)!-sqrt(9) 142 = 1+(sqrt(9)!)!!*sqrt(9)-sqrt(9) 143 = (1+sqrt(9)+9)!!/9!! 144 = (1-9)*(-9-9) 145 = 1+sqrt(9)*(9-sqrt(9))!! 146 = -1+(sqrt(9)!)!!+99 147 = (-1+sqrt(9)!)!+sqrt(9)*9 148 = 1+(sqrt(9)!)!!+99 149 = -1+sqrt(9)!+(sqrt(9)!)!!*sqrt(9) 150 = (1+9)*(sqrt(9)!+9) 151 = 199-(sqrt(9)!)!! 152 = -1+(sqrt(9)!)!!+9!!/9 153 = (1-9-9)*-9 154 = 1+(sqrt(9)!)!!+9!!/9 155 = -1+(9!!-9)/sqrt(9)! 156 = (1-sqrt(9)*9)*-sqrt(9)! 157 = 1+(9!!-9)/sqrt(9)! 158 = -1+(9!!+9)/sqrt(9)! 159 = (1-sqrt(9)!*9)*-sqrt(9) 160 = (1-sqrt(9))*-(sqrt(9)!)!/9 161 = -1+9*(9+9) 162 = 19*9-9 163 = 1+9*(9+9) 164 = ? 165 = 19*9-sqrt(9)! 166 = ? 167 = -1+9!/sqrt(9)/(sqrt(9)!)! 168 = 19*9-sqrt(9) 169 = 1+9!/sqrt(9)/(sqrt(9)!)! 170 = -1+sqrt(9)*((sqrt(9)!)!!+9) 171 = (1+9+9)*9 172 = 1+sqrt(9)*((sqrt(9)!)!!+9) 173 = (-1+sqrt(9)!)^sqrt(9)+(sqrt(9)!)!! 174 = 19*9+sqrt(9) 175 = ((1+sqrt(9)!)!!+9!!)/sqrt(9)! 176 = (-1+9)!!/sqrt(9)+(sqrt(9)!)!! 177 = 19*9+sqrt(9)! 178 = 1+9!!-(sqrt(9)!)!!-(sqrt(9)!)! 179 = -1+(sqrt(9)!)!*sqrt(sqrt(9)/(sqrt(9)!)!!) 180 = 19*9+9 181 = 1+(sqrt(9)!)!*sqrt(sqrt(9)/(sqrt(9)!)!!) 182 = ? 183 = (1+sqrt(9))*(sqrt(9)!)!!-9 184 = -1+(9!!+(sqrt(9)!)!)/9 185 = 1*(9!!+(sqrt(9)!)!)/9 186 = (1+sqrt(9)!)!!+9*9 187 = (-(-1+9)!!+9!!)/sqrt(9) 188 = (1-(sqrt(9)!)!!)*-sqrt((sqrt(9)!)!!/sqrt(9)) 189 = (1+sqrt(9)!)*sqrt(9)*9 190 = 199-9 191 = -1+9!/(9!!+9!!) 192 = (1+sqrt(9))^sqrt(9)*sqrt(9) 193 = 199-sqrt(9)! 194 = ? 195 = -(-1+sqrt(9)!)!+9!!/sqrt(9) 196 = 199-sqrt(9) 197 = -19+sqrt(9)!^sqrt(9) 198 = (19+sqrt(9))*9 199 = sqrt(1+9!/9-(sqrt(9)!)!) 200 = (-1+sqrt(9)!)!+(sqrt(9)!)!/9