THE YEAR PUZZLE (program by Heiner Marxen) Version: $Revision: 1.18 $ $Date: 2006/02/01 17:22:10 $ Target signature = 9999 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 3 of 201 values [1.5%]. 0 = 99-99 1 = 99/99 2 = 99/9-9 3 = (9+9+9)/9 4 = 9/sqrt(9)+9/9 5 = 9-sqrt(9)-9/9 6 = sqrt(9+9+9+9) 7 = 9-(9+9)/9 8 = (9*9-9)/9 9 = 9+9*(9-9) 10 = (99-9)/9 11 = 9+(9+9)/9 12 = (9+99)/9 13 = sqrt(9)+9+9/9 14 = sqrt(9)+99/9 15 = 9+9-9/sqrt(9) 16 = sqrt(9)!+9+9/9 17 = 9+9-9/9 18 = 99-9*9 19 = 9+9+9/9 20 = 9+99/9 21 = 9+9+9/sqrt(9) 22 = sqrt(9)!*(sqrt(9)+sqrt(9)!/9) 23 = (sqrt(9)!^sqrt(9)-9)/9 24 = 99/sqrt(9)-9 25 = sqrt(9)*(9-sqrt(9)!/9) 26 = sqrt(9)*9-9/9 27 = sqrt(9)*9*9/9 28 = sqrt(9)*9+9/9 29 = sqrt(9)*(9+sqrt(9)!/9) 30 = sqrt(9+9*99) 31 = (99-sqrt(9)!)/sqrt(9) 32 = (99-sqrt(9))/sqrt(9) 33 = sqrt(9)*99/9 34 = (sqrt(9)+99)/sqrt(9) 35 = sqrt(9)!*sqrt(9)!-9/9 36 = 9+9+9+9 37 = sqrt(9)!*sqrt(9)!+9/9 38 = sqrt(9)!*(sqrt(9)!+sqrt(9)/9) 39 = sqrt(9)+9+sqrt(9)*9 40 = (9-sqrt(9))!/(9+9) 41 = (sqrt(9)+(sqrt(9)!)!/sqrt(9)!)/sqrt(9) 42 = 9+99/sqrt(9) 43 = sqrt(9)+(sqrt(9)!)!/(9+9) 44 = (sqrt(9)!)!/9-sqrt(9)!*sqrt(9)! 45 = 9+9+sqrt(9)*9 46 = sqrt(9)!+(sqrt(9)!)!/(9+9) 47 = 9!/9/(sqrt(9)!)!-9 48 = sqrt(9)!*(9-9/9) 49 = 9+(sqrt(9)!)!/(9+9) 50 = sqrt(9)!*(9-sqrt(9)!/9) 51 = sqrt(9)*(9+9)-sqrt(9) 52 = sqrt(9)!*(9-sqrt(9)/9) 53 = sqrt(9)!*9-9/9 54 = 9*9-sqrt(9)*9 55 = sqrt(9)!*9+9/9 56 = 9!/9/(9-sqrt(9))! 57 = sqrt(9)+sqrt(9)*(9+9) 58 = sqrt(9)!*(9+sqrt(9)!/9) 59 = sqrt(9)+9!/9/(sqrt(9)!)! 60 = sqrt(9)!*(9+9/9) 61 = (sqrt(9)!/sqrt(9))^sqrt(9)!-sqrt(9) 62 = (sqrt(9)!)!/9-9-9 63 = 9*9-9-9 64 = (sqrt(9)+9/9)^sqrt(9) 65 = 9+9!/9/(sqrt(9)!)! 66 = sqrt(9)!*99/9 67 = sqrt(9+9!/9/9) 68 = (sqrt(9)!)!/9-sqrt(9)-9 69 = 9*9-sqrt(9)-9 70 = 9!*9/sqrt(9)!^sqrt(9)! 71 = (9-sqrt(9))!/9-9 72 = 9*(9-9/9) 73 = 9+(sqrt(9)!/sqrt(9))^sqrt(9)! 74 = sqrt(9)+(sqrt(9)!)!/9-9 75 = sqrt(9)+9*9-9 76 = ((sqrt(9)!)!-9)/9-sqrt(9) 77 = (9-sqrt(9))!/9-sqrt(9) 78 = 9*9-9/sqrt(9) 79 = 9*9-sqrt(9)!/sqrt(9) 80 = 9*9-9/9 81 = 99-9-9 82 = 9*9+9/9 83 = 9*9+sqrt(9)!/sqrt(9) 84 = 9*9+9/sqrt(9) 85 = sqrt(9)!+((sqrt(9)!)!-9)/9 86 = sqrt(9)!+(9-sqrt(9))!/9 87 = 99-sqrt(9)-9 88 = 9+((sqrt(9)!)!-9)/9 89 = 9+(9-sqrt(9))!/9 90 = 9*(9+9/9) 91 = ((sqrt(9)!)!+99)/9 92 = sqrt(9)+9+(sqrt(9)!)!/9 93 = sqrt(9)+99-9 94 = (9!!-99)/9 95 = sqrt(9)!+9+(sqrt(9)!)!/9 96 = 99-9/sqrt(9) 97 = 99-sqrt(9)!/sqrt(9) 98 = 99-9/9 99 = 9*99/9 100 = 9/9+99 101 = sqrt(9)!/sqrt(9)+99 102 = 9/sqrt(9)+99 103 = (9!!-9-9)/9 104 = ((sqrt(9)!)!+sqrt(9)!^sqrt(9))/9 105 = 9+99-sqrt(9) 106 = 9!!/9+9/9 107 = (sqrt(9)!)!/9+sqrt(9)*9 108 = sqrt(9*9)+99 109 = sqrt(9)+(9!!+9)/9 110 = (99/9)!/9! 111 = 999/9 112 = ((sqrt(9)!)!+sqrt(9)!)/sqrt(9)!-9 113 = ((sqrt(9)!)!-sqrt(9)!)/sqrt(9)!-sqrt(9)! 114 = sqrt(9)!+9+99 115 = ((sqrt(9)!)!+sqrt(9)!)/sqrt(9)!-sqrt(9)! 116 = sqrt(9)!*sqrt(9)!+(sqrt(9)!)!/9 117 = 9+9+99 118 = ((sqrt(9)!)!-sqrt(9)-9)/sqrt(9)! 119 = (sqrt(9)!)!/sqrt(9)!-9/9 120 = (9-sqrt(9)-9/9)! 121 = (sqrt(9)!)!/sqrt(9)!+9/9 122 = (sqrt(9)+9^sqrt(9))/sqrt(9)! 123 = (9+9^sqrt(9))/sqrt(9)! 124 = sqrt(9)+((sqrt(9)!)!+sqrt(9)!)/sqrt(9)! 125 = (sqrt(9)!-9/9)^sqrt(9) 126 = sqrt(9)*9+99 127 = sqrt(9)!+((sqrt(9)!)!+sqrt(9)!)/sqrt(9)! 128 = 9+((sqrt(9)!)!-sqrt(9)!)/sqrt(9)! 129 = 9+(sqrt(9)!-9/9)! 130 = 9+((sqrt(9)!)!+sqrt(9)!)/sqrt(9)! 131 = (9+9!/9!!)/sqrt(9) 132 = 9*(sqrt(9)!+9)-sqrt(9) 133 = sqrt(9)*((sqrt(9)!)!!/.9-9) 134 = (sqrt(9)!)!/9+sqrt(9)!*9 135 = 9*(9+9-sqrt(9)) 136 = sqrt(9)!^sqrt(9)-(sqrt(9)!)!/9 137 = 9+9!/sqrt(9)/9!! 138 = sqrt(9)+9*(sqrt(9)!+9) 139 = 9!!-sqrt(9)!-(sqrt(9)!)!/.9 140 = ((sqrt(9)!)!+(sqrt(9)!)!/sqrt(9)!)/sqrt(9)! 141 = (sqrt(9)!)!/sqrt(9)-99 142 = sqrt(9)*((sqrt(9)!)!!-sqrt(9)!/9) 143 = (sqrt(9)!)!!*sqrt(9)-9/9 144 = (sqrt(9)+9)*(sqrt(9)+9) 145 = (sqrt(9)!)!!*sqrt(9)+9/9 146 = sqrt(9)*((sqrt(9)!)!!+sqrt(9)!/9) 147 = sqrt(9)*9+(sqrt(9)!)!/sqrt(9)! 148 = (9!!-sqrt(9))/sqrt(9)!-9 149 = (9!!+sqrt(9))/sqrt(9)!-9 150 = (9!!+9)/sqrt(9)!-9 151 = ((sqrt(9)!)!+(sqrt(9)!)!)/9-9 152 = (sqrt(9)!)!!+(9!!-9)/9 153 = 9*(9+9)-9 154 = ((sqrt(9)!)!+(sqrt(9)!)!)/9-sqrt(9)! 155 = (9!!-sqrt(9)!-9)/sqrt(9)! 156 = 9*(9+9)-sqrt(9)! 157 = ((sqrt(9)!)!+(sqrt(9)!)!)/9-sqrt(9) 158 = (9!!+9/sqrt(9))/sqrt(9)! 159 = 9*(9+9)-sqrt(9) 160 = (sqrt(9)!)!*sqrt(9)!/9/sqrt(9) 161 = 9*9+(sqrt(9)!)!/9 162 = 9*9+9*9 163 = sqrt(9)+((sqrt(9)!)!+(sqrt(9)!)!)/9 164 = sqrt(9)!+(9!!+sqrt(9))/sqrt(9)! 165 = sqrt(9)+9*(9+9) 166 = (9!/(sqrt(9)!)!-sqrt(9)!)/sqrt(9) 167 = (9!/(sqrt(9)!)!-sqrt(9))/sqrt(9) 168 = sqrt(9)!+9*(9+9) 169 = 9+((sqrt(9)!)!+(sqrt(9)!)!)/9 170 = (sqrt(9)!+9!/(sqrt(9)!)!)/sqrt(9) 171 = 9+9*(9+9) 172 = 9!!/sqrt(9)!/.9-sqrt(9) 173 = ? 174 = sqrt(9)!+9!/sqrt(9)/(sqrt(9)!)! 175 = (9!!+9!!/9)/sqrt(9)! 176 = (9!!+(sqrt(9)!)!)/9-9 177 = 9+9!/sqrt(9)/(sqrt(9)!)! 178 = sqrt(9)+9!!/sqrt(9)!/.9 179 = (sqrt(9)!)!/9+99 180 = 9*9+99 181 = sqrt(9)!+9!!/sqrt(9)!/.9 182 = (9!!+(sqrt(9)!)!)/9-sqrt(9) 183 = 9!/(9!!+9!!)-9 184 = (9!!+(sqrt(9)!)!-9)/9 185 = (sqrt(9)!)!/9+9!!/9 186 = (sqrt(9)!)!/sqrt(9)-sqrt(9)!*9 187 = (9!!-9!/9!!)/sqrt(9) 188 = sqrt(9)+(9!!+(sqrt(9)!)!)/9 189 = 9*(sqrt(9)+9+9) 190 = ((sqrt(9)!)!-sqrt(9)!)/sqrt(9)-(sqrt(9)!)!! 191 = sqrt(9)!+(9!!+(sqrt(9)!)!)/9 192 = (sqrt(9)+9)^sqrt(9)/9 193 = ((sqrt(9)!)!+sqrt(9))/sqrt(9)-(sqrt(9)!)!! 194 = 9+(9!!+(sqrt(9)!)!)/9 195 = sqrt(9)+9!/(9!!+9!!) 196 = ? 197 = ? 198 = 99+99 199 = sqrt((9!+9)/9-(sqrt(9)!)!) 200 = (sqrt(9)!)!/9+(sqrt(9)!)!/sqrt(9)!