# A080035: "Orderly" Friedman numbers (or "good" Friedman numbers): Friedman numbers (A036057) where the construction digits are used in the proper order. # see c: Friedman numbers: can be written in a nontrivial way using their digits and the operations + - * / ^ and concatenation of digits (but not of results). # as per http://www2.stetson.edu/~efriedma/mathmagic/0800.html # Last revised 28 May 2010. 1 127 = - 1 + 2^7 2 343 = (3 + 4)^3 3 736 = 7 + 3^6 4 1285 = (1 + 2^8) * 5 5 2187 = (2 + 1^8)7 6 2502 = 2 + 50^2 7 2592 = 2^5 * 9^2 8 2737 = (2 * 7)^3 - 7 9 3125 = (3 + 1 * 2)^5 10 3685 = (3^6 + 8) * 5 11 3864 = 3 * (- 8 + 6^4) 12 3972 = 3 + (9 * 7)^2 13 4096 = (4 + 0 * 9)^6 14 11264 = 11 * 2^(6+4) 15 11664 = 1 * 1 * 6^6 / 4 16 12850 = (-1 + 2^8) * 50 17 13825 = 1 + (3 * 8)^(-2+5) 18 14641 = (1+4+6)^(4*1) 19 15552 = (1^5 + 5)^5 * 2 20 15585 = 1 * (5^5 - 8) * 5 21 15612 = - 1 + 5^6 - 12 22 15613 = 1 + 5^6 - 13 23 15617 = -1 + 5^6 - 1 * 7 24 15618 = 1 + 5^6 - 1 * 8 25 15621 = -1 + 5^6 - 2 - 1 26 15622 = 1 + 5^6 - 2 - 2 27 15623 = -1 + 5^6 + 2 - 3 28 15624 = 1 + 5^6 + 2 - 4 29 15626 = 1 + 5^(6*2-6) 30 15632 = 1 + 5^6 + 3 * 2 31 15633 = - 1 + 5^6 + 3 * 3 32 15642 = 1 + 5^6 + 4^2 33 15645 = 1* 5^6 + 4 * 5 34 15655 = 1 * 5 * (6 + 5^5) 35 15656 = 1 + 5^6 + 5 * 6 36 15662 = 1 + 5^6 + 6^2 37 15667 = 1 * 5^6 + 6 * 7 38 15688 = -1 + 5^6 + 8 * 8 39 15698 = 1 + 5^6 + 9 * 8 40 16377 = (1 + 6 - 3)^7 - 7 41 16384 = 16^3 * (8 - 4) 42 16447 = - 1 + 64 + 4^7 43 16875 = 1 * 68 + 7^5 44 17536 = 1 + 7^5 + 3^6 45 18432 = 18 * 4^(3+2) 46 19453 = 19 * 4^5 - 3 47 19683 = 1 * (9 - 6)^8 * 3 48 19739 = (- 1 + 9) * 7 + 3^9 49 23328 = (2 * 3^3)^2 * 8 50 23546 = 23 * 4^5 - 6 51 24546 = (2 + 4) * (-5 + 4^6) 52 24576 = (2 / 4)^(-5-7) * 6 53 26244 = (2 / 6)^(-2*4) * 4 54 26364 = 26^3 * 6 / 4 55 27639 = 2^7 * 6^3 - 9 56 28224 = (2 + 82)^2 * 4 57 28559 = -2 + (8 + 5)^(-5+9) 58 28671 = (2 / 8)^(-6) * 7 - 1 59 29282 = 2 * (9+2)^(8/2) 60 29524 = (2 * 9^5 - 2) / 4 61 32759 = (3 - 2 + 7)^5 - 9 62 32765 = -3 + (2 * 7 - 6)^5 63 32768 = (3 - 2 + 7)^6 / 8 64 32771 = 3 + 2^(7+7+1) 65 32785 = 3 + 2 + 7 * 8^5 66 34425 = 3^4 * 425 67 35721 = 3^5 * 7 * 21 68 36850 = (3^6 + 8) * 50 69 37179 = 3^7 * (1 + 7 + 9) 70 38856 = (3^8 - 85) * 6 71 39283 = 3^9 * 2 - 83 72 39342 = (3^9 - 3 * 4) * 2 73 39343 = 39 + 34^3 74 39358 = 3^9 * (-3 + 5) - 8 75 39363 = 3^9 / 3 * 6 - 3 76 39366 = 3^9 / (-3 + 6) * 6 77 39369 = 3 + 9^3 * 6 * 9 78 39372 = (3 + 9 * 3^7) * 2 79 39382 = ((3 * 9)^3 + 8) * 2 80 43775 = (4 * 3^7 + 7) * 5 81 45632 = -4^5 + 6^(3*2) 82 45927 = ((4 + 5) * 9)^2 * 7 83 45947 = 4 * 5 + 9^4 * 7 84 46626 = -4 + 6^6 - 26 85 46630 = 4 + 6^6 - 30 86 46632 = -4 * 6 + 6^(3*2) 87 46633 = 4 + 6^6 - 3^3 88 46644 = 4 + 6^6 - 4 * 4 89 46648 = 4 * 6^6 / 4 - 8 90 46651 = -4 + 6 * 6^5 - 1 91 46652 = -4 + (6 * 6)^(5-2) 92 46655 = 4 + 6 * 6^5 - 5 93 46656 = (-4 * 6 + 6 * 5)^6 94 46660 = 4 + 6^6 + 6 * 0 95 46663 = 4 + 6^6 + 6 - 3 96 46673 = -4 + 6^6 + 7 * 3 97 46684 = -4 + 6^6 + 8*4 98 46688 = (4 + 6^6 / 8) * 8 99 52488 = (5 + 2 - 4)^8 * 8 100 59052 = 5 + 9^(0+5) - 2 101 63945 = 63 * (-9 + 4^5) 102 64550 = (6^4 - 5) * 50 103 65471 = -65 + 4^(7+1) 104 66339 = (6 * 6)^3 + 3^9 105 66554 = 65 * 4^5 - 6 106 67234 = 6 + 7^(2+3) * 4 107 69984 = 6^(-9/9+8) / 4 108 98415 = 9^(8-4) * 15 ??? 103823 = (-1 + 0 + 3*8*2)3 ??? 114244 = (1 + 14 - 2)4 * 4 ??? 116565 = (-1 + 16) * (-5 + 65) ??? 117128 = 117-1-2 * 8 ??? 117476 = 1 - 174 + 76 ??? 117576 = 1 + 1 -75 + 76 ??? 117597 = 11 + (75 - 9) * 7 ??? 117619 = -11 + 76 - 19 ??? 117624 = -1 * 1 + 7^6 - 2^4 ??? 117625 = 1 * 1 + 76 - 25 ??? 117629 = -1 - 1 + 76 - 2 * 9 ??? 117630 = 11 + 76 - 30 ??? 117633 = 11 + 76 - 33 ??? 117635 = 1 * 1 + 76 - 3 * 5 ??? 117637 = -1 - 1 + 76 - 3 - 7 ??? 117638 = 1 - 1 + 76 - 3 - 8 ??? 117639 = 1 + 1 + 76 - 3 - 9 ??? 117641 = -11 + 76 + 4 - 1 ??? 117642 = -1 * 1 + 76 - 4 - 2 ??? 117643 = 1 * 1 + 76 - 4 - 3 ??? 117644 = -1 + (-1 + 76 / 4) * 4 ??? 117646 = -1 * 1 + 76 + 4 - 6 ??? 117647 = 1 * 1 + 76 + 4 - 7 ??? 117648 = 11 + 76 - 4 - 8 ??? 117650 = 1 * 1 + 76 + 5 * 0 ??? 117651 = -1 - 1 + 76 + 5 - 1 ??? 117652 = 1 - 1 + 76 + 5 - 2 ??? 117653 = 1 + 1 + 76 + 5 - 3 ??? 117655 = 1 + (1 + 76 / 5) * 5 ??? 117660 = 11 + 76 + 6 * 0 ??? 117662 = 1 * 1 + 76 + 6 * 2 ??? 117663 = 11 + 76 + 6 - 3 ??? 117695 = 1 * 1 + 76 + 9 * 5 ??? 117763 = 117 + 76 - 3 ??? 117777 = (1 + 1)7 + 77 / 7 ??? 118328 = (1 + (-1 + 8)3)2 - 8 ??? 124386 = (124 + 3 - 8) * 6 ??? 124416 = ((1 + 2) * 4)4) * 1 * 6 ??? 125003 = 1 + 2 + (50 + 0)3 ??? 125012 = 12 + 501+2 ??? 128500 = (1 + 28) * 500 ??? 129283 = (-1 + 29) * (28 - 3) ??? 131071 = (-1 + 3)10+7 - 1 ??? 131072 = (1 + 3)1+0+7 * 2 ??? 134456 = (1 * 3 + 4)4 * 56 ??? 136162 = 1 + (3 + 61 * 6)2 ??? 137718 = (-1 + 37) * 7 * (1 + 8) ??? 137772 = (-1 + 37 * 7) * (7 + 2) ??? 137781 = 1 * 37 * 7 * (8 + 1) ??? 137790 = (1 + 37 * 7) * 9 + 0 ??? 137791 = (1 + 37 * 7) * 9 + 1 ??? 137792 = (1 + 37 * 7) * 9 + 2 ??? 137793 = (1 + 37 * 7) * 9 + 3 ??? 137794 = (1 + 37 * 7) * 9 + 4 ??? 137795 = (1 + 37 * 7) * 9 + 5 ??? 137796 = (1 + 37 * 7) * 9 + 6 ??? 137797 = (1 + 37 * 7) * 9 + 7 ??? 137798 = (1 + 37 * 7) * 9 + 8 ??? 137799 = (1 + 37 * 7) * 9 + 9 ??? 137839 = -1 + 3 + 7 * (8 + 39) ??? 137948 = -1 + 3 * 7 * (94 + 8) ??? 139965 = -1 * 3 + (9 + 9) * 65 ??? 139966 = 1 + 3 * (-9 / 9 + 66) ??? 146410 = (1 + 4 + 6)4 * 10 ??? 146461 = (14 + 6)4 * 61 ??? 146875 = (1 + 4)6 * (8 + 7 / 5) ??? 147249 = (1 + 47 - 24) * 9 ??? 147349 = 1 + (47 - 3 * 4) * 9 ??? 147419 = -1 + (47 - 4) * 1 * 9 ??? 147429 = (-1 + 47) - 4 + 2) * 9 ??? 147447 = (-1 + 47) * (4 * 4 - 7) ??? 147453 = 1 * 47 * (4 + 5) - 3 ??? 147455 = -1 + 47 * 45 / 5 ??? 147491 = (1 * 47 + 4) * 9 - 1 ??? 147519 = (1 + 47 + 5 + 1) * 9 ??? 151875 = 1 / 5 * 1 * (8 + 7)5 ??? 155520 = (15 + 5)5 * 20 ??? 155850 = 1 * (55 - 8) * 50 ??? 156225 = (-1 + (56 - 2) * 2) * 5 ??? 156235 = 1 * (56 * 2 - 3) * 5 ??? 156245 = (-1 + (56 * (-2 + 4)) * 5 ??? 156249 = -1 + 56 * 2 * (-4 + 9) ??? 156250 = 1 * 56 * (2 + 5) + 0 ??? 156251 = 1 * 56 * (2 + 5) + 1 ??? 156252 = 1 * 56 * (2 + 5) + 2 ??? 156253 = 1 * 56 * (2 + 5) + 3 ??? 156254 = 1 * 56 * (2 + 5) + 4 ??? 156255 = 1 * 56 * (2 + 5) + 5 ??? 156256 = 1 * 56 * (2 + 5) + 6 ??? 156257 = 1 * 56 * (2 + 5) + 7 ??? 156258 = 1 * 56 * (2 + 5) + 8 ??? 156259 = 1 * 56 * (2 + 5) + 9 ??? 156275 = ((-1 + 56) * 2 + 7) * 5 ??? 156285 = ((-1 + 56 * 2 + 8) * 5 ??? 156295 = 1 * (56 * 2 + 9) * 5 ??? 157463 = -1 + ((5 + 7) * 4 + 6)3 ??? 158466 = (15 - 8)4 * 66 ??? 161051 = (16 + 10)5 * 1 ??? 163855 = (-1 + 6) * 3 + 85 * 5 ??? 163875 = (163 * 8 + 7) * 5 ??? 167042 = (16 + 70)4 * 2 ??? 167286 = (1672 - 8) * 6 ??? 170471 = (1 * 7 + 0)4 * 71 ??? 175232 = (-1 + 75)2 * 32 ??? 175274 = 1 + (75 - 2) * 74 ??? 176466 = (-1 + 76) / 4 * 6 - 6 ??? 176469 = (1 + 76 - 4) / 6 * 9 ??? 176472 = (-1 + 76) * (-4 + 7) / 2 ??? 177147 = (1 + 7/7 + 1)4+7 ??? 182476 = (1 + 8 - 2)4 * 76 ??? 184275 = (-1 + 84) * (2 + 7) * 5 ??? 184325 = (1 + 84 * 32) * 5 ??? 184329 = (1 + 84 * (3 + 2)) * 9 ??? 184335 = (1 + 84 * 3) * 3 * 5 ??? 184365 = (1 + 84) * (3 + 6) * 5 ??? 184495 = (-1 + (84 + 4) * 9 ) * 5 ??? 184545 = 1 * (84 + 5) * 45 ??? 185193 = 1 * ((8 - 5) * 19)3 ??? 186615 = -1 + 8 + 66 * (-1 + 5) ??? 186622 = 1 * 8 * 66 / 2 - 2 ??? 186624 = (18 * (6 + 6))2 * 4 ??? 186628 = (18 + 66) / 2 * 8 ??? 186631 = -1 + 8 + 66 * (3 + 1) ??? 186641 = 18 + 66 * 4 - 1 ??? 186642 = (1 + 8) * ((6 + 6)4 + 2) ??? 186644 = (18 + 66 + 4) * 4 ??? 186646 = (-1 + 8 + 66) * 4 - 6 ??? 186648 = (1 * 8 + 66) * 4 - 8 ??? 186684 = (-1 + 8 + 66 + 8) * 4 ??? 187278 = ((-1 + 8) * 7)2 * 78 ??? 196608 = ((-1 + 9)6 * 6 + 0) / 8 ??? 196830 = 1 * (9 - 6)8 * 30 ??? 206486 = (20 + 6)4 * 86 ??? 209944 = (2 + 0) * ((9 + 9)4 - 4) ??? 209946 = (2 + 0) * (9 + 9)4 - 6 ??? 209952 = (2 * (0 + 9))9-5 * 2 ??? 210125 = (210 + 1)2 / 5 ??? 216003 = 2 + 1 + (60 + 0)3 ??? 216021 = 21 + 602+1 ??? 218491 = (-2 + 1 + 8)4 * 91 ??? 227529 = (22 * 7 + 5)2 * 9 ??? 229373 = 22*9-3 * 7 - 3 ??? 229378 = 2 + 29+3 * 7 * 8 ??? 232324 = (-2 + 32+3)2 * 4 ??? 233255 = ((2 * 3)3*2 - 5) * 5 ??? 233280 = (2 * 33)2 * 80 ??? 234224 = -2 + 34 + 224 ??? 234248 = ((2 + 3) * 4 + 2)4 - 8 ??? 234254 = -2 + (34 / 2 + 5)4 ??? 234264 = 23 + (-4 + 26)4 ??? 234375 = (2 + 3)4 * 375 ??? 234377 = 2 + 3 * (4 * 3 - 7)7 ??? 235296 = -2 + (-3 + 5) * (-2 + 9)6 ??? 235768 = 2 * (35 + 76 - 8) ??? 236194 = -2 + 36 * 1 * 94 ??? 236196 = 2 * 36+1 * 9 * 6 ??? 236764 = 2 * (36 + 76 + 4) ??? 238648 = 23 * (8 * 64 + 8) ??? 245760 = (-2 + 4)5+7 * 60 ??? 247167 = 2 * 47 - 1 + 67 ??? 248830 = -2 + (4 + 8)8-3 + 0 ??? 248831 = -2 + (4 + 8)8-3 + 1 ??? 248832 = -2 + (4 + 8)8-3 + 2 ??? 248833 = -2 + (4 + 8)8-3 + 3 ??? 248834 = -2 + (4 + 8)8-3 + 4 ??? 248835 = -2 + (4 + 8)8-3 + 5 ??? 248836 = -2 + (4 + 8)8-3 + 6 ??? 248837 = -2 + (4 + 8)8-3 + 7 ??? 248838 = -2 + (4 + 8)8-3 + 8 ??? 248839 = -2 + (4 + 8)8-3 + 9 ??? 249318 = (2 + 4 * 9) * (3 * 1)8 ??? 250002 = 2 + (500 + 0)2 ??? 253135 = (2 + (5 + 3)1+3) * 5 ??? 255886 = -2 * 55 - 8 + 86 ??? 257049 = (25 + 7 + 0)4 / 9 ??? 259549 = -2595 + 49 ??? 261883 = -261 + (8 * 8)3 ??? 262118 = -26 + (2 * 1)18 ??? 262122 = 26*(2+1) - 22 ??? 262128 = 26*(2+1) - 2 * 8 ??? 262136 = -2 + 6 + (2 * 1)3*6 ??? 262137 = (-2 + 6)2+1+3 - 7 ??? 262139 = -2 + 6 / 2 + (1 + 3)9 ??? 262140 = 26*(2+1) - 4 + 0 ??? 262141 = 26*(2+1) - 4 + 1 ??? 262142 = 26*(2+1) - 4 + 2 ??? 262143 = 26*(2+1) - 4 + 3 ??? 262144 = 26*(2+1) - 4 + 4 ??? 262145 = 26*(2+1) - 4 + 5 ??? 262146 = 26*(2+1) - 4 + 6 ??? 262147 = 26*(2+1) - 4 + 7 ??? 262148 = 26*(2+1) - 4 + 8 ??? 262149 = 26*(2+1) - 4 + 9 ??? 262156 = 2 * 6 + (2 + 1 + 5)6 ??? 262176 = 26 / 2 + (1 + 7)6 ??? 262196 = 26 * 2 + (-1 + 9)6 ??? 262286 = (2 * 6)2 - 2 + 86 ??? 262438 = -2 + (62 + 4) * 38 ??? 262440 = (2 / 6)-2*4 * 40 ??? 263866 = (2 * 6)3 + 86 - 6 ??? 263866 = -2 - 6 + 56 * 17 ??? 265689 = 26 + 56 * (8 + 9) ??? 266565 = 26+6 + 5 * 65 ??? 268321 = -2 + (6 + 83)2 - 1 ??? 268323 = 2 + (6 + 83)2 - 3 ??? 268324 = (2 * (6 + 83))2 / 4 ??? 273375 = (2 + 7)3) * 375 ??? 274673 = -2 + (7 - 4 + 62)3 ??? 275686 = (2 * 7)5 + 6 - 86 ??? 279666 = ((2 - 7) * 9 + 66) * 6 ??? 279841 = (2 * 7 + 9)8-4*1 ??? 279867 = 2 - 79 + 8 + 67 ??? 279934 = -2 + (7 - 9 / 9)3+4 ??? 279936 = ((2 - 7 + 9) * 9)3 * 6 ??? 279937 = (2 + 7) / 9 + (9 - 3)7 ??? 279967 = 279 / 9 + 67 ??? 282240 = (2 + 82)2 * 40 ??? 287496 = ((2 + 8) * 7 - 4)9-6 ??? 289536 = 28 * (9 * 53 + 6) ??? 291602 = 2 + (9 * 1 * 60)2 ??? 294778 = 2 * 9 * (47 - 7) - 8 ??? 294782 = -2 + 94 * (7 * 8)2 ??? 294829 = -2 + 9 * (48 / 2 - 9) ??? 294838 = -2 + 9 * (4 * 8)3 - 8) ??? 294894 = 2 * (-9 + 48 * 9 / 4) ??? 294895 = (2 + (94 - 8) * 9) * 5 ??? 294912 = 2 * 9 * 49-1*2 ??? 294928 = 2 * (9 * 49-2 + 8) ??? 295195 = (-2 + 95 + 1 - 9) * 5 ??? 295225 = (-2 + 95 / 2) * 2 * 5 ??? 295235 = (-2 + 95) * (-2 + 3) * 5 ??? 295243 = -2 + 95 * (2 * 4 - 3) ??? 295245 = 2 * 95 * 2 / 4 * 5 ??? 295247 = 2 + 95 * (2 - 4 + 7) ??? 295255 = (2 + 95) * 25 / 5 ??? 295285 = (2 + 95 - 2 + 8) * 5 ??? 295465 = (-2 + 95 + 46) * 5 ??? 295505 = (2 + 95 + 50) * 5 ??? 296346 = ((-2 + 9) * 6)3 * 4 - 6 ??? 296384 = ((-2 + 9) * 6)3 + 8 * 4 ??? 299575 = (29 + 9) * 575 ??? 312325 = 312 * 325 ??? 314431 = ((3 + 14) * 4)3 - 1 ??? 314928 = (3 * 14)9 * 2 * 8 ??? 325125 = ((3 + 2) * 51)2 * 5 ??? 326557 = ((3 * 2) * 65 - 5) * 7 ??? 326586 = 3 * (-2 + 65 * (8 + 6)) ??? 326592 = 3 * 2 * 65 * (9 - 2)) ??? 326617 = 32 + (66 - 1) * 7 ??? 326634 = ((3 * 2)6 + 6) * (3 + 4) ??? 326697 = ((3 * 2)6 + 6 + 9) * 7 ??? 327485 = (-32 - 7 + 48) * 5 ??? 331683 = 3 * (-31 + (6 * 8)3) ??? 331773 = -3 + (31 - 7)7-3) ??? 333234 = (33 * 3)2 * 34 ??? 344250 = 34 * 4250 ??? 344250 = 34 * 4250 ??? 347736 = 3 + 477 * 36 ??? 351232 = (3 + 51 + 2)3 * 2 ??? 352926 = 3 * (-5 - 2 + (9 - 2)6) ??? 352932 = 3 * (-5 + (-2 + 9)3*2) ??? 352947 = 3 * (5 + 2)9-4 * 7 ??? 352961 = 3 * (5 + (-2 + 9)6) - 1 ??? 354277 = ((3 * 5)4 - 2 * 7) * 7 ??? 354292 = 35+4 * 2 * 9 - 2 ??? 354294 = 35+4 / 2 * 9 * 4 ??? 354627 = ((3 * 5)4 + 62) * 7 ??? 357210 = 35 * 7 * 210 ??? 357210 = 35 * 7 * 210 ??? 360855 = (-3 + 6 + 0)8 * 55 ??? 367272 = (36 * 7 - 2) * 72 ??? 368500 = (36 + 8) * 500 ??? 368500 = (36 + 8) * 500 ??? 371314 = 3 * 7 + 131+4 ??? 372573 = 37 + 2 * 573 ??? 373239 = (-3 + 73 + 2)3 - 9 ??? 373248 = (3 * (7 - 3))2+4 / 8 ??? 374439 = (-3 + 74 * 4) * 39 ??? 374529 = 3 * (74 * 52 - 9) ??? 375021 = 3 * (7 + 502+1) ??? 375168 = 3 * (7 + 51*6) * 8 ??? 379793 = (-3 + 7)9 + 79-3 ??? 386758 = -3867 + 58 ??? 388560 = (38 - 85) * 60 ??? 388560 = (38 - 85) * 60 ??? 388993 = -3 * 8 + (-8 + 9 * 9)3 ??? 389342 = ((3 + 89)3 - 4) / 2 ??? 390358 = -3 + 90 * 3 + 58 ??? 390583 = -39 + 0 + 58 - 3 ??? 390589 = (-3 * 9 + 0) + 58 - 9 ??? 390628 = 3 + (90 + 6 - 2)8 ??? 390658 = (3 * 9 + 0 + 6 + 5)8 ??? 390658 = 39 + 0 - 6 + 58 ??? 391864 = (-39 + (1 - 8)6) * 4 ??? 393189 = 3 * (-9 + (3 - 1)8+9) ??? 393216 = (3 + 9 / 3) * 216 ??? 393420 = (39 - 3 * 4) * 20 ??? 393420 = (39 - 3 * 4) * 20 ??? 393660 = 39 / (-3 + 6) * 60 ??? 393660 = 39 / (-3 + 6) * 60 ??? 393720 = (3 + 9 * 37) * 20 ??? 393720 = (3 + 9 * 37) * 20 ??? 393820 = ((3 * 9)3 + 8) * 20 ??? 393820 = ((3 * 9)3 + 8) * 20 ??? 397535 = (3 * (9 + 7) - 5)3 * 5 ??? 411772 = (41-1 + 77) / 2 ??? 413466 = (413 - 4 - 6) * 6 ??? 413496 = (413 + 4 - 9) * 6 ??? 413518 = 413 * (5 + 1) - 8 ??? 413536 = (413 + 5 / 3) * 6 ??? 417625 = (4 + 176-2) * 5 ??? 419904 = 4 * (9 + 9 + 0)4 ??? 420175 = (4 + 20 + 1) * 75 ??? 425984 = (4 * 2)5 * (9 + 8 - 4) ??? 432964 = 4 * 3296-4 ??? 437564 = 43 + 7 * 56 * 4 ??? 437656 = 4 * (-3 + 7 * (6 + 56)) ??? 437750 = (4 * 37 + 7) * 50 ??? 455625 = (4 * 5 - 5)6 / 25 ??? 456533 = (4 + 5 + 65 + 3)3 ??? 456976 = (4 * 5 + 6)-9+7+6 ??? 459270 = (4 + 5) * 9)2 * 70 ??? 466520 = (-4 + 66) * 5 * 2 + 0 ??? 466521 = (-4 + 66) * 5 * 2 + 1 ??? 466522 = (-4 + 66) * 5 * 2 + 2 ??? 466523 = (-4 + 66) * 5 * 2 + 3 ??? 466524 = (-4 + 66) * 5 * 2 + 4 ??? 466525 = (-4 + 66) * 5 * 2 + 5 ??? 466526 = (-4 + 66) * 5 * 2 + 6 ??? 466527 = (-4 + 66) * 5 * 2 + 7 ??? 466528 = (-4 + 66) * 5 * 2 + 8 ??? 466529 = (-4 + 66) * 5 * 2 + 9 ??? 466536 = (-4 + (66 * 5 / 3) * 6 ??? 466552 = (-4 + 6 * 65 * 5) * 2 ??? 466553 = (-4 + 66 * (5 + 5) - 3 ??? 466557 = (4 + 66 * (5 + 5) - 7 ??? 466560 = (4 + 6) * 65 * 6 + 0 ??? 466561 = (4 + 6) * 65 * 6 + 1 ??? 466562 = (4 + 6) * 65 * 6 + 2 ??? 466563 = (4 + 6) * 65 * 6 + 3 ??? 466564 = (4 + 6) * 65 * 6 + 4 ??? 466565 = (4 + 6) * 65 * 6 + 5 ??? 466566 = (4 + 6) * 65 * 6 + 6 ??? 466567 = (4 + 6) * 65 * 6 + 7 ??? 466568 = (4 + 6) * 65 * 6 + 8 ??? 466569 = (4 + 6) * 65 * 6 + 9 ??? 466652 = (46 + 66 * 5) * 2 ??? 466880 = (4 + 66 / 8) * 80 ??? 470576 = 4 * (7 * 0 - 5 + 76) ??? 470596 = 4 * (7 + 0 * 59)6 ??? 470616 = 4 * ((7 + 0)6 - 1 + 6) ??? 470628 = (4 + ((7 + 0)6 / 2)) * 8 ??? 470632 = 4 * ((7 + 0)6 + 32) ??? 471576 = (471 + 57) * 6 ??? 472364 = 4 * (-7 + 2 * 36+4) ??? 472384 = -4 + 72 * 38 - 4) ??? 472388 = 4 + 72 * 38 - 8) ??? 472392 = (4 + 7 * 2)3 * 92 ??? 472395 = -4 + 7 + 23 * 92 ??? 472398 = (-4 + 7) * (2 + 39 * 8) ??? 472439 = 47 + 24 * 39 ??? 474552 = (4 + 74)5/5+2 ??? 475136 = 47 * (5 + (1 + 3) * 6) ??? 475281 = (47 + 5) * (28 + 1) ??? 476254 = 4 + 762 * 54 ??? 483153 = ((-4 + 8) * 3 - 1)5 * 3 ??? 484128 = (48 * 41)2 / 8 ??? 492205 = 492 * 205 ??? 493837 = -4 + 9 * 383 - 7 ??? 493852 = 4 + 9 * 385-2 ??? 497657 = 4 * (9 + 7) * 65 - 2 ??? 497662 = (-4 + 9 +7)6 / 6 - 2 ??? 497664 = 4 * (9 + 7) * 6 * 64 ??? 508276 = (5 + 0)8 + 2 + 76 ??? 523665 = ((5 - 2) * 3)6 - 65 ??? 524248 = (-5 + (-2 + 4)24) * 8 ??? 524268 = (-5 / 2 + 42+6) * 8 ??? 524282 = -5 + (-2 + 42+8) / 2 ??? 524283 = -5 + 2(4-2)*8+3 ??? 524285 = -5 + 2 + 42 * 85 ??? 524288 = (5 + (2 - 4) / 2)8 * 8 ??? 524293 = 5 + 2 * 4 * 29-3 ??? 524298 = 5 * 2 + 4 * 29+8 ??? 524880 = (5 + 2 - 4)8 * 80 ??? 526833 = (-5 + (26 - 8)3) * 3 ??? 531296 = -5 * (31 - 2) + 96 ??? 531396 = -5 * 3 * 1 * 3 + 96 ??? 531426 = -5 * 3 + (1 + 4 * 2)6 ??? 531428 = -5 + 314-2 - 8 ??? 531433 = -5 + 31*4*3 - 3 ??? 531436 = -5 + 314 / (3 + 6) ??? 531438 = 5 + 31*4*3 - 8 ??? 531439 = -5 + 3 + 1 - 43+9 ??? 531441 = (5 - 3 + 1)4(4-1) ??? 531443 = 5 + (31- 4)4 - 3 ??? 531446 = 5 + 314+4-6 ??? 531456 = 5 * 3 * 1 + (4 + 5)6 ??? 531494 = 53 + ((-1 + 4) * 9)4 ??? 531496 = 5 * (-3 + 14) + 96 ??? 531966 = 531 + 96 - 6 ??? 538412 = (5 + 38) * 41 * 2 ??? 546875 = 54-6+8 * 7 * 5 ??? 549365 = 5 * (493 - 65) ??? 551343 = -5 * 5 + (1 + 34)3 ??? 559539 = (55 + 95 - 3) * 9 ??? 562419 = ((56 - 2) * 4 - 1) * 9 ??? 563922 = ((56 + 3) * 9)2 * 2 ??? 577602 = -5 + 7 + 7602 ??? 578125 = 57 * (8 - 1 + 2 / 5) ??? 583443 = (-5 - 8 + 34)4 * 3 ??? 583889 = -5 * 8 + 38 * 89 ??? 584647 = (5 + 8 / 4 * 6)4 * 7 ??? 585640 = 5 * 8 * (5 + 6)4 + 0 ??? 585641 = 5 * 8 * (5 + 6)4 + 1 ??? 585642 = 5 * 8 * (5 + 6)4 + 2 ??? 585643 = 5 * 8 * (5 + 6)4 + 3 ??? 585644 = 5 * 8 * (5 + 6)4 + 4 ??? 585645 = 5 * 8 * (5 + 6)4 + 5 ??? 585646 = 5 * 8 * (5 + 6)4 + 6 ??? 585647 = 5 * 8 * (5 + 6)4 + 7 ??? 585648 = 5 * 8 * (5 + 6)4 + 8 ??? 585649 = 5 * 8 * (5 + 6)4 + 9 ??? 588765 = (5 + 8) * 8 + 76 * 5 ??? 589748 = -5 + (-8 + 9 * (-7 + 48)) ??? 589864 = 5 * 8 + 9 * 86 / 4 ??? 590945 = 5 + 90 * (94 + 5) ??? 592763 = 59 + (2 * 7 * 6)3 ??? 597878 = 5 + (97 + 8 + 7) / 8 ??? 606476 = ((6 + 0)6 - 4) * (7 + 6) ??? 614125 = (6 * 14 + 1)-2+5 ??? 624978 = -6 + (2 + (-4 + 9)7) * 8 ??? 629844 = 6 * (-2 + (9 * 8 / 4)4) ??? 629848 = (6 / 2)9) * 8 * 4 - 8 ??? 635993 = -63 + (5 + 9 * 9)3) ??? 640024 = (6 + 4002) * 4 ??? 645500 = (64 - 5) * 500 ??? 649495 = (6 - 4 + 9) * (-4 + 95) ??? 649529 = -6 - 4 + 95 * (2 + 9) ??? 653184 = 65 * (3 + 18) * 4 ??? 655284 = (65 + 52) * 84 ??? 655354 = -6 + 5 * (5 + 3)5 * 4 ??? 655935 = (6 * 55 - 9) * 35 ??? 656187 = (6 * 56 - 1 - 8) * 7 ??? 656244 = -6 + 56 * (-2 + 44) ??? 656250 = 6 * 56 * (2 + 5) + 0 ??? 656251 = 6 * 56 * (2 + 5) + 1 ??? 656252 = 6 * 56 * (2 + 5) + 2 ??? 656253 = 6 * 56 * (2 + 5) + 3 ??? 656254 = 6 * 56 * (2 + 5) + 4 ??? 656255 = 6 * 56 * (2 + 5) + 5 ??? 656256 = 6 * 56 * (2 + 5) + 6 ??? 656257 = 6 * 56 * (2 + 5) + 7 ??? 656258 = 6 * 56 * (2 + 5) + 8 ??? 656259 = 6 * 56 * (2 + 5) + 9 ??? 656298 = 6 * (56 * (-2 + 9) + 8) ??? 656373 = 6 * (56 + 3) * 7 - 3 ??? 656376 = (6 + 56 - 3) * 7 * 6 ??? 656418 = 6 * (56 + 4) * (-1 + 8) ??? 656790 = 6 * (56 * 7 + 90) ??? 656817 = (6 * 56 + 81) * 7 ??? 657874 = (-6 + 5 * 7 * 8) * 74 ??? 658503 = (((6 + 5) * 8) - 50)3 ??? 659685 = (65 - 9 - 6) * 85 ??? 663552 = 6 * (6 * (3 + 5) + 55-2) ??? 677328 = 6 * ((-7 + 73)2 - 8) ??? 699875 = (69 / 9 / 8 + 7) * 5 ??? 705642 = ((7 - 0)5 - 6) * 42 ??? 728993 = -7 + ((2 + 8) * 9) * 99/3 ??? 741321 = (7 * 41 * 3)2*1 ??? 742572 = ((7 + 4 + 2)5 - 7) * 2 ??? 742586 = (7 + 4 + 2)5 * (8 - 6) ??? 756045 = (75 - 6 + 0) * 45 ??? 756315 = 75 * (6 - 3) * 15 ??? 756325 = (75 * (6 + 3) + 2) * 5 ??? 756549 = ((75 + 6) * 5 - 4) * 9 ??? 756585 = (75 + 6) * (5 * 8 + 5) ??? 759359 = -7 + (5 * 9 / 3)5 - 9 ??? 759375 = (-7 + 59 - 37)5 ??? 765392 = 76 * 5 + 39+2 ??? 766927 = (7 + 6 * 6 * 9)2 * 7 ??? 774137 = 7 * (7 + 41)3 - 7 ??? 777922 = ((7 + 7) * 7 * 9)2 - 2 ??? 777924 = 7 * 7 * (7 * 9)2 * 4 ??? 781257 = 7 + (81 + 2) * 57 ??? 786369 = (-7 + 86 / (-3 + 6)) * 9 ??? 786385 = (-7 + 86 * 3) - 8 * 5 ??? 786393 = (-7 + 86 + 3 - 9) * 3 ??? 786396 = (-7 + 86) * 3 - 9 - 6 ??? 786411 = (-7 + 86) * (4 - 1) * 1 ??? 786413 = -7 + (86 - 4) * 1 * 3 ??? 786425 = -7 + 8 * 6 * 42+5 ??? 786433 = -7 + 8 + 643 * 3 ??? 786439 = 7 + (8 * 6 * 4)3 / 9 ??? 786441 = 7 + 86 - 4 * (4 - 1) ??? 786453 = 7 + 86 * (4 + 5) / 3 ??? 789264 = 7 * (89 - 2) * 64 ??? 805255 = (8 + 0 + 5 - 2)5 * 5 ??? 805655 = (80 + (5 + 6)5) * 5 ??? 806752 = (8 + 0) * 6 * 75 + 2 ??? 823297 = -82 * 3 + (-2 + 9)7 ??? 823461 = -82 + (3 + 4)6+1 ??? 823527 = -8 * 2 + (-3 + 5 * 2)7 ??? 823543 = (8 - 2 * 3 + 5)4+3 ??? 824577 = 8 + 2 + 45 + 77 ??? 839424 = 8 * (-3 + 94) * 24 ??? 839673 = ((-8 + 3) * 9 + 67) * 3 ??? 839812 = 8 + (-3 + 9)8 * 1 / 2 ??? 839827 = -8 + 3 * (9 + (8 - 2)7) ??? 839867 = 8 + 3 * (9 + 8 + 67) ??? 844277 = (8 + 4)4 - 2 + 77 ??? 851942 = (85 - 1) * (9 + 4) * 2 ??? 851968 = (8 + 5) * (1 + 9 - 6)8 ??? 857383 = 8 + (57 + 38)3 ??? 861327 = (86 - 1) * (3 + 2 / 7) ??? 875056 = 8 * 7 * (50 + 56) ??? 875336 = 8 * 7 * (53 + 3 + 6) ??? 884733 = (8 * 84 / 7)3 - 3 ??? 884736 = 8 * 84 * (7 * 3 + 6) ??? 886464 = (8 * 86 - 4) * 64 ??? 907569 = 9 * (0 + 7)5 * 6 - 9 ??? 912247 = (9 + 12 - 2)4 * 7 ??? 923314 = -9 * 23 + 314 ??? 924385 = (9 - 2)4 * 385 ??? 937577 = (9 + 3) * (7 + 57) - 7 ??? 944784 = 94 * (4 * 7 + 8) + 4 ??? 973944 = ((9 * 7)3 - 94) * 4 ??? 979767 = -9 + 7 / (9 - 7) * 67 ??? 984150 = 98-4 * 150 ??? 268435179 = -268 + 4^(3*5 - 1^7) - 9 ??? 99999999 = (9 + 9/9)9-9/9 - 9/9 ??? 333333333 = ((3*3 + 3/3)3*3 - 3/3) / 3 ??? 5555555555 = (5(5+5)5+5 - 5) / (5 + 5 - 5/5) ??? 11111111111 = ((11-1)11 - 1*1) / (11-1-1) ??? 22222222222222 = (2((22-2)/2)22+2-2-2) / (2+2/2)2 ??? 77777777777777 = (7((77-7)/7)7+7 - 7 + 7 - 7) / (7 + (7+7)/7) ??? 88888888888888 = (8((88-8)/8)8+8-(8+8)/8 - 8) / (8 + 8/8) ??? 444444444444444 = (4(44/4 - 4/4)4*4-4/4 - 4) / (4 + 4 + 4/4) ??? 6666666666666666 = (6((66-6)/6)6 + (66-6)/6 - 6) / (6 + (6+6+6)/6)