From: tjl@cbnews.cb.att.com (timothy.j.lipetz)
Subject: Solutions for four 2s puzzle
Organization: AT&T
Date: Thu, 10 Sep 1992 19:35:28 GMT


As promissed earlier, here are the results of a program
(to be posted soon) to solve the four 2s puzzle.  The
expressions are in postfix format.

Timothy Lipetz
tjl@cbzoo.att.com

------------------------------------------------------

 1 = 2 2 2 2 + / * 
 2 = 2 2 2 2 + - - sqrt 
 3 = 2 2 2 2 + sqrt / + 
 4 = 2 2 2 2 + - - 
 5 = 2 2 2 2 / + + 
 6 = 2 2 2 2 + ^ sqrt + 
 7 = 2 2 2 .2 * / + 
 8 = 2 2 2 2 + + + 
 9 = 2 2 2 _2 - - / 
 10 = 2 2 2 2 + * + 
 11 = 2 2 _2 2 ^ sqrt / + 
 12 = 2 2 2 2 + + * 
 13 = 2 2 2 _2 / + + 
 14 = 2 2 2 .2 / + + 
 15 = 2 2 sqrt .2 _2 sqrt * * / 
 16 = 2 2 2 2 + * * 
 17 = 2 2 sqrt .2 _2 sqrt * / + 
 18 = 2 2 2 2 + ^ + 
 19 = 2 2 + ! .2 -2 ^ sqrt - 
 20 = 2 2 2 _2 / * + 
 21 = -2 2 .2 -2 ^ - - 
 22 = 2 2 2 .2 / * + 
 23 = -2 .2 2 -2 * ^ sqrt + 
 24 = 2 2 2 2 + - - ! 
 25 = 2 2 .2 2 ^ * / 
 26 = 2 2 2 2 + ^ sqrt ! + 
 27 = 2 2 sqrt _2 _2 sqrt * / * 
 28 = 2 2 2 2 + ! + + 
 29 = 2 2 .2 -2 ^ + + 
 30 = 2 2 sqrt .2 _2 sqrt * / * 
 31 = 2 _2 / sqrt ! .2 -2 ^ + 
 32 = 2 2 2 2 + ^ * 
 33 = 2 2 + ! 2 _2 / + 
 34 = 2 2 2 .2 / ^ sqrt + 
 35 = 2 .2 / .2 -2 ^ + 
 36 = 2 2 2 _2 / * * 
 38 = 2 2 2 sqrt _2 sqrt / ! ! + * sqrt 
 40 = 2 2 2 .2 / * * 
 42 = -2 2 22 * + 
 43 = -2 2 .2 _2 * / + 
 44 = 2 -2 2 2 + ! + * 
 45 = 2 2 _2 .2 - * / 
 46 = 2 -2 .2 -2 ^ + * 
 47 = 2 2 .2 _2 * / + 
 48 = 2 2 2 2 + ^ sqrt ! * 
 49 = 2 2 + ! .2 -2 ^ + 
 50 = 2 2 2 2 + ! * + 
 51 = .2 2 .2 / + .2 / 
 52 = 2 2 2 2 + ! + * 
 54 = 2 2 .2 -2 ^ + * 
 55 = 2 .2 + .2 2 ^ / 
 57 = 2 2 sqrt _2 sqrt / ! ! + _2 / sqrt 
 58 = -2 2 sqrt _2 sqrt / ! ! .2 / sqrt + 
 59 = 2 .2 -2 ^ sqrt ! - -2 / 
 60 = 2 .2 2 _2 / sqrt ! / / 
 61 = 2 .2 -2 ^ sqrt ! + 2 / 
 62 = -2 2 2 2 + ! ^ sqrt sqrt + 
 64 = 2 2 2 2 + + ^ 
 66 = 2 2 2 2 + ! ^ sqrt sqrt + 
 72 = 2 sqrt _2 sqrt 2 2 + ! / / 
 75 = 2 sqrt .2 .2 _2 sqrt * * / 
 79 = -2 2 _2 / 2 ^ + 
 80 = 2 sqrt _2 sqrt .2 -2 ^ sqrt ! * * 
 81 = 2 2 _2 2 ^ / * 
 83 = 2 2 _2 / 2 ^ + 
 88 = -2 2 .2 _2 - / - 
 90 = 2 2 .2 _2 * / * 
 92 = 2 2 .2 _2 - / - 
 95 = .2 -2 ^ sqrt ! .2 -2 ^ - 
 96 = 2 2 2 2 + ! * * 
 97 = -2 22 _2 / + 
 98 = -2 2 .2 / 2 ^ + 
 99 = 2 .2 + _2 .2 - / 
 100 = 2 2 .2 2 ^ / * 
 101 = 2 22 _2 / + 
 102 = 2 2 .2 / 2 ^ + 
 106 = -2 2 2 + ! _2 / + 
 107 = 2 2 + ! _2 - _2 / 
 108 = .2 _2 .2 -2 ^ sqrt ! / / 
 109 = _2 2 2 + ! + _2 / 
 110 = 2 2 2 + ! _2 / + 
 111 = .2 -2 ^ sqrt ! 2 _2 / - 
 112 = 2 22 .2 / + 
 114 = .2 -2 ^ sqrt ! 2 _2 / sqrt ! - 
 115 = .2 -2 ^ sqrt ! .2 -2 ^ sqrt - 
 116 = -2 2 .2 -2 ^ sqrt ! - - 
 117 = .2 -2 ^ sqrt ! 2 _2 / sqrt - 
 118 = -2 2 2 .2 * / ! + 
 119 = 2 -2 / .2 -2 ^ sqrt ! + 
 120 = 2 2 2 2 / + + ! 
 121 = 2 2 / .2 -2 ^ sqrt ! + 
 122 = 2 2 2 .2 * / ! + 
 123 = -2 .2 .2 sqrt * -2 ^ + 
 124 = 2 2 .2 -2 ^ sqrt ! + + 
 125 = .2 2 .2 -2 ^ sqrt - ^ 
 126 = 2 _2 / sqrt ! .2 -2 ^ sqrt ! + 
 127 = 2 .2 .2 sqrt * -2 ^ + 
 128 = 2 2 2 2 + ! ^ sqrt sqrt * 
 129 = 2 _2 / .2 -2 ^ sqrt ! + 
 130 = 2 .2 / .2 -2 ^ sqrt ! + 
 132 = 22 2 _2 / sqrt ! * 
 135 = 2 sqrt _2 sqrt _2 .2 - * / 
 142 = -2 .2 2 sqrt _2 sqrt / ! ! * + 
 144 = .2 2 2 2 + + ! * 
 145 = .2 -2 ^ .2 -2 ^ sqrt ! + 
 146 = 2 .2 2 sqrt _2 sqrt / ! ! * + 
 150 = 2 _2 / sqrt ! .2 2 ^ / 
 158 = -2 _2 2 sqrt _2 sqrt / ! ! * + 
 160 = _2 2 2 2 + + ! * 
 162 = 2 _2 2 sqrt _2 sqrt / ! ! * + 
 180 = 2 2 _2 .2 - / * 
 198 = 2 _2 22 / / 
 200 = 2 2 .2 / 2 ^ * 
 216 = 2 _2 2 2 + ! / / 
 220 = 2 .2 22 / / 
 222 = 222 2 ^ sqrt 
 224 = 2 222 + 
 225 = 2 .2 .2 _2 * * / 
 236 = 2 -2 .2 -2 ^ sqrt ! + * 
 238 = -2 2 .2 -2 ^ sqrt ! * + 
 240 = 2 2 2 .2 * / ! * 
 242 = 2 2 .2 -2 ^ sqrt ! * + 
 243 = 2 _2 / 2 .2 / ^ sqrt sqrt 
 244 = 2 2 .2 -2 ^ sqrt ! + * 
 250 = 2 .2 2 _2 / sqrt ^ / 
 256 = 2 2 2 2 + * ^ 
 264 = 2 .2 + .2 -2 ^ sqrt ! * 
 270 = 2 _2 / sqrt ! _2 .2 - / 
 288 = 2 .2 2 sqrt _2 sqrt / ! ! * * 
 300 = .2 -2 ^ sqrt ! 2 .2 * / 
 304 = 2 sqrt _2 sqrt / ! ! .2 _2 + * 
 320 = 2 _2 2 sqrt _2 sqrt / ! ! * * 
 324 = 2 _2 sqrt / 2 2 + ^ 
 358 = -2 2 sqrt _2 sqrt / ! ! 2 / + 
 359 = 2 2 sqrt _2 sqrt / ! ! - -2 / 
 360 = 2 sqrt _2 sqrt .2 -2 ^ sqrt ! / / 
 361 = 2 2 sqrt _2 sqrt / ! ! + 2 / 
 362 = 2 2 sqrt _2 sqrt / ! ! 2 / + 
 400 = 2 .2 sqrt / 2 2 + ^ 
 405 = 2 _2 _2 .2 - * / 
 444 = 2 222 * 
 450 = 2 .2 _2 .2 - * / 
 480 = 2 2 .2 -2 ^ sqrt ! * * 
 482 = -2 22 2 ^ + 
 484 = -2 2 2 + ! + 2 ^ 
 486 = 2 2 + ! _2 2 ^ / 
 495 = 22 .2 _2 * / 
 500 = 2 .2 .2 sqrt * / 2 ^ 
 504 = 2 _2 / ! 2 sqrt _2 sqrt / ! ! / 
 510 = -2 2 2 _2 / ^ + 
 512 = 2 2 2 _2 / * ^ sqrt 
 514 = 2 2 2 _2 / ^ + 
 528 = 22 2 2 + ! * 
 529 = -2 .2 -2 ^ + 2 ^ 
 531 = -2 .2 -2 ^ sqrt ! + _2 / 
 538 = -2 .2 -2 ^ sqrt ! _2 / + 
 539 = .2 -2 ^ sqrt ! _2 - _2 / 
 540 = 2 2 + ! .2 _2 * / 
 541 = _2 .2 -2 ^ sqrt ! + _2 / 
 542 = 2 .2 -2 ^ sqrt ! _2 / + 
 549 = 2 .2 -2 ^ sqrt ! + _2 / 
 550 = 22 .2 2 ^ / 
 574 = -2 2 2 + ! 2 ^ + 
 576 = 2 2 + ! 2 2 + ^ sqrt 
 578 = 2 2 2 + ! 2 ^ + 
 590 = -2 .2 -2 ^ sqrt ! + .2 / 
 598 = -2 .2 -2 ^ sqrt ! .2 / + 
 599 = .2 -2 ^ sqrt ! .2 - .2 / 
 600 = 2 2 + ! .2 2 ^ / 
 601 = .2 .2 -2 ^ sqrt ! + .2 / 
 602 = 2 .2 -2 ^ sqrt ! .2 / + 
 610 = 2 .2 -2 ^ sqrt ! + .2 / 
 623 = -2 .2 2 -2 * ^ + 
 625 = .2 2 2 .2 / - ^ sqrt 
 627 = 2 .2 2 -2 * ^ + 
 648 = .2 _2 2 sqrt _2 sqrt / ! ! / / 
 676 = 2 2 2 + ! + 2 ^ 
 695 = 2 sqrt _2 sqrt / ! ! .2 -2 ^ - 
 696 = 2 sqrt _2 sqrt / ! ! 2 2 + ! - 
 698 = 2 sqrt _2 sqrt / ! ! 22 - 
 710 = 2 sqrt _2 sqrt / ! ! 2 .2 / - 
 711 = 2 sqrt _2 sqrt / ! ! 2 _2 / - 
 714 = 2 sqrt _2 sqrt / ! ! 2 _2 / sqrt ! - 
 715 = 2 sqrt _2 sqrt / ! ! .2 -2 ^ sqrt - 
 716 = -2 2 2 sqrt _2 sqrt / ! ! - - 
 717 = 2 sqrt _2 sqrt / ! ! 2 _2 / sqrt - 
 718 = -2 2 2 2 + + ! + 
 719 = 2 -2 / 2 sqrt _2 sqrt / ! ! + 
 720 = 2 2 2 2 + ^ sqrt + ! 
 721 = 2 2 / 2 sqrt _2 sqrt / ! ! + 
 722 = 2 2 2 2 + + ! + 
 723 = 2 _2 / sqrt 2 sqrt _2 sqrt / ! ! + 
 724 = 2 2 2 sqrt _2 sqrt / ! ! + + 
 725 = 2 sqrt _2 sqrt / ! ! .2 -2 ^ sqrt + 
 726 = 2 _2 / sqrt ! 2 sqrt _2 sqrt / ! ! + 
 729 = 2 _2 / 2 _2 / sqrt ^ 
 730 = 2 .2 / 2 sqrt _2 sqrt / ! ! + 
 742 = 22 2 sqrt _2 sqrt / ! ! + 
 744 = 2 2 + ! 2 sqrt _2 sqrt / ! ! + 
 745 = 2 sqrt _2 sqrt / ! ! .2 -2 ^ + 
 800 = _2 .2 2 sqrt _2 sqrt / ! ! / / 
 840 = 2 sqrt _2 sqrt / ! ! .2 -2 ^ sqrt ! + 
 900 = .2 2 _2 / sqrt ! / -2 ^ 
 960 = 2 _2 - sqrt 2 sqrt _2 sqrt / ! ! * 
 968 = 2 22 2 ^ * 
 990 = 22 _2 .2 - / 
 999 = 222 _2 / 
 1000 = 2 .2 / 2 _2 / sqrt ^ 
Newsgroups: rec.puzzles