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The five 3īs (Posted on 2008-07-07) Difficulty: 2 of 5
This is a real story. A long long time ago, based on the "Four fours" problem, I wondered if I could do the same using exactly five 3īs, the restrictions a bit tighter: I could use only the 4 basic math operations, exponentiation, factorial, and all parentheses I may need. Besides, I didnīt disallow me to join two "3īs" to make "33".

Using this, and only this, I succeeded in writing expressions for all integers from 0 to 100.

To narrow your work, since a great number of integers can be easily obtained, can you find expressions for 47, 50, 56, 58, 64, 70, 71, 73, 74, 76, 77, 85, 88, 94, and 95?

See The Solution Submitted by pcbouhid    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(5): all hundred | Comment 32 of 35 |
(In reply to re(4): all hundred by Charlie)

333,33-                      333-33                         300 
3!,33,3,3**+                 3!+33*3*3                      303
3!!,3/,3!,3/,3!^+            3!!/3+(3!/3)^3!                304
333,3,3^-                    333-3^3                        306
3!,3!+!,3!!,3*/,3!!/         ((3!+3!)!/(3!!*3))/3!!         308
3!,3^,3!!+,3/,3-             (3!^3+3!!)/3-3                 309
3!,3^,3!!+,3!-,3/            (3!^3+3!!-3!)/3                310
3!!,3!,3^,3-+,3/             (3!!+3!^3-3)/3                 311
3!!,3,3+,3^+,3/              (3!!+(3+3)^3)/3                312
3!!,3!,3^,3++,3/             (3!!+3!^3+3)/3                 313
3!,3^,3!+,3!!+,3/            (3!^3+3!+3!!)/3                314
333,3!,3*-                   333-3!*3                       315
3!!,3/,3!!+,3/,3-            (3!!/3+3!!)/3-3                317
3!!,3!/,33,3!*+              3!!/3!+33*3!                   318
3!!,3,3!!,3/--,3/            (3!!-(3-3!!/3))/3              319
3,3+!,3!!,3/+,3/             ((3+3)!+3!!/3)/3               320
333,3!,3!+-                  333-(3!+3!)                    321
3!!,3/,3!+,3!!+,3/           (3!!/3+3!+3!!)/3               322
3,3!^,3!!,3/+,3/             (3^3!+3!!/3)/3                 323
333,3,3*-                    333-3*3                        324
3!,3!!,3!!,3/+,3/+           3!+(3!!+3!!/3)/3               326
333,3-,3-                    333-3-3                        327
333,3!,3--                   333-(3!-3)                     330
333,3!,3/-                   333-3!/3                       331
333,3,3/-                    333-3/3                        332
333,3,3/^                    333^(3/3)                      333
3,3/,333+                    3/3+333                        334
333,3!,3/+                   333+3!/3                       335
333,3!+,3-                   333+3!-3                       336
3,3/,3!+,3^,3!-              (3/3+3!)^3-3!                  337
333,3+,3+                    333+3+3                        339
3!,3,3/+,3^,3-               (3!+3/3)^3-3                   340
333,3,3*+                    333+3*3                        342
3,3,3,3/++,3^                (3+3+3/3)^3                    343
3!,3!+,333+                  3!+3!+333                      345
3,3/,3!+,3^,3+               (3/3+3!)^3+3                   346
3,3!!,3!/,3-*,3-             3*(3!!/3!-3)-3                 348
3,3/,3!+,3^,3!+              (3/3+3!)^3+3!                  349
3,3!*,333+                   3*3!+333                       351
3!!,3*,3!-,3!/,3!-           (3!!*3-3!)/3!-3!               353
3,3+!,3*,3!/,3!-             (3+3)!*3/3!-3!                 354
3,3!!*,3!+,3!/,3!-           (3*3!!+3!)/3!-3!               355
3!!,3*,3!-,3!/,3-            (3!!*3-3!)/3!-3                356
3!!,3,3,3/-/,3-              3!!/(3-3/3)-3                  357
3!!,3-,3*,3-,3!/             ((3!!-3)*3-3)/3!               358
3,3+!,3*,3!-,3!/             ((3+3)!*3-3!)/3!               359
3,3^,333+                    3^3+333                        360
3,3/,3!!,3,3!/*+             3/3+3!!*3/3!                   361
3,3,3,3!!+*+,3!/             (3+3*(3+3!!))/3!               362
33,33,3/*                    33*33/3                        363
3,3,3!^*,3-,3!/              (3*3^3!-3)/3!                  364
3,3,3!^,3*+,3!/              (3+3^3!*3)/3!                  365
33,333+                      33+333                         366
3,3!!*,3!+,3!/,3!+           (3*3!!+3!)/3!+3!               367
3!,3!*,333+                  3!*3!+333                      369
3,3,3!!,3!/+*,3+             3*(3+3!!/3!)+3                 372
3,3,3!,3/+,3^*               3*(3+3!/3)^3                   375
3!!,3,3/,3!+,3^-             3!!-(3/3+3!)^3                 377
3,3!*,3+,3!,3**              (3*3!+3)*3!*3                  378
3!!,3!/,3,3!!*+,3!/          (3!!/3!+3*3!!)/3!              380
3!!,333-,3!-                 3!!-333-3!                     381
3!!,3-,333-                  3!!-3-333                      384
3,3+!,333-                   (3+3)!-333                     387
3!!,3+,333-                  3!!+3-333                      390
3!,333-,3!!+                 3!-333+3!!                     393
3!,33,33+*                   3!*(33+33)                     396
3,33,3!,3!+*+                3+33*(3!+3!)                   399
3,3!!*,3!!,3/+,3!/           (3*3!!+3!!/3)/3!               400
3!,33,3!,3!+*+               3!+33*(3!+3!)                  402
3!,3*,3-,3,3^*               (3!*3-3)*3^3                   405
3,3!,3^*,3!!,3/-             3*3!^3-3!!/3                   408
3!,33*,3!,3^+                3!*33+3!^3                     414
3!,3,3!,3^,3!-//             3!/(3/(3!^3-3!))               420
3!!,3,3,33**-                3!!-3*3*33                     423
3!,3!,3^,3-,3/*              3!*(3!^3-3)/3                  426
3!,3,3!,3^//,3-              3!/(3/3!^3)-3                  429
3!,3!,3^*,3!-,3/             (3!*3!^3-3!)/3                 430
3!,3!,3^*,3-,3/              (3!*3!^3-3)/3                  431
3,33+,3!,3!+*                (3+33)*(3!+3!)                 432
3!,3^,3!*,3+,3/              (3!^3*3!+3)/3                  433
3!,3!,3^*,3!+,3/             (3!*3!^3+3!)/3                 434
3!,3^,3,3!,3^++              3!^3+3+3!^3                    435
3!!,3/,3!,33*+               3!!/3+3!*33                    438
3!,3!+!,3/,3,3*!/            ((3!+3!)!/3)/(3*3)!            440
3,3,3!*+,3!,3/^              (3+3*3!)^(3!/3)                441
3!,3!,3^,3!+*,3/             3!*(3!^3+3!)/3                 444
3!!,3!!,3/,33+-              3!!-(3!!/3+33)                 447
3,3^,3*,3!-,3!*              (3^3*3-3!)*3!                  450
333,3!!,3!/+                 333+3!!/3!                     453
3!,3^,3!,3!!-,3/-            3!^3-(3!-3!!)/3                454
3!,3^,3,3!!-,3/-             3!^3-(3-3!!)/3                 455
3!,3^,3,3+!,3/+              3!^3+(3+3)!/3                  456
3,3!!+,3/,3!,3^+             (3+3!!)/3+3!^3                 457
3!!,3!+,3/,3!,3^+            (3!!+3!)/3+3!^3                458
3!!,3!/,33+,3*               (3!!/3!+33)*3                  459
3!!,3,3*/,3-,3!*             (3!!/(3*3)-3)*3!               462
3!,3!+,33,3!+*               (3!+3!)*(33+3!)                468
3!!,3!!+,33-,3/              (3!!+3!!-33)/3                 469
3!!,3!,3^,33+-               3!!-(3!^3+33)                  471
3!!,3!-,3!!+,3/,3!-          (3!!-3!+3!!)/3-3!              472
3!!,3!-,3,3!!+,3/-           3!!-3!-(3+3!!)/3               473
3!!,3/,3-,3,3!//             (3!!/3-3)/(3/3!)               474
3!!,3,3!^,3!+,3/-            3!!-(3^3!+3!)/3                475
3!!,3,3!^,3+,3/-             3!!-(3^3!+3)/3                 476
3!,3,3^*,3-,3*               (3!*3^3-3)*3                   477
3!!,3-,3,3!/,3*/             (3!!-3)/((3/3!)*3)             478
3!!,3,3!//,3-,3/             (3!!/(3/3!)-3)/3               479
3,3+!,3,3*,3!//              (3+3)!/(3*3/3!)                480
3!!,3+,3,3+!+,3/             (3!!+3+(3+3)!)/3               481
3,3!!+,3,3*/,3!*             ((3+3!!)/(3*3))*3!             482
3,3^,3!,3**,3-               3^3*3!*3-3                     483
3,3!!+,3,3!^+,3/             (3+3!!+3^3!)/3                 484
3,3!^,3!!,3!++,3/            (3^3!+3!!+3!)/3                485
33,3!-,3!*,3*                (33-3!)*3!*3                   486
3,3!^,3!!,3!+,3/-            3^3!-(3!!+3!)/3                487
3,3!^,3!!,3+,3/-             3^3!-(3!!+3)/3                 488
3,3!,3,3^*,3*+               3+3!*3^3*3                     489
3,3!^,3!!,3-,3/-             3^3!-(3!!-3)/3                 490
3!!,3!!,33-,3/-              3!!-(3!!-33)/3                 491
3!,3,3!,3,3^**+              3!+3*3!*3^3                    492
3,3!*,3-,33*                 (3*3!-3)*33                    495
3,3*!,3!!-,3!!/,3!-          ((3*3)!-3!!)/3!!-3!            497
3!!,3-,3!,3^-,3-             3!!-3-3!^3-3                   498
3!!,3,3*!+,3!!/,3!-          (3!!+(3*3)!)/3!!-3!            499
3,3*!,3!!-,3!!/,3-           ((3*3)!-3!!)/3!!-3             500
3,3*!,3,3+!/,3-              (3*3)!/(3+3)!-3                501
3!!,3!,3/,3!,3^+-            3!!-(3!/3+3!^3)                502
3,3*!,3!!/,3,3/-             (3*3)!/3!!-3/3                 503
3,3^,3*,3+,3!*               (3^3*3+3)*3!                   504
3,3/,3,3*!,3!!/+             3/3+(3*3)!/3!!                 505
3!,3/,3,3*^,3!-              (3!/3)^(3*3)-3!                506
3,3,3+!+,3!,3^-              3+(3+3)!-3!^3                  507
3,3,3*!,3!!+,3!!/+           3+((3*3)!+3!!)/3!!             508
3!,3/,3,3*^,3-               (3!/3)^(3*3)-3                 509
3,3!^,3!,3^-,3-              3^3!-3!^3-3                    510
3!!,3,3*!+,3!!/,3!+          (3!!+(3*3)!)/3!!+3!            511
33,3/,3-,3^                  (33/3-3)^3                     512
3,3,3+^,3!,3^-               3^(3+3)-3!^3                   513
3!,3/,3^,3^,3+               (3!/3)^3^3+3                   515
3,3!^,3!,3^-,3+              3^3!-3!^3+3                    516
3!,3!,3/,3^,3^+              3!+(3!/3)^3^3                  518
3!!,3,33,3!*+-               3!!-(3+33*3!)                  519
3!!,3!!,3!/,3!!-,3/+         3!!+(3!!/3!-3!!)/3             520
3!!,3,3+,33*-                3!!-(3+3)*33                   522
3,3!,33*,3!!--               3-(3!*33-3!!)                  525
3!,3!!+,3!,33*-              3!+3!!-3!*33                   528
3,3!^,3!,33*-                3^3!-3!*33                     531
33,3!!,3!,3^-+               33+3!!-3!^3                    537
3!,3,33,3-**                 3!*3*(33-3)                    540
333,3!,3^+                   333+3!^3                       549
3!!,3!-,3,3^,3!*-            3!!-3!-3^3*3!                  552
3!!,3,3^,3!*,3+-             3!!-(3^3*3!+3)                 555
3,33*,3!-,3!*                (3*33-3!)*3!                   558
3,3*!,3/,3!,3^/              ((3*3)!/3)/3!^3                560
3,3,3^,3!*,3!!--             3-(3^3*3!-3!!)                 561
3!!,3!+,3!,3,3^*-            3!!+3!-3!*3^3                  564
3,3^,3!,3*,3+*               3^3*(3!*3+3)                   567
3!,3!+,3^,3/,3!-             (3!+3!)^3/3-3!                 570
3!!,3/,333+                  3!!/3+333                      573
3!,3!+,3^,3!-,3/             ((3!+3!)^3-3!)/3               574
3!,3!+,3^,3-,3/              ((3!+3!)^3-3)/3                575
3!,3,33*,3-*                 3!*(3*33-3)                    576
3,3!,3!+,3^+,3/              (3+(3!+3!)^3)/3                577
3!,3!+,3^,3!+,3/             ((3!+3!)^3+3!)/3               578
3,3!,3!+,3^,3/+              3+(3!+3!)^3/3                  579
3!!,3!!,3!/,3!!+,3!/-        3!!-(3!!/3!+3!!)/3!            580
3!,3!+,3^,3/,3!+             (3!+3!)^3/3+3!                 582
3!,33*,3-,3*                 (3!*33-3)*3                    585
33,3,3!**,3!-                33*3*3!-3!                     588
3!,33*,3*,3-                 3!*33*3-3                      591
3!!,3!!,3!+,3!/-,3!-         3!!-(3!!+3!)/3!-3!             593
33,3,3,3+**                  33*3*(3+3)                     594
3!!,3!,3,3/-,3^-             3!!-(3!-3/3)^3                 595
3!!,3,3!,3!!+,3!/+-          3!!-(3+(3!+3!!)/3!)            596
3,3!*,33*,3+                 3*3!*33+3                      597
3!!,3,3!^,3+,3!/-            3!!-(3^3!+3)/3!                598
3!!,3,3,3!^-,3!/+            3!!+(3-3^3!)/3!                599
3!,3,33*,3!*+                3!+3*33*3!                     600

  Posted by Charlie on 2008-07-09 11:39:07
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