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?
(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
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Posted by Charlie
on 2008-07-09 11:39:07 |
re(5): all hundred
