# Tony Horncastle's number

When Tony Horncastle wakes up, and sees the digital clock, he need to reach that number using 75, 25, 1, 3, 5, 7.

For example, 4:37 could be (75 - 3) x (7 - 1) + 5.

Tony believes that there is just one time between 1:00 and 8:00 for which there is no solution.

What number is Tony thinking of? Is he right?

• What operations can we use? And can we use a computer to solve this? – Beastly Gerbil Sep 18 '17 at 16:56
• what are special about these numbers? – Oray Sep 18 '17 at 17:38
• Nice! Reminds me of the French TV Game des chiffres et des lettres – sousben Sep 18 '17 at 18:15
• I believe divisions are allowed too if the result is an integer – sousben Sep 18 '17 at 18:54
• Why does your example leave out one of the numbers required by the puzzle? – feelinferrety Sep 18 '17 at 19:41

I wrote a program to go over every possible equation that can be made using those 6 numbers. If we leave out division then there is an answer:

Tony thinks it is 7:59 but he is wrong since he only used +-* but you can get that time by including division

I do not believe this problem is solvable without a computer. so I put this into a code that I just wrote and found the answer as below:

   (75+7)+((5+1)*(3)) ||| 100
   ((75*7)/(5))-(3+1) ||| 101
   (75+7)+((5)*(3+1)) ||| 102
   (((75*7)/(5))-(3))+(1) ||| 103
   ((75)+((7+1)*(3)))+(5) ||| 104
   ((75)*((7/3)-(1)))+(5) ||| 105
   ((75)+(7*5))-(3+1) ||| 106
   (((75)+(7*5))-(3))*(1) ||| 107
   (((75)+(7*5))-(3))+(1) ||| 108
   (((75*7)/(5))+(3))+(1) ||| 109
   ((75)+((7+5)*(3)))-(1) ||| 110
   ((75)+((7+5)*(3)))*(1) ||| 111
   ((75)+((7+5)*(3)))+(1) ||| 112
   (((75)+(7*5))+(3))*(1) ||| 113
   (((75)+(7*5))+(3))+(1) ||| 114
   (75)+((7+3)*(5-1)) ||| 115
   ((((1+3)+(5))+(25))+(7))+(75) ||| 116
   ((75)-((7*5)+(1)))*(3) ||| 117
   ((75)+((7+1)*(5)))+(3) ||| 118
   (((75)-(7*5))*(3))-(1) ||| 119
   (((75)-(7*5))*(3))*(1) ||| 120
   (((75)-(7*5))*(3))+(1) ||| 121
   (((1-3)*(5-25))+(75))+(7) ||| 122
   (75)+((7+5)*(3+1)) ||| 123
   (75)+((7)*((5+3)-(1))) ||| 124
   (75)*(((7-5)/(3))+(1)) ||| 125
   ((75)-(7+5))*(3-1) ||| 126
   (((75*5)+(7))-(1))/(3) ||| 127
   ((75/3)+(7))*(5-1) ||| 128
   (((75+1)*(5))+(7))/(3) ||| 129
   ((75)+((7)*(5+3)))-(1) ||| 130
   ((75)+((7)*(5+3)))*(1) ||| 131
   ((75)+((7)*(5+3)))+(1) ||| 132
   (((75*5)/(3))+(7))+(1) ||| 133
   ((75)-(7+1))*(5-3) ||| 134
   ((75-7)*(5-3))-(1) ||| 135
   ((75-7)*(5-3))*(1) ||| 136
   ((75-7)*(5-3))+(1) ||| 137
   (75)+((7)*((5+3)+(1))) ||| 138
   (75)+((7+1)*(5+3)) ||| 139
   ((75+5)*(7))/(3+1) ||| 140
   ((75)-((7)*(5-1)))*(3) ||| 141
   ((75)*(5-3))-(7+1) ||| 142
   (((75)*(5-3))-(7))*(1) ||| 143
   (((75)*(5-3))-(7))+(1) ||| 144
   (75)+((7*5)*(3-1)) ||| 145
   ((75)*(7-5))-(3+1) ||| 146
   (((75)*(7-5))-(3))*(1) ||| 147
   (((75)*(7-5))-(3))+(1) ||| 148
   (((75)*(7+3))/(5))-(1) ||| 149
   (75/7)*((5*3)-(1)) ||| 150
   (((75)*(7+3))/(5))+(1) ||| 151
   (((75)*(7-5))+(3))-(1) ||| 152
   (((75)*(7-5))+(3))*(1) ||| 153
   ((75+7)-(5))*(3-1) ||| 154
   (((75)*(7-1))/(3))+(5) ||| 155
   (((75)*(5-3))+(7))-(1) ||| 156
   (((75)*(5-3))+(7))*(1) ||| 157
   (((75)*(5-3))+(7))+(1) ||| 158
   (75)+(((7)*(5-1))*(3)) ||| 159
   (((75-7)*(3))-(5))+(1) ||| 200
   (75)+(((7)*(5+1))*(3)) ||| 201
   (((75-7)+(1))*(3))-(5) ||| 202
   (((75-5)*(3))-(7))*(1) ||| 203
   (75-7)*((5-3)+(1)) ||| 204
   ((75+7)*(5))/(3-1) ||| 205
   (((75)-(7+1))*(3))+(5) ||| 206
   ((75)*((5/3)+(1)))+(7) ||| 207
   (((75-7)*(3))+(5))-(1) ||| 208
   (((75-7)*(3))+(5))*(1) ||| 209
   ((75*7)/(5))*(3-1) ||| 210
   (((75/3)+(5))*(7))+(1) ||| 211
   (((75-7)+(1))*(3))+(5) ||| 212
   ((75*3)-(7+5))*(1) ||| 213
   (((75)-(5+1))*(3))+(7) ||| 214
   (75)+((7*5)*(3+1)) ||| 215
   (((75-7)+(5))-(1))*(3) ||| 216
   (((75-5)*(3))+(7))*(1) ||| 217
   (((75-7)+(5))*(3))-(1) ||| 218
   (((75-7)+(5))*(3))*(1) ||| 219
   ((75)+(7*5))*(3-1) ||| 220
   ((1)+((3/5)*(75)))+(25*7) ||| 221
   ((75)*((7-5)+(1)))-(3) ||| 222
   (((75*3)-(7))+(5))*(1) ||| 223
   (((75*3)-(7))+(5))+(1) ||| 224
   ((75)*(7+5))/(3+1) ||| 225
   ((75*3)+(7))-(5+1) ||| 226
   (((75*3)+(7))-(5))*(1) ||| 227
   ((75+7)-(5+1))*(3) ||| 228
   (((1)-((3)*(5-75)))+(25))-(7) ||| 229
   (((75+7)-(5))*(3))-(1) ||| 230
   (((75+7)-(5))*(3))*(1) ||| 231
   (((75+7)-(5))*(3))+(1) ||| 232
   (((75+5)*(3))-(7))*(1) ||| 233
   (((75+7)-(5))+(1))*(3) ||| 234
   ((75)-((7)*(3+1)))*(5) ||| 235
   (((75+5)+(1))*(3))-(7) ||| 236
   (((75*3)+(7))+(5))*(1) ||| 237
   (((75+7)-(1))*(3))-(5) ||| 238
   ((1+3)+((5)*(25+7)))+(75) ||| 239
   (75)*(((7/5)*(3))-(1)) ||| 240
   (((75+7)*(3))-(5))*(1) ||| 241
   (((75+7)*(3))-(5))+(1) ||| 242
   ((1)+(((3+5)/(25))*(7)))*(75) ||| 243
   (((75+7)+(1))*(3))-(5) ||| 244
   ((75)*((7/3)+(1)))-(5) ||| 245
   (75+7)*((5-3)+(1)) ||| 246
   (((75+5)*(3))+(7))*(1) ||| 247
   (((75+7)-(1))*(3))+(5) ||| 248
   (((1+3)-(5))+(25*7))+(75) ||| 249
   (((75+7)*(3))+(5))-(1) ||| 250
   (((75+7)*(3))+(5))*(1) ||| 251
   ((75)-(7+5))*(3+1) ||| 252
   (75*3)+((7)*(5-1)) ||| 253
   (((75+7)+(1))*(3))+(5) ||| 254
   (75)*(((7/5)+(3))-(1)) ||| 255
   (1)+((3)*(((5)*(25+7))-(75))) ||| 256
   ((75-1)*(3))+(7*5) ||| 257
   (((75+7)+(5))-(1))*(3) ||| 258
   ((75*3)+(7*5))-(1) ||| 259
   (((75)*(7+5))/(3))*(1) ||| 300
   (((75)*(7+5))/(3))+(1) ||| 301
   (((75)*(3+1))+(7))-(5) ||| 302
   ((1+3)*(7-25))+(75*5) ||| 303
   (((75)*(7-3))+(5))-(1) ||| 304
   (((75)*(7-3))+(5))*(1) ||| 305
   (((75)*(7-3))+(5))+(1) ||| 306
   (((1-3)+(5))*(25+75))+(7) ||| 307
   ((75+7)-(5))*(3+1) ||| 308
   ((75)+((7)*(5-1)))*(3) ||| 309
   (((75)*(5-1))+(7))+(3) ||| 310
   ((1-3)*(7+25))+(75*5) ||| 311
   (((75*7)/(5))-(1))*(3) ||| 312
   ((75+5)*(3+1))-(7) ||| 313
   (((75*7)/(5))*(3))-(1) ||| 314
   (((75*7)/(5))*(3))*(1) ||| 315
   (((75*7)/(5))*(3))+(1) ||| 316
   ((1+3)*((5+75)-(7)))+(25) ||| 317
   (((75*7)/(5))+(1))*(3) ||| 318
   ((75+5)*(7-3))-(1) ||| 319
   ((75)-((7+3)+(1)))*(5) ||| 320
   ((75+5)*(7-3))+(1) ||| 321
   (((75/5)*(3))+(1))*(7) ||| 322
   ((75+7)*(3+1))-(5) ||| 323
   (((75)-(7+3))*(5))-(1) ||| 324
   (75)*((7)-((5/3)+(1))) ||| 325
   (((75)-(7+3))*(5))+(1) ||| 326
   (((75)+(7*5))-(1))*(3) ||| 327
   (1)*((((5)*(75-3))-(7))-(25)) ||| 328
   (((75)+(7*5))*(3))-(1) ||| 329
   (((75)+(7*5))*(3))*(1) ||| 330
   (((75)+(7*5))*(3))+(1) ||| 331
   (((75)-(7+1))*(5))-(3) ||| 332
   (((75)+(7*5))+(1))*(3) ||| 333
   (1)*((5)-(((3)-(75-25))*(7))) ||| 334
   ((75)*(3+1))+(7*5) ||| 335
   ((75-7)*(5))-(3+1) ||| 336
   (((75-7)*(5))-(3))*(1) ||| 337
   (((75-7)*(5))-(3))+(1) ||| 338
   ((1-3)*(25-7))+(5*75) ||| 339
   ((75+7)+(3))*(5-1) ||| 340
   ((1-3)+(5*75))-(25+7) ||| 341
   (((75-7)*(5))+(3))-(1) ||| 342
   (((75-7)*(5))+(3))*(1) ||| 343
   (((75-7)*(5))+(3))+(1) ||| 344
   ((75)+((7+1)*(5)))*(3) ||| 345
   ((1)+((3*5)*(25-7)))+(75) ||| 346
   (75*5)-((7)*(3+1)) ||| 347
   ((75+7)+(5))*(3+1) ||| 348
   ((75-1)*(5))-(7*3) ||| 349
   (((75-7)+(3))-(1))*(5) ||| 350
   ((75)+((7)*(5+1)))*(3) ||| 351
   ((75-3)*(5))-(7+1) ||| 352
   (75*5)-((7*3)+(1)) ||| 353
   (((75-7)+(3))*(5))-(1) ||| 354
   (((75-7)+(3))*(5))*(1) ||| 355
   (((75-7)+(3))*(5))+(1) ||| 356
   (75*5)-((7-1)*(3)) ||| 357
   (((75-3)+(1))*(5))-(7) ||| 358
   ((75+1)*(5))-(7*3) ||| 359
   ((75)*((7)-(5/3)))*(1) ||| 400
   ((75)*((7)-(5/3)))+(1) ||| 401
   (((75+7)-(1))*(5))-(3) ||| 402
   (75*5)+((7)*(3+1)) ||| 403
   ((1+3)-(5*25))+(7*75) ||| 404
   (75)*(((7/5)+(3))+(1)) ||| 405
   ((75+7)*(5))-(3+1) ||| 406
   (((75+7)*(5))-(3))*(1) ||| 407
   (((75+7)*(5))-(3))+(1) ||| 408
   (((1)+((3+75)*(5)))+(25))-(7) ||| 409
   (((1*3)+(5*75))+(25))+(7) ||| 410
   ((75-7)*(5+1))+(3) ||| 411
   (((75+7)*(5))+(3))-(1) ||| 412
   (((75+7)*(5))+(3))*(1) ||| 413
   (((75+7)*(5))+(3))+(1) ||| 414
   ((1-3)*((5)-(25*7)))+(75) ||| 415
   ((1)+((3)*(5+75)))+(25*7) ||| 416
   ((75-5)*(7-1))-(3) ||| 417
   (((75+7)+(1))*(5))+(3) ||| 418
   (((75)-(5*3))*(7))-(1) ||| 419
   ((75*7)/(5))*(3+1) ||| 420
   (((75)-(5*3))*(7))+(1) ||| 421
   (((1)+((3+75)/(5)))*(25))+(7) ||| 422
   ((75-5)*(7-1))+(3) ||| 423
   (((75+7)+(3))*(5))-(1) ||| 424
   (75)*((7)-((5-1)/(3))) ||| 425
   (((75+7)+(3))*(5))+(1) ||| 426
   (((75)-(5*3))+(1))*(7) ||| 427
   (((1+3)*(7))+(25))+(75*5) ||| 428
   ((75)*(5+1))-(7*3) ||| 429
   (((75+7)+(3))+(1))*(5) ||| 430
   (25)-((3)-(((5)*(75+7))-(1))) ||| 431
   ((((1+3)*(5))*(25))+(7))-(75) ||| 432
   ((1-3)+((5)*(75+7)))+(25) ||| 433
   ((1/3)-(5))*((7)-(25+75)) ||| 434
   ((75)*(7-1))-(5*3) ||| 435
   ((75)-(7/3))*(5+1) ||| 436
   ((75-3)*(7-1))+(5) ||| 437
   ((75-5)+(3))*(7-1) ||| 438
   ((75-3)*(5+1))+(7) ||| 439
   ((75)+(7*5))*(3+1) ||| 440
   ((75)-((5-1)*(3)))*(7) ||| 441
   ((75)*(7-1))-(5+3) ||| 442
   ((((1*3)*(5))*(25))-(7))+(75) ||| 443
   ((75-1)*(7-5))*(3) ||| 444
   ((75)+((7)*(3-1)))*(5) ||| 445
   (((75)*(5+1))-(7))+(3) ||| 446
   (((75)*(7-5))-(1))*(3) ||| 447
   (((75)*(7-1))-(5))+(3) ||| 448
   (((75)*(7-5))*(3))-(1) ||| 449
   ((75)*(7+5))/(3-1) ||| 450
   (((75)*(7-5))*(3))+(1) ||| 451
   (((75)*(7-1))+(5))-(3) ||| 452
   (((75)*(7-5))+(1))*(3) ||| 453
   (((75)*(5+1))+(7))-(3) ||| 454
   ((75)-((5)*(3-1)))*(7) ||| 455
   ((75+1)*(7-5))*(3) ||| 456
   (1)-((3+5)*((25)-(75+7))) ||| 457
   (((75)*(7-1))+(5))+(3) ||| 458
   ((((1+3)*(7))/(25))+(5))*(75) ||| 459
   (((75-5)+(1))*(7))+(3) ||| 500
   (1)-((3-5)*((25*7)+(75))) ||| 501
   (((75)-(3+1))*(7))+(5) ||| 502
   ((75-1)*(7))-(5*3) ||| 503
   (((75-5)+(3))-(1))*(7) ||| 504
   (75*7)-((5)*(3+1)) ||| 505
   (((75-3)+(1))*(7))-(5) ||| 506
   (75*7)-((5+1)*(3)) ||| 507
   (((75-3)*(7))+(5))-(1) ||| 508
   (75*7)-((5*3)+(1)) ||| 509
   ((75*7)-(5*3))*(1) ||| 510
   ((75*7)-(5*3))+(1) ||| 511
   (((75-5)+(3))*(7))+(1) ||| 512
   (75*7)-((5-1)*(3)) ||| 513
   (1-3)*(((5)*(25-75))-(7)) ||| 514
   (75*7)-((5)*(3-1)) ||| 515
   (75*7)-((5+3)+(1)) ||| 516
   ((75*7)-(5+3))*(1) ||| 517
   ((75*7)-(5+3))+(1) ||| 518
   ((((1*3)-(5))/(25))+(7))*(75) ||| 519
   (75)*((7)-((1)/(5*3))) ||| 520
   ((((1-3)+(5))+(75))*(7))-(25) ||| 521
   (((75*7)-(5))+(3))-(1) ||| 522
   (((75*7)-(5))+(3))*(1) ||| 523
   (((75*7)-(5))+(3))+(1) ||| 524
   (75*7)*((5)-(3+1)) ||| 525
   ((75*7)+(5))-(3+1) ||| 526
   (((75*7)+(5))-(3))*(1) ||| 527
   (((75*7)+(5))-(3))+(1) ||| 528
   (1)*((((3/25)+(7))*(75))-(5)) ||| 529
   (75)*((7)+((1)/(5*3))) ||| 530
   (1)+(((3)*((5/75)+(7)))*(25)) ||| 531
   (((75*7)+(5))+(3))-(1) ||| 532
   (((75*7)+(5))+(3))*(1) ||| 533
   (((75*7)+(5))+(3))+(1) ||| 534
   (75*7)+((5)*(3-1)) ||| 535
   ((75)-(7+1))*(5+3) ||| 536
   (75*7)+((5-1)*(3)) ||| 537
   (((75+5)-(3))*(7))-(1) ||| 538
   ((75*7)+(5*3))-(1) ||| 539
   ((75*7)+(5*3))*(1) ||| 540
   ((75*7)+(5*3))+(1) ||| 541
   (((75+3)*(7))-(5))+(1) ||| 542
   ((75-7)*(5+3))-(1) ||| 543
   ((75-7)*(5+3))*(1) ||| 544
   (75*7)+((5)*(3+1)) ||| 545
   (((75+5)-(3))+(1))*(7) ||| 546
   ((75+1)*(7))+(5*3) ||| 547
   (((75+3)+(1))*(7))-(5) ||| 548
   ((75)*((7/3)+(5)))-(1) ||| 549
   ((75)*((7/3)+(5)))*(1) ||| 550
   ((75)*((7/3)+(5)))+(1) ||| 551
   ((75-7)+(1))*(5+3) ||| 552
   (((1-3)+(5))+(25))+(75*7) ||| 553
   ((1+3)+(5*75))+(25*7) ||| 554
   (75)*(((7)-(3/5))+(1)) ||| 555
   ((75+5)*(7))-(3+1) ||| 556
   (((75+5)*(7))-(3))*(1) ||| 557
   (((75+5)*(7))-(3))+(1) ||| 558
   (((1+3)+(5))+(25))+(7*75) ||| 559
   (75)*((7+5)-(3+1)) ||| 600
   ((75)*((5*3)-(7)))+(1) ||| 601
   (((75)*(7+1))+(5))-(3) ||| 602
   ((1+3)*((5*25)+(7)))+(75) ||| 603
   (1+3)-((5+7)*(25-75)) ||| 604
   ((((1*3)*(5))+(75))*(7))-(25) ||| 605
   (((75)*(5+3))+(7))-(1) ||| 606
   (((75)*(5+3))+(7))*(1) ||| 607
   (((75)*(7+1))+(5))+(3) ||| 608
   ((75)+((5-1)*(3)))*(7) ||| 609
   ((((1+3)/(5))+(7))*(75))+(25) ||| 610
   ((1+5)*((3)+(75+25)))-(7) ||| 611
   (75-7)*((5+3)+(1)) ||| 612
   ((((1+3)+(5))+(75))*(7))+(25) ||| 613
   (((1)+((3/25)+(7)))*(75))+(5) ||| 614
   ((75)*(7+1))+(5*3) ||| 615
   ((75+5)-(3))*(7+1) ||| 616
   (1)+((3+25)*((7)+(75/5))) ||| 617
   ((((1*3)+(5))*(75))+(25))-(7) ||| 618
   ((75+3)*(7+1))-(5) ||| 619
   ((((1)+(3/5))+(7))*(75))-(25) ||| 620
   (1*3)*(((5*25)+(7))+(75)) ||| 621
   (1)+((3)*(((5*25)+(7))+(75))) ||| 622
   (((75)+(5*3))-(1))*(7) ||| 623
   (((1)+((3+5)/(25)))+(7))*(75) ||| 624
   (75)*((7)+((5-1)/(3))) ||| 625
   ((1)+(((3*5)+(7))*(25)))+(75) ||| 626
   ((1)/((3/75)/(25)))-(5-7) ||| 627
   (1-5)*(((3)*(25-75))-(7)) ||| 628
   (((75)+(5*3))*(7))-(1) ||| 629
   (75-5)*((7+3)-(1)) ||| 630
   (((75)+(5*3))*(7))+(1) ||| 631
   ((((1*3)+(5))*(75))+(25))+(7) ||| 632
   (((1)+((3+5)*(75)))+(25))+(7) ||| 633
   (((1)+((5)+(75*25)))/(3))+(7) ||| 634
   (((1+3)*(7))*(25-5))+(75) ||| 635
   (((1-3)+(75))*(7))+(5*25) ||| 636
   ((75+5)*(7+1))-(3) ||| 637
   ((1)+(3+25))*((7)+(75/5)) ||| 638
   (((1+5)*(7))+(75*25))/(3) ||| 639
   ((((1+3)*(5))+(75))*(7))-(25) ||| 640
   (1)-(((3/5)-(7))*(25+75)) ||| 641
   (((1)+((3*25)+(5)))*(7))+(75) ||| 642
   ((75+5)*(7+1))+(3) ||| 643
   ((1+7)*(3+75))-(5-25) ||| 644
   (75)*(((7)+(3/5))+(1)) ||| 645
   (1)+((3)*((75)-((5-25)*(7)))) ||| 646
   (((1)+(5+7))*(75-25))-(3) ||| 647
   ((75+7)-(1))*(5+3) ||| 648
   ((75)*((7)+(5/3)))-(1) ||| 649
   ((75)*((7)+(5/3)))*(1) ||| 650
   ((75)*((7)+(5/3)))+(1) ||| 651
   (((25*5)+(3))-(1))+(7*75) ||| 652
   ((1*3)+(7*75))+(25*5) ||| 653
   (((1+3)-(7/25))+(5))*(75) ||| 654
   ((75+7)*(5+3))-(1) ||| 655
   ((75+7)*(5+3))*(1) ||| 656
   ((75+7)*(5+3))+(1) ||| 657
   ((25+3)*(5))+((75-1)*(7)) ||| 658
   (((25)/(3/75))+(5*7))-(1) ||| 659
   ((75*7)*(5-1))/(3) ||| 700
   (1)+(((3*75)-(5*25))*(7)) ||| 701
   (((1)-((3-25)*(5)))*(7))-(75) ||| 702
   ((1-3)+((7)*(25+75)))+(5) ||| 703
   (1)+((3)+((7)*(75+25))) ||| 704
   (1*3)*((75)+((5)*(25+7))) ||| 705
   (1)+((3)*((75)+((5)*(25+7)))) ||| 706
   (((1)+(3*75))-(5*25))*(7) ||| 707
   ((1*3)+((7)*(25+75)))+(5) ||| 708
   ((1+3)+((7)*(25+75)))+(5) ||| 709
   ((75-5)+(1))*(7+3) ||| 710
   ((1-3)*((7)-(75*5)))-(25) ||| 711
   (((1)+((3)*(5+25)))*(7))+(75) ||| 712
   (((1+3)+(5))*(75+7))-(25) ||| 713
   (1-3)*(((25)-(5*75))-(7)) ||| 714
   (((75)*(3-1))-(7))*(5) ||| 715
   ((1)+(3*5))+((25+75)*(7)) ||| 716
   (1)+((((3)+(75+25))*(7))-(5)) ||| 717
   ((1+5)*(3))+((7)*(75+25)) ||| 718
   (((25+3)-(1-75))*(7))+(5) ||| 719
   (75+5)*((7+3)-(1)) ||| 720
   (1)-((3-75)*((7*5)-(25))) ||| 721
   (1)+(((3+75)+(25))*(7)) ||| 722
   (((1)+((3)+(75+25)))*(7))-(5) ||| 723
   ((25)*(3+5))-((1)-(7*75)) ||| 724
   (75)*(((7)+(5/3))+(1)) ||| 725
   ((1)+((3+7)*(75-5)))+(25) ||| 726
   (1)+((((3)+(75+25))*(7))+(5)) ||| 727
   (((1+3)+(75))+(25))*(7) ||| 728
   (1*3)*(((5)*(75-25))-(7)) ||| 729
   ((1)-(3-75))*((7*5)-(25)) ||| 730
   (((1)+((3+7)*(75)))-(25))+(5) ||| 731
   (1)*((((5)+(75+25))*(7))-(3)) ||| 732
   (1-3)+(((75+5)+(25))*(7)) ||| 733
   ((7)*((25)+(75+5)))-(1) ||| 734
   (75)*((7+3)-(1/5)) ||| 735
   ((75*5)-(7))*(3-1) ||| 736
   ((((25)+(5+75))*(7))-(1))+(3) ||| 737
   (75+7)*((5+3)+(1)) ||| 738
   (1+3)+(((75+5)+(25))*(7)) ||| 739
   (((1)-(3/5))+(7))*(25+75) ||| 740
   (((1-5)*(7-75))-(25))*(3) ||| 741
   (((1+5)+(75))+(25))*(7) ||| 742
   ((75*5)*(3-1))-(7) ||| 743
   ((75)*(7+3))-(5+1) ||| 744
   (((75)*(7+3))-(5))*(1) ||| 745
   (((75)*(7+3))-(5))+(1) ||| 746
   (1)*((((5*7)-(25))*(75))-(3)) ||| 747
   ((75)-(1/5))*(7+3) ||| 748
   (1)+((3+7)*((75)-(5/25))) ||| 749
   (75)*(((7+5)-(3))+(1)) ||| 750
   (1)+((((3)*(75-5))*(25))/(7)) ||| 751
   ((75)+(1/5))*(7+3) ||| 752
   (1*3)+((75)*((5*7)-(25))) ||| 753
   (((75)*(7+3))+(5))-(1) ||| 754
   (((75)*(7+3))+(5))*(1) ||| 755
   (((75)*(7+3))+(5))+(1) ||| 756
   ((75*5)*(3-1))+(7) ||| 757
   ((1)-((3*5)*(25-75)))+(7) ||| 758
   ((25+75)*((3/5)+(7)))-(1) ||| 759


With only $4$ operators and parentheses,

Every single hour can be found. so he is not right and I have no idea what number he was thinking since I have found every single hours and minutes between $1:00$ to $8:00$.

• Would it still work for any number between 0 and 1000 ? – sousben Sep 18 '17 at 19:20
• @sousben no idea, I just checked these and it takes some time to find. – Oray Sep 18 '17 at 19:28
• I'm sure it does! youtube.com/watch?v=X1jwjiEQG9Y – sousben Sep 18 '17 at 19:43
• I think your assumption of 4 operators is wrong, (or right but solves only half of the riddle) See my answer below – lPlant Sep 18 '17 at 20:25
• Why don't you use = – paparazzo Sep 18 '17 at 20:30