# 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? Commented Sep 18, 2017 at 16:56
• what are special about these numbers?
– Oray
Commented Sep 18, 2017 at 17:38
• Nice! Reminds me of the French TV Game des chiffres et des lettres Commented Sep 18, 2017 at 18:15
• I believe divisions are allowed too if the result is an integer Commented Sep 18, 2017 at 18:54
• Why does your example leave out one of the numbers required by the puzzle? Commented Sep 18, 2017 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:

[100]   (75+7)+((5+1)*(3)) ||| 100
[101]   ((75*7)/(5))-(3+1) ||| 101
[102]   (75+7)+((5)*(3+1)) ||| 102
[103]   (((75*7)/(5))-(3))+(1) ||| 103
[104]   ((75)+((7+1)*(3)))+(5) ||| 104
[105]   ((75)*((7/3)-(1)))+(5) ||| 105
[106]   ((75)+(7*5))-(3+1) ||| 106
[107]   (((75)+(7*5))-(3))*(1) ||| 107
[108]   (((75)+(7*5))-(3))+(1) ||| 108
[109]   (((75*7)/(5))+(3))+(1) ||| 109
[110]   ((75)+((7+5)*(3)))-(1) ||| 110
[111]   ((75)+((7+5)*(3)))*(1) ||| 111
[112]   ((75)+((7+5)*(3)))+(1) ||| 112
[113]   (((75)+(7*5))+(3))*(1) ||| 113
[114]   (((75)+(7*5))+(3))+(1) ||| 114
[115]   (75)+((7+3)*(5-1)) ||| 115
[116]   ((((1+3)+(5))+(25))+(7))+(75) ||| 116
[117]   ((75)-((7*5)+(1)))*(3) ||| 117
[118]   ((75)+((7+1)*(5)))+(3) ||| 118
[119]   (((75)-(7*5))*(3))-(1) ||| 119
[120]   (((75)-(7*5))*(3))*(1) ||| 120
[121]   (((75)-(7*5))*(3))+(1) ||| 121
[122]   (((1-3)*(5-25))+(75))+(7) ||| 122
[123]   (75)+((7+5)*(3+1)) ||| 123
[124]   (75)+((7)*((5+3)-(1))) ||| 124
[125]   (75)*(((7-5)/(3))+(1)) ||| 125
[126]   ((75)-(7+5))*(3-1) ||| 126
[127]   (((75*5)+(7))-(1))/(3) ||| 127
[128]   ((75/3)+(7))*(5-1) ||| 128
[129]   (((75+1)*(5))+(7))/(3) ||| 129
[130]   ((75)+((7)*(5+3)))-(1) ||| 130
[131]   ((75)+((7)*(5+3)))*(1) ||| 131
[132]   ((75)+((7)*(5+3)))+(1) ||| 132
[133]   (((75*5)/(3))+(7))+(1) ||| 133
[134]   ((75)-(7+1))*(5-3) ||| 134
[135]   ((75-7)*(5-3))-(1) ||| 135
[136]   ((75-7)*(5-3))*(1) ||| 136
[137]   ((75-7)*(5-3))+(1) ||| 137
[138]   (75)+((7)*((5+3)+(1))) ||| 138
[139]   (75)+((7+1)*(5+3)) ||| 139
[140]   ((75+5)*(7))/(3+1) ||| 140
[141]   ((75)-((7)*(5-1)))*(3) ||| 141
[142]   ((75)*(5-3))-(7+1) ||| 142
[143]   (((75)*(5-3))-(7))*(1) ||| 143
[144]   (((75)*(5-3))-(7))+(1) ||| 144
[145]   (75)+((7*5)*(3-1)) ||| 145
[146]   ((75)*(7-5))-(3+1) ||| 146
[147]   (((75)*(7-5))-(3))*(1) ||| 147
[148]   (((75)*(7-5))-(3))+(1) ||| 148
[149]   (((75)*(7+3))/(5))-(1) ||| 149
[150]   (75/7)*((5*3)-(1)) ||| 150
[151]   (((75)*(7+3))/(5))+(1) ||| 151
[152]   (((75)*(7-5))+(3))-(1) ||| 152
[153]   (((75)*(7-5))+(3))*(1) ||| 153
[154]   ((75+7)-(5))*(3-1) ||| 154
[155]   (((75)*(7-1))/(3))+(5) ||| 155
[156]   (((75)*(5-3))+(7))-(1) ||| 156
[157]   (((75)*(5-3))+(7))*(1) ||| 157
[158]   (((75)*(5-3))+(7))+(1) ||| 158
[159]   (75)+(((7)*(5-1))*(3)) ||| 159
[200]   (((75-7)*(3))-(5))+(1) ||| 200
[201]   (75)+(((7)*(5+1))*(3)) ||| 201
[202]   (((75-7)+(1))*(3))-(5) ||| 202
[203]   (((75-5)*(3))-(7))*(1) ||| 203
[204]   (75-7)*((5-3)+(1)) ||| 204
[205]   ((75+7)*(5))/(3-1) ||| 205
[206]   (((75)-(7+1))*(3))+(5) ||| 206
[207]   ((75)*((5/3)+(1)))+(7) ||| 207
[208]   (((75-7)*(3))+(5))-(1) ||| 208
[209]   (((75-7)*(3))+(5))*(1) ||| 209
[210]   ((75*7)/(5))*(3-1) ||| 210
[211]   (((75/3)+(5))*(7))+(1) ||| 211
[212]   (((75-7)+(1))*(3))+(5) ||| 212
[213]   ((75*3)-(7+5))*(1) ||| 213
[214]   (((75)-(5+1))*(3))+(7) ||| 214
[215]   (75)+((7*5)*(3+1)) ||| 215
[216]   (((75-7)+(5))-(1))*(3) ||| 216
[217]   (((75-5)*(3))+(7))*(1) ||| 217
[218]   (((75-7)+(5))*(3))-(1) ||| 218
[219]   (((75-7)+(5))*(3))*(1) ||| 219
[220]   ((75)+(7*5))*(3-1) ||| 220
[221]   ((1)+((3/5)*(75)))+(25*7) ||| 221
[222]   ((75)*((7-5)+(1)))-(3) ||| 222
[223]   (((75*3)-(7))+(5))*(1) ||| 223
[224]   (((75*3)-(7))+(5))+(1) ||| 224
[225]   ((75)*(7+5))/(3+1) ||| 225
[226]   ((75*3)+(7))-(5+1) ||| 226
[227]   (((75*3)+(7))-(5))*(1) ||| 227
[228]   ((75+7)-(5+1))*(3) ||| 228
[229]   (((1)-((3)*(5-75)))+(25))-(7) ||| 229
[230]   (((75+7)-(5))*(3))-(1) ||| 230
[231]   (((75+7)-(5))*(3))*(1) ||| 231
[232]   (((75+7)-(5))*(3))+(1) ||| 232
[233]   (((75+5)*(3))-(7))*(1) ||| 233
[234]   (((75+7)-(5))+(1))*(3) ||| 234
[235]   ((75)-((7)*(3+1)))*(5) ||| 235
[236]   (((75+5)+(1))*(3))-(7) ||| 236
[237]   (((75*3)+(7))+(5))*(1) ||| 237
[238]   (((75+7)-(1))*(3))-(5) ||| 238
[239]   ((1+3)+((5)*(25+7)))+(75) ||| 239
[240]   (75)*(((7/5)*(3))-(1)) ||| 240
[241]   (((75+7)*(3))-(5))*(1) ||| 241
[242]   (((75+7)*(3))-(5))+(1) ||| 242
[243]   ((1)+(((3+5)/(25))*(7)))*(75) ||| 243
[244]   (((75+7)+(1))*(3))-(5) ||| 244
[245]   ((75)*((7/3)+(1)))-(5) ||| 245
[246]   (75+7)*((5-3)+(1)) ||| 246
[247]   (((75+5)*(3))+(7))*(1) ||| 247
[248]   (((75+7)-(1))*(3))+(5) ||| 248
[249]   (((1+3)-(5))+(25*7))+(75) ||| 249
[250]   (((75+7)*(3))+(5))-(1) ||| 250
[251]   (((75+7)*(3))+(5))*(1) ||| 251
[252]   ((75)-(7+5))*(3+1) ||| 252
[253]   (75*3)+((7)*(5-1)) ||| 253
[254]   (((75+7)+(1))*(3))+(5) ||| 254
[255]   (75)*(((7/5)+(3))-(1)) ||| 255
[256]   (1)+((3)*(((5)*(25+7))-(75))) ||| 256
[257]   ((75-1)*(3))+(7*5) ||| 257
[258]   (((75+7)+(5))-(1))*(3) ||| 258
[259]   ((75*3)+(7*5))-(1) ||| 259
[300]   (((75)*(7+5))/(3))*(1) ||| 300
[301]   (((75)*(7+5))/(3))+(1) ||| 301
[302]   (((75)*(3+1))+(7))-(5) ||| 302
[303]   ((1+3)*(7-25))+(75*5) ||| 303
[304]   (((75)*(7-3))+(5))-(1) ||| 304
[305]   (((75)*(7-3))+(5))*(1) ||| 305
[306]   (((75)*(7-3))+(5))+(1) ||| 306
[307]   (((1-3)+(5))*(25+75))+(7) ||| 307
[308]   ((75+7)-(5))*(3+1) ||| 308
[309]   ((75)+((7)*(5-1)))*(3) ||| 309
[310]   (((75)*(5-1))+(7))+(3) ||| 310
[311]   ((1-3)*(7+25))+(75*5) ||| 311
[312]   (((75*7)/(5))-(1))*(3) ||| 312
[313]   ((75+5)*(3+1))-(7) ||| 313
[314]   (((75*7)/(5))*(3))-(1) ||| 314
[315]   (((75*7)/(5))*(3))*(1) ||| 315
[316]   (((75*7)/(5))*(3))+(1) ||| 316
[317]   ((1+3)*((5+75)-(7)))+(25) ||| 317
[318]   (((75*7)/(5))+(1))*(3) ||| 318
[319]   ((75+5)*(7-3))-(1) ||| 319
[320]   ((75)-((7+3)+(1)))*(5) ||| 320
[321]   ((75+5)*(7-3))+(1) ||| 321
[322]   (((75/5)*(3))+(1))*(7) ||| 322
[323]   ((75+7)*(3+1))-(5) ||| 323
[324]   (((75)-(7+3))*(5))-(1) ||| 324
[325]   (75)*((7)-((5/3)+(1))) ||| 325
[326]   (((75)-(7+3))*(5))+(1) ||| 326
[327]   (((75)+(7*5))-(1))*(3) ||| 327
[328]   (1)*((((5)*(75-3))-(7))-(25)) ||| 328
[329]   (((75)+(7*5))*(3))-(1) ||| 329
[330]   (((75)+(7*5))*(3))*(1) ||| 330
[331]   (((75)+(7*5))*(3))+(1) ||| 331
[332]   (((75)-(7+1))*(5))-(3) ||| 332
[333]   (((75)+(7*5))+(1))*(3) ||| 333
[334]   (1)*((5)-(((3)-(75-25))*(7))) ||| 334
[335]   ((75)*(3+1))+(7*5) ||| 335
[336]   ((75-7)*(5))-(3+1) ||| 336
[337]   (((75-7)*(5))-(3))*(1) ||| 337
[338]   (((75-7)*(5))-(3))+(1) ||| 338
[339]   ((1-3)*(25-7))+(5*75) ||| 339
[340]   ((75+7)+(3))*(5-1) ||| 340
[341]   ((1-3)+(5*75))-(25+7) ||| 341
[342]   (((75-7)*(5))+(3))-(1) ||| 342
[343]   (((75-7)*(5))+(3))*(1) ||| 343
[344]   (((75-7)*(5))+(3))+(1) ||| 344
[345]   ((75)+((7+1)*(5)))*(3) ||| 345
[346]   ((1)+((3*5)*(25-7)))+(75) ||| 346
[347]   (75*5)-((7)*(3+1)) ||| 347
[348]   ((75+7)+(5))*(3+1) ||| 348
[349]   ((75-1)*(5))-(7*3) ||| 349
[350]   (((75-7)+(3))-(1))*(5) ||| 350
[351]   ((75)+((7)*(5+1)))*(3) ||| 351
[352]   ((75-3)*(5))-(7+1) ||| 352
[353]   (75*5)-((7*3)+(1)) ||| 353
[354]   (((75-7)+(3))*(5))-(1) ||| 354
[355]   (((75-7)+(3))*(5))*(1) ||| 355
[356]   (((75-7)+(3))*(5))+(1) ||| 356
[357]   (75*5)-((7-1)*(3)) ||| 357
[358]   (((75-3)+(1))*(5))-(7) ||| 358
[359]   ((75+1)*(5))-(7*3) ||| 359
[400]   ((75)*((7)-(5/3)))*(1) ||| 400
[401]   ((75)*((7)-(5/3)))+(1) ||| 401
[402]   (((75+7)-(1))*(5))-(3) ||| 402
[403]   (75*5)+((7)*(3+1)) ||| 403
[404]   ((1+3)-(5*25))+(7*75) ||| 404
[405]   (75)*(((7/5)+(3))+(1)) ||| 405
[406]   ((75+7)*(5))-(3+1) ||| 406
[407]   (((75+7)*(5))-(3))*(1) ||| 407
[408]   (((75+7)*(5))-(3))+(1) ||| 408
[409]   (((1)+((3+75)*(5)))+(25))-(7) ||| 409
[410]   (((1*3)+(5*75))+(25))+(7) ||| 410
[411]   ((75-7)*(5+1))+(3) ||| 411
[412]   (((75+7)*(5))+(3))-(1) ||| 412
[413]   (((75+7)*(5))+(3))*(1) ||| 413
[414]   (((75+7)*(5))+(3))+(1) ||| 414
[415]   ((1-3)*((5)-(25*7)))+(75) ||| 415
[416]   ((1)+((3)*(5+75)))+(25*7) ||| 416
[417]   ((75-5)*(7-1))-(3) ||| 417
[418]   (((75+7)+(1))*(5))+(3) ||| 418
[419]   (((75)-(5*3))*(7))-(1) ||| 419
[420]   ((75*7)/(5))*(3+1) ||| 420
[421]   (((75)-(5*3))*(7))+(1) ||| 421
[422]   (((1)+((3+75)/(5)))*(25))+(7) ||| 422
[423]   ((75-5)*(7-1))+(3) ||| 423
[424]   (((75+7)+(3))*(5))-(1) ||| 424
[425]   (75)*((7)-((5-1)/(3))) ||| 425
[426]   (((75+7)+(3))*(5))+(1) ||| 426
[427]   (((75)-(5*3))+(1))*(7) ||| 427
[428]   (((1+3)*(7))+(25))+(75*5) ||| 428
[429]   ((75)*(5+1))-(7*3) ||| 429
[430]   (((75+7)+(3))+(1))*(5) ||| 430
[431]   (25)-((3)-(((5)*(75+7))-(1))) ||| 431
[432]   ((((1+3)*(5))*(25))+(7))-(75) ||| 432
[433]   ((1-3)+((5)*(75+7)))+(25) ||| 433
[434]   ((1/3)-(5))*((7)-(25+75)) ||| 434
[435]   ((75)*(7-1))-(5*3) ||| 435
[436]   ((75)-(7/3))*(5+1) ||| 436
[437]   ((75-3)*(7-1))+(5) ||| 437
[438]   ((75-5)+(3))*(7-1) ||| 438
[439]   ((75-3)*(5+1))+(7) ||| 439
[440]   ((75)+(7*5))*(3+1) ||| 440
[441]   ((75)-((5-1)*(3)))*(7) ||| 441
[442]   ((75)*(7-1))-(5+3) ||| 442
[443]   ((((1*3)*(5))*(25))-(7))+(75) ||| 443
[444]   ((75-1)*(7-5))*(3) ||| 444
[445]   ((75)+((7)*(3-1)))*(5) ||| 445
[446]   (((75)*(5+1))-(7))+(3) ||| 446
[447]   (((75)*(7-5))-(1))*(3) ||| 447
[448]   (((75)*(7-1))-(5))+(3) ||| 448
[449]   (((75)*(7-5))*(3))-(1) ||| 449
[450]   ((75)*(7+5))/(3-1) ||| 450
[451]   (((75)*(7-5))*(3))+(1) ||| 451
[452]   (((75)*(7-1))+(5))-(3) ||| 452
[453]   (((75)*(7-5))+(1))*(3) ||| 453
[454]   (((75)*(5+1))+(7))-(3) ||| 454
[455]   ((75)-((5)*(3-1)))*(7) ||| 455
[456]   ((75+1)*(7-5))*(3) ||| 456
[457]   (1)-((3+5)*((25)-(75+7))) ||| 457
[458]   (((75)*(7-1))+(5))+(3) ||| 458
[459]   ((((1+3)*(7))/(25))+(5))*(75) ||| 459
[500]   (((75-5)+(1))*(7))+(3) ||| 500
[501]   (1)-((3-5)*((25*7)+(75))) ||| 501
[502]   (((75)-(3+1))*(7))+(5) ||| 502
[503]   ((75-1)*(7))-(5*3) ||| 503
[504]   (((75-5)+(3))-(1))*(7) ||| 504
[505]   (75*7)-((5)*(3+1)) ||| 505
[506]   (((75-3)+(1))*(7))-(5) ||| 506
[507]   (75*7)-((5+1)*(3)) ||| 507
[508]   (((75-3)*(7))+(5))-(1) ||| 508
[509]   (75*7)-((5*3)+(1)) ||| 509
[510]   ((75*7)-(5*3))*(1) ||| 510
[511]   ((75*7)-(5*3))+(1) ||| 511
[512]   (((75-5)+(3))*(7))+(1) ||| 512
[513]   (75*7)-((5-1)*(3)) ||| 513
[514]   (1-3)*(((5)*(25-75))-(7)) ||| 514
[515]   (75*7)-((5)*(3-1)) ||| 515
[516]   (75*7)-((5+3)+(1)) ||| 516
[517]   ((75*7)-(5+3))*(1) ||| 517
[518]   ((75*7)-(5+3))+(1) ||| 518
[519]   ((((1*3)-(5))/(25))+(7))*(75) ||| 519
[520]   (75)*((7)-((1)/(5*3))) ||| 520
[521]   ((((1-3)+(5))+(75))*(7))-(25) ||| 521
[522]   (((75*7)-(5))+(3))-(1) ||| 522
[523]   (((75*7)-(5))+(3))*(1) ||| 523
[524]   (((75*7)-(5))+(3))+(1) ||| 524
[525]   (75*7)*((5)-(3+1)) ||| 525
[526]   ((75*7)+(5))-(3+1) ||| 526
[527]   (((75*7)+(5))-(3))*(1) ||| 527
[528]   (((75*7)+(5))-(3))+(1) ||| 528
[529]   (1)*((((3/25)+(7))*(75))-(5)) ||| 529
[530]   (75)*((7)+((1)/(5*3))) ||| 530
[531]   (1)+(((3)*((5/75)+(7)))*(25)) ||| 531
[532]   (((75*7)+(5))+(3))-(1) ||| 532
[533]   (((75*7)+(5))+(3))*(1) ||| 533
[534]   (((75*7)+(5))+(3))+(1) ||| 534
[535]   (75*7)+((5)*(3-1)) ||| 535
[536]   ((75)-(7+1))*(5+3) ||| 536
[537]   (75*7)+((5-1)*(3)) ||| 537
[538]   (((75+5)-(3))*(7))-(1) ||| 538
[539]   ((75*7)+(5*3))-(1) ||| 539
[540]   ((75*7)+(5*3))*(1) ||| 540
[541]   ((75*7)+(5*3))+(1) ||| 541
[542]   (((75+3)*(7))-(5))+(1) ||| 542
[543]   ((75-7)*(5+3))-(1) ||| 543
[544]   ((75-7)*(5+3))*(1) ||| 544
[545]   (75*7)+((5)*(3+1)) ||| 545
[546]   (((75+5)-(3))+(1))*(7) ||| 546
[547]   ((75+1)*(7))+(5*3) ||| 547
[548]   (((75+3)+(1))*(7))-(5) ||| 548
[549]   ((75)*((7/3)+(5)))-(1) ||| 549
[550]   ((75)*((7/3)+(5)))*(1) ||| 550
[551]   ((75)*((7/3)+(5)))+(1) ||| 551
[552]   ((75-7)+(1))*(5+3) ||| 552
[553]   (((1-3)+(5))+(25))+(75*7) ||| 553
[554]   ((1+3)+(5*75))+(25*7) ||| 554
[555]   (75)*(((7)-(3/5))+(1)) ||| 555
[556]   ((75+5)*(7))-(3+1) ||| 556
[557]   (((75+5)*(7))-(3))*(1) ||| 557
[558]   (((75+5)*(7))-(3))+(1) ||| 558
[559]   (((1+3)+(5))+(25))+(7*75) ||| 559
[600]   (75)*((7+5)-(3+1)) ||| 600
[601]   ((75)*((5*3)-(7)))+(1) ||| 601
[602]   (((75)*(7+1))+(5))-(3) ||| 602
[603]   ((1+3)*((5*25)+(7)))+(75) ||| 603
[604]   (1+3)-((5+7)*(25-75)) ||| 604
[605]   ((((1*3)*(5))+(75))*(7))-(25) ||| 605
[606]   (((75)*(5+3))+(7))-(1) ||| 606
[607]   (((75)*(5+3))+(7))*(1) ||| 607
[608]   (((75)*(7+1))+(5))+(3) ||| 608
[609]   ((75)+((5-1)*(3)))*(7) ||| 609
[610]   ((((1+3)/(5))+(7))*(75))+(25) ||| 610
[611]   ((1+5)*((3)+(75+25)))-(7) ||| 611
[612]   (75-7)*((5+3)+(1)) ||| 612
[613]   ((((1+3)+(5))+(75))*(7))+(25) ||| 613
[614]   (((1)+((3/25)+(7)))*(75))+(5) ||| 614
[615]   ((75)*(7+1))+(5*3) ||| 615
[616]   ((75+5)-(3))*(7+1) ||| 616
[617]   (1)+((3+25)*((7)+(75/5))) ||| 617
[618]   ((((1*3)+(5))*(75))+(25))-(7) ||| 618
[619]   ((75+3)*(7+1))-(5) ||| 619
[620]   ((((1)+(3/5))+(7))*(75))-(25) ||| 620
[621]   (1*3)*(((5*25)+(7))+(75)) ||| 621
[622]   (1)+((3)*(((5*25)+(7))+(75))) ||| 622
[623]   (((75)+(5*3))-(1))*(7) ||| 623
[624]   (((1)+((3+5)/(25)))+(7))*(75) ||| 624
[625]   (75)*((7)+((5-1)/(3))) ||| 625
[626]   ((1)+(((3*5)+(7))*(25)))+(75) ||| 626
[627]   ((1)/((3/75)/(25)))-(5-7) ||| 627
[628]   (1-5)*(((3)*(25-75))-(7)) ||| 628
[629]   (((75)+(5*3))*(7))-(1) ||| 629
[630]   (75-5)*((7+3)-(1)) ||| 630
[631]   (((75)+(5*3))*(7))+(1) ||| 631
[632]   ((((1*3)+(5))*(75))+(25))+(7) ||| 632
[633]   (((1)+((3+5)*(75)))+(25))+(7) ||| 633
[634]   (((1)+((5)+(75*25)))/(3))+(7) ||| 634
[635]   (((1+3)*(7))*(25-5))+(75) ||| 635
[636]   (((1-3)+(75))*(7))+(5*25) ||| 636
[637]   ((75+5)*(7+1))-(3) ||| 637
[638]   ((1)+(3+25))*((7)+(75/5)) ||| 638
[639]   (((1+5)*(7))+(75*25))/(3) ||| 639
[640]   ((((1+3)*(5))+(75))*(7))-(25) ||| 640
[641]   (1)-(((3/5)-(7))*(25+75)) ||| 641
[642]   (((1)+((3*25)+(5)))*(7))+(75) ||| 642
[643]   ((75+5)*(7+1))+(3) ||| 643
[644]   ((1+7)*(3+75))-(5-25) ||| 644
[645]   (75)*(((7)+(3/5))+(1)) ||| 645
[646]   (1)+((3)*((75)-((5-25)*(7)))) ||| 646
[647]   (((1)+(5+7))*(75-25))-(3) ||| 647
[648]   ((75+7)-(1))*(5+3) ||| 648
[649]   ((75)*((7)+(5/3)))-(1) ||| 649
[650]   ((75)*((7)+(5/3)))*(1) ||| 650
[651]   ((75)*((7)+(5/3)))+(1) ||| 651
[652]   (((25*5)+(3))-(1))+(7*75) ||| 652
[653]   ((1*3)+(7*75))+(25*5) ||| 653
[654]   (((1+3)-(7/25))+(5))*(75) ||| 654
[655]   ((75+7)*(5+3))-(1) ||| 655
[656]   ((75+7)*(5+3))*(1) ||| 656
[657]   ((75+7)*(5+3))+(1) ||| 657
[658]   ((25+3)*(5))+((75-1)*(7)) ||| 658
[659]   (((25)/(3/75))+(5*7))-(1) ||| 659
[700]   ((75*7)*(5-1))/(3) ||| 700
[701]   (1)+(((3*75)-(5*25))*(7)) ||| 701
[702]   (((1)-((3-25)*(5)))*(7))-(75) ||| 702
[703]   ((1-3)+((7)*(25+75)))+(5) ||| 703
[704]   (1)+((3)+((7)*(75+25))) ||| 704
[705]   (1*3)*((75)+((5)*(25+7))) ||| 705
[706]   (1)+((3)*((75)+((5)*(25+7)))) ||| 706
[707]   (((1)+(3*75))-(5*25))*(7) ||| 707
[708]   ((1*3)+((7)*(25+75)))+(5) ||| 708
[709]   ((1+3)+((7)*(25+75)))+(5) ||| 709
[710]   ((75-5)+(1))*(7+3) ||| 710
[711]   ((1-3)*((7)-(75*5)))-(25) ||| 711
[712]   (((1)+((3)*(5+25)))*(7))+(75) ||| 712
[713]   (((1+3)+(5))*(75+7))-(25) ||| 713
[714]   (1-3)*(((25)-(5*75))-(7)) ||| 714
[715]   (((75)*(3-1))-(7))*(5) ||| 715
[716]   ((1)+(3*5))+((25+75)*(7)) ||| 716
[717]   (1)+((((3)+(75+25))*(7))-(5)) ||| 717
[718]   ((1+5)*(3))+((7)*(75+25)) ||| 718
[719]   (((25+3)-(1-75))*(7))+(5) ||| 719
[720]   (75+5)*((7+3)-(1)) ||| 720
[721]   (1)-((3-75)*((7*5)-(25))) ||| 721
[722]   (1)+(((3+75)+(25))*(7)) ||| 722
[723]   (((1)+((3)+(75+25)))*(7))-(5) ||| 723
[724]   ((25)*(3+5))-((1)-(7*75)) ||| 724
[725]   (75)*(((7)+(5/3))+(1)) ||| 725
[726]   ((1)+((3+7)*(75-5)))+(25) ||| 726
[727]   (1)+((((3)+(75+25))*(7))+(5)) ||| 727
[728]   (((1+3)+(75))+(25))*(7) ||| 728
[729]   (1*3)*(((5)*(75-25))-(7)) ||| 729
[730]   ((1)-(3-75))*((7*5)-(25)) ||| 730
[731]   (((1)+((3+7)*(75)))-(25))+(5) ||| 731
[732]   (1)*((((5)+(75+25))*(7))-(3)) ||| 732
[733]   (1-3)+(((75+5)+(25))*(7)) ||| 733
[734]   ((7)*((25)+(75+5)))-(1) ||| 734
[735]   (75)*((7+3)-(1/5)) ||| 735
[736]   ((75*5)-(7))*(3-1) ||| 736
[737]   ((((25)+(5+75))*(7))-(1))+(3) ||| 737
[738]   (75+7)*((5+3)+(1)) ||| 738
[739]   (1+3)+(((75+5)+(25))*(7)) ||| 739
[740]   (((1)-(3/5))+(7))*(25+75) ||| 740
[741]   (((1-5)*(7-75))-(25))*(3) ||| 741
[742]   (((1+5)+(75))+(25))*(7) ||| 742
[743]   ((75*5)*(3-1))-(7) ||| 743
[744]   ((75)*(7+3))-(5+1) ||| 744
[745]   (((75)*(7+3))-(5))*(1) ||| 745
[746]   (((75)*(7+3))-(5))+(1) ||| 746
[747]   (1)*((((5*7)-(25))*(75))-(3)) ||| 747
[748]   ((75)-(1/5))*(7+3) ||| 748
[749]   (1)+((3+7)*((75)-(5/25))) ||| 749
[750]   (75)*(((7+5)-(3))+(1)) ||| 750
[751]   (1)+((((3)*(75-5))*(25))/(7)) ||| 751
[752]   ((75)+(1/5))*(7+3) ||| 752
[753]   (1*3)+((75)*((5*7)-(25))) ||| 753
[754]   (((75)*(7+3))+(5))-(1) ||| 754
[755]   (((75)*(7+3))+(5))*(1) ||| 755
[756]   (((75)*(7+3))+(5))+(1) ||| 756
[757]   ((75*5)*(3-1))+(7) ||| 757
[758]   ((1)-((3*5)*(25-75)))+(7) ||| 758
[759]   ((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 ? Commented Sep 18, 2017 at 19:20
• @sousben no idea, I just checked these and it takes some time to find.
– Oray
Commented Sep 18, 2017 at 19:28
• I'm sure it does! youtube.com/watch?v=X1jwjiEQG9Y Commented Sep 18, 2017 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 Commented Sep 18, 2017 at 20:25
• Why don't you use = Commented Sep 18, 2017 at 20:30