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The trivial answer is that any two numbers that reverse to each other will have this property. For example:

19 * 91 = 91 * 19

237 * 732 = 732 * 237

etc.


But apart from those, here are the two-digit pairs where this works:


12*42 = 21*24 = 504

12*63 = 21*36 = 756

12*84 = 21*48 = 1008

13*62 = 31*26 = 806

13*93 = 31*39 = 1209

14*82 = 41*28 = 1148

21*24 = 12*42 = 504

21*36 = 12*63 = 756

21*48 = 12*84 = 1008

23*64 = 32*46 = 1472

23*96 = 32*69 = 2208

24*63 = 42*36 = 1512

24*84 = 42*48 = 2016

26*31 = 62*13 = 806

26*93 = 62*39 = 2418

28*41 = 82*14 = 1148

31*39 = 13*93 = 1209

32*46 = 23*64 = 1472

32*69 = 23*96 = 2208

34*86 = 43*68 = 2924

36*42 = 63*24 = 1512

36*84 = 63*48 = 3024

39*62 = 93*26 = 2418

42*48 = 24*84 = 2016

43*68 = 34*86 = 2924

46*96 = 64*69 = 4416

48*63 = 84*36 = 3024

64*69 = 46*96 = 4416


Here are the two-digit numbers paired with three-digit numbers where this works:


12*231 = 21*132 = 2772

12*462 = 21*264 = 5544

12*693 = 21*396 = 8316

13*341 = 31*143 = 4433

13*682 = 31*286 = 8866

14*451 = 41*154 = 6314

15*561 = 51*165 = 8415

16*671 = 61*176 = 10736

17*781 = 71*187 = 13277

18*891 = 81*198 = 16038

21*132 = 12*231 = 2772

21*264 = 12*462 = 5544

21*396 = 12*693 = 8316

23*352 = 32*253 = 8096

24*231 = 42*132 = 5544

24*462 = 42*264 = 11088

24*693 = 42*396 = 16632

25*572 = 52*275 = 14300

26*341 = 62*143 = 8866

26*682 = 62*286 = 17732

27*792 = 72*297 = 21384

28*451 = 82*154 = 12628

31*143 = 13*341 = 4433

31*286 = 13*682 = 8866

32*253 = 23*352 = 8096

34*473 = 43*374 = 16082

35*583 = 53*385 = 20405

36*231 = 63*132 = 8316

36*462 = 63*264 = 16632

36*693 = 63*396 = 24948

39*341 = 93*143 = 13299

39*682 = 93*286 = 26598

41*154 = 14*451 = 6314

42*132 = 24*231 = 5544

42*264 = 24*462 = 11088

42*396 = 24*693 = 16632

43*374 = 34*473 = 16082

45*594 = 54*495 = 26730

46*352 = 64*253 = 16192

48*231 = 84*132 = 11088

48*462 = 84*264 = 22176

48*693 = 84*396 = 33264

51*165 = 15*561 = 8415

52*275 = 25*572 = 14300

53*385 = 35*583 = 20405

54*495 = 45*594 = 26730

61*176 = 16*671 = 10736

62*143 = 26*341 = 8866

62*286 = 26*682 = 17732

63*132 = 36*231 = 8316

63*264 = 36*462 = 16632

63*396 = 36*693 = 24948

64*253 = 46*352 = 16192

68*473 = 86*374 = 32164

69*352 = 96*253 = 24288

71*187 = 17*781 = 13277

72*297 = 27*792 = 21384

81*198 = 18*891 = 16038

82*154 = 28*451 = 12628

84*132 = 48*231 = 11088

84*264 = 48*462 = 22176

84*396 = 48*693 = 33264

86*374 = 68*473 = 32164

93*143 = 39*341 = 13299

93*286 = 39*682 = 26598

96*253 = 69*352 = 24288



Here are the three-digit numbers where this works:


102*402 = 201*204 = 41004

102*603 = 201*306 = 61506

102*804 = 201*408 = 82008

103*602 = 301*206 = 62006

103*903 = 301*309 = 93009

104*802 = 401*208 = 83408

112*422 = 211*224 = 47264

112*633 = 211*336 = 70896

112*844 = 211*448 = 94528

113*622 = 311*226 = 70286

113*933 = 311*339 = 105429

114*822 = 411*228 = 93708

122*442 = 221*244 = 53924

122*663 = 221*366 = 80886

122*884 = 221*488 = 107848

123*642 = 321*246 = 78966

123*963 = 321*369 = 118449

124*842 = 421*248 = 104408

132*462 = 231*264 = 60984

132*693 = 231*396 = 91476

133*662 = 331*266 = 88046

133*993 = 331*399 = 132069

134*862 = 431*268 = 115508

142*482 = 241*284 = 68444

143*682 = 341*286 = 97526

144*882 = 441*288 = 127008

201*204 = 102*402 = 41004

201*306 = 102*603 = 61506

201*408 = 102*804 = 82008

203*604 = 302*406 = 122612

203*906 = 302*609 = 183918

204*603 = 402*306 = 123012

204*804 = 402*408 = 164016

206*301 = 602*103 = 62006

206*903 = 602*309 = 186018

208*401 = 802*104 = 83408

211*224 = 112*422 = 47264

211*336 = 112*633 = 70896

211*448 = 112*844 = 94528

213*624 = 312*426 = 132912

213*936 = 312*639 = 199368

214*824 = 412*428 = 176336

221*244 = 122*442 = 53924

221*366 = 122*663 = 80886

221*488 = 122*884 = 107848

223*644 = 322*446 = 143612

223*966 = 322*669 = 215418

224*633 = 422*336 = 141792

224*844 = 422*448 = 189056

226*311 = 622*113 = 70286

226*933 = 622*339 = 210858

228*411 = 822*114 = 93708

231*264 = 132*462 = 60984

231*396 = 132*693 = 91476

233*664 = 332*466 = 154712

233*996 = 332*699 = 232068

234*864 = 432*468 = 202176

241*284 = 142*482 = 68444

243*684 = 342*486 = 166212

244*663 = 442*366 = 161772

244*884 = 442*488 = 215696

246*321 = 642*123 = 78966

246*963 = 642*369 = 236898

248*421 = 842*124 = 104408

264*693 = 462*396 = 182952

266*331 = 662*133 = 88046

266*993 = 662*399 = 264138

268*431 = 862*134 = 115508

286*341 = 682*143 = 97526

288*441 = 882*144 = 127008

301*309 = 103*903 = 93009

302*406 = 203*604 = 122612

302*609 = 203*906 = 183918

304*806 = 403*608 = 245024

306*402 = 603*204 = 123012

306*804 = 603*408 = 246024

309*602 = 903*206 = 186018

311*339 = 113*933 = 105429

312*426 = 213*624 = 132912

312*639 = 213*936 = 199368

314*826 = 413*628 = 259364

321*369 = 123*963 = 118449

322*446 = 223*644 = 143612

322*669 = 223*966 = 215418

324*846 = 423*648 = 274104

331*399 = 133*993 = 132069

332*466 = 233*664 = 154712

332*699 = 233*996 = 232068

334*866 = 433*668 = 289244

336*422 = 633*224 = 141792

336*844 = 633*448 = 283584

339*622 = 933*226 = 210858

342*486 = 243*684 = 166212

344*886 = 443*688 = 304784

366*442 = 663*244 = 161772

366*884 = 663*488 = 323544

369*642 = 963*246 = 236898

396*462 = 693*264 = 182952

399*662 = 993*266 = 264138

402*408 = 204*804 = 164016

403*608 = 304*806 = 245024

406*906 = 604*609 = 367836

408*603 = 804*306 = 246024

412*428 = 214*824 = 176336

413*628 = 314*826 = 259364

422*448 = 224*844 = 189056

423*648 = 324*846 = 274104

426*936 = 624*639 = 398736

432*468 = 234*864 = 202176

433*668 = 334*866 = 289244

442*488 = 244*884 = 215696

443*688 = 344*886 = 304784

446*966 = 644*669 = 430836

448*633 = 844*336 = 283584

466*996 = 664*699 = 464136

488*663 = 884*366 = 323544

604*609 = 406*906 = 367836

624*639 = 426*936 = 398736

644*669 = 446*966 = 430836

664*699 = 466*996 = 464136




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