9–Digit Pandigital Friedman Numbers
123456789 = ((86 + 2 × 7)5 – 91) / 34 123469758 = 471 × 86 – 9 × (5 + 2) – 3 123469785 = 471 × 86 – 2 × 3 × 5 – 9
123469875 = 471 × 86 + 5 × 9 + 2 × 3 134286579 = 89 + 413 – 65 – 7 + 2 134286597 = 89 + 413 – 52 × (7 – 6)
134295678 = 89 + 57 – 61 × 3 + 2 × 4 134295687 = 23×9 + 57 – 86 + 14 134295768 = 23×9 + 57 – 86 + 14
134295786 = 23×9 + 57 – 68 + 14 134295867 = 23×9 + 57 + 6 + 8 × 14 134295876 = 23×9 + 57 + 4 × 6 – 18
135768924 = 485 × 67 – 9 × (3 + 2 – 1) 135768942 = 485 × 67 – 9 × (3 + 1 – 2) 135796824 = 5143 + 8 × (9 + 6 + 2 – 7)
135796842 = 5143 + 98 × (2 + 6 – 7) 135897246 = 23×9 + 68 – 57 – 41 135897264 = 89 + 364 – 2 × 5 × (7 + 1)
135897426 = 23×9 + 68 + 41 × (7 – 5) 135897462 = 23×9 + 68 + 125 – 7 145286739 = 519 × 67 – 8 × (4 + 2) + 3
145286793 = 519 × 67 + 8 + 3 + 2 – 4 147539864 = 96 + 435 – 28 + 7 + 1 152843769 = (12368 – 5)4+7–9 (BC)
154368729 = 89 + 674 – 5 × (23 + 1) 154368792 = 89 + 674 – 51 – 2 × 3 157326849 = 125437+9–6–8 (BC)
172538946 = 68 + 157 – 42 – 9 / 3 172538964 = 68 + 157 – 24 – 9 / 3 179653248 = 89 + 345 + 6 × 2 × (7 + 1)
187432956 = 715 × 49 – 8 + 6 / 3 + 2 187432965 = 715 × 49 + 6 + 8 – 32 192675834 = 735 × 49 – 8 + 6 / (2 + 1)
194825763 = 139582 – (7 – 6)4 196345728 = 749 × 86 – 25+3–1 196345782 = 749 × 86 – 53 – 21
196345827 = 749 × 86 – 2 × 3 × 5 + 1 196345872 = 749 × 86 + 15 + 3 – 2

213847659 = 5983 + 467 × (2 – 1) 214356789 = (9 + 7 – 6 + 1)8 – 4 × 523 214356798 = (2+9)8 – 6 × 347 – 15
214356879 = (4+7)8 – 91 × (25 – 6 + 3) 214356897 = (7 + 6 – 2)3+5 – 1984 214356978 = (6+5)8 – 1924 + 3 × 7
214356987 = (7 + 6 – 2)3+5 – 1894 214357689 = (4+7)8 – 2 × 596 × 13 214357698 = (5 × 2 + 4 – 3)8 – 7 × 169
214357869 = (9 + 7 – 6 + 1)8 – 4 × 253 214357896 = (4+7)2+6 – 985 × 13 214357968 = (6+5)8 – 913 × (2 × 4 – 7)
214357986 = (4+7)2+6 – 895 × 13 214358679 = (6+5)8 – 217 + 3 × (9 – 4) 214358697 = (6+5)8 – 174 – 9 – 3 + 2
214358769 = (6+5)8 – 127 + 3 × (9 – 4) 214358796 = (6+5)8 – 7 × 4 × 9 / 3 + 2 × 1 (CW) 214358967 = (6+5)8 – 72 + 3 × (9 – 4) – 1
214358976 = (6+5)8 + 1 × 94 – 3 × 2 + 7 (CW) 214359678 = (6+5)8 + 793 + 4 × 12 214359687 = (4 + 5 + 9 – 7)8 + 13 × 62
214359768 = (5+6)8 +37 × 24 – 19 214359786 = (5+6)8 + 912 – 7 × (4 – 3) 214359867 = (5 × 2 + 4 – 3)7+1 + 986
214359876 = (2+9)8 + (4 + 6)3 – 5 × 17 214365789 = (2 × 4 + 3)8 + 6915 – 7 214365798 = (5 × 2 + 4 – 3)8 + 6917
214365879 = (6+5)8 + 7 × (1 + 9)3 – 4 / 2 214365897 = (6+5)8 + 7 × (1 + 9)3 + 42 214365978 = (6+5)8 + 7124 – 3 × 9
214365987 = (6+5)8 + 78 × 91 + 23 214856973 = 14658(32–7) + 9 218953467 = 412 × 96 – 3 × 5 × (7 + 8)
218953476 = 412 × 96 – (5 + 8 – 7)3 218953674 = 412 × 96 – 3 × 5 + 7 – 8) 218953746 = 412 × 96 + 53 + 8 – 7
218953764 = 412 × 96 + 8 × (7 + 5 – 3) 231475679 = 6143 + 5 × 9 × (8 – 7 + 2) 231475697 = 6143 + 9 × (2 × 7 + 8 – 5)
231475869 = (618 – 4)3 + 5 × (7 × 9 + 2) 239861745 = 915 × 86 – 3 × (7 + 2 – 4) 239861754 = 915 × 86 – 7 – 4 + 3 + 2
241796835 = 619 × 58 – 4 × (7 + 3) / 2 241796853 = 619 × 58 – 7 × 4 + 3 × 2 245893761 = (15683 – 2)4+7–9 (BC)
246395817 = 156972 + 8 × (4 – 3) 247936518 = 157462 + 3 + 8 – 9 249576813 = 157984/2 + 3 + 6
251634789 = 158632 + 4 + 7 + 9 254817369 = 159632 × (8 – 7)4 (BC) 263419758 = 941 × 67 – 8 – 5 – 3 – 2
263419785 = 941 × 67 + 8 + 2 × 3 – 5 268435179 = –268 + 4(3×5 – 17) – 9 268435197 = –268 + 4(3×5 – 17) + 9
268435719 = 28 + 167 + 9 / 3 × 4 – 5 268435791 = 28 + 167 + 94 – 3 × 5 268435917 = 29 + 167 – 58 + 3 + 4
268435971 = 29 + 167 + 3 × (5 + 4 – 8) 268439517 = 84 + (2 + 6 + 9 – 1)7 – 35 268439571 = 84 + 167 + 2 + 3 + 5 + 9
275493618 = 165982 + 3 + 4 + 7 275894136 = 6513 – 7 × (49 – 8 / 2) 275894163 = 6519/3 – 8 × 4 × (7 + 2)
275894316 = (654 – 2 – 1)3 – 9 × (8 + 7) 275894361 = 6513 – 9 × 2 × (4 + 8 – 7) 275894613 = 6513 + 9 × (7 + 2) × 8 / 4
275894631 = (652 – 1)3 + 9 × (4 × 7 – 8) 289453167 = 741 × 58 + 2 × (3 × 9 – 6) 289453176 = 741 × 58 + 39 + 2 × 6
298437516 = 764 × 58 + 9 + 1 + 3 × 2 298437561 = 764 × 58 + 92 – 31

312475689 = 149 × 87 + 2 × 3 × 6 + 5 312475698 = 149 × 87 + 6 × (5 + 3) + 2 318729645 = (17856 – 3)2 + 4 × 9
324165789 = 193 × 68 – 57 – 42 324165798 = 193 × 68 – 5 × (7 × 2 + 4)) 324165879 = 193 × 68 – 7 – 2 × (5 – 4)
324165897 = 193 × 68 + 7 + 2 × (5 – 4) 324165978 = 193 × 68 + 5 × (7 × 2 + 4)) 324165987 = 193 × 68 + 57 + 42
357421869 = 183 × 59 – 6 × (7 – 4 – 2) 357421896 = 183 × 59 + 7 × 6 / (4 – 2) 368947215 = 64 × 78 – 59 + 32 + 1
368947251 = 64 × 78 – 9 – 5 + 3 – 2 × 1 368947512 = 64 × 78 + 251 – 9 / 3 368947521 = 64 × 78 + 259 + 1 – 3
371694825 = 7193 – (65 + 2) × 8 / 4 371694852 = 7193 – 86 – 25 + 4 375468129 = (19375 + 2)4+6–8 (BC)
378419265 = (19456 – 3)2 + & × 8 381574629 = 718 × 96 – 5 – 4 × (3 – 2) 381574692 = 718 × 96 + 54 × (3 – 2)
381574926 = 718 × 96 + 32 × (5 + 4) 382657149 = 7263 – 1 – 4 – 5 – 8 – 9 382657194 = 7263 – 1 × 4 + 5 + 8 + 9
382945761 = (19572 – 3)4+6–8 (BC) 385294617 = 725 × 96 – (8 + 1) × 3 × 4 385294716 = 725 × 96 – 8 + 1 × (4 – 3)
385297641 = (19634 – 5)2×(8–7) (BC) 387412569 = 92+7 – 3 × 48 × (56 – 1) 387412596 = 94+5 – 7861 – 32
387412659 = 94+5 – 7826 – 3 – 1 387412695 = 92+7 – 65 – 3 × (14 – 8) 387412956 = 93+6 – 7528 – 4 – 1
387412965 = 916–8+1 – 7524 387415269 = 94+5 – 87 × (63 – 2 – 1) 387415296 = 92+7 – 5186 – 3 – 4
387415629 = 91+8 – 3 × 27 × (56 + 4) 387415692 = 98+2–1 – 75 × 64 + 3 387415926 = 92+7 – 53 × 86 – 4 – 1
387415962 = 98–4+5 – 62 × 73 – 1 387416259 = 92×6 – 3 – 5 × 18 × 47 387416295 = 92+7 – 46 – 83 – 15
387416529 = 93+6 – 72 × (58 – 4 +1) 387416592 = 93+6 – 54 × 72 – 1 – 8 387416925 = 91+8 – 54 × (67 + 2 –3)
387416952 = 92+7 – 58 × 61 + 4 – 3 387419256 = 93+6 – 82 × 15 – 7 + 4 387419265 = 93(5–2) – 87 × 14 – 6
387419526 = 94+5 – 37 × 26 – 18 387419562 = 94+5 – 78 × 12 + 6 + 3 387419625 = 94+5 – 867 + 2 + 13
387419652 = (6–3)2×9 – 817 – 4 × 5 (CW) 387421569 = 93+6 + 8 × 15 × (7 + 4 – 2) 387421596 = 92+7 + 85 × 13 + 6 – 4
387421659 = 93+6 + 78 × 5 × (4 + 1 – 2) 387421695 = 92+7 + 86 × 14 + 5 – 3 387421956 = 94+5 + 86 × 17 + 2 + 3
387421965 = 92+7 + 36 × (5 × 8 + 14) 387425169 = 91+8 + 72 × 65 × (4 – 3) 387425196 = 92+7 + 84 × 56 × 1 + 3
387425619 = 91+8 + 57 × 3 × (24 + 6) 387425691 = 98/4 + 7 + 512 × 6 / 3 387425916 = 94+5 + 67 × 81 × (3 – 2)
387425961 = 94+5 + 72 × (83 – 6 – 1) 387426159 = 94+5 + 81 × (76 – 2 × 3) 387426195 = 98+4–3 + 5712 – 6
387426519 = 94+5 + 67 × (81 + 32) 387426591 = 93(5–2) + 71 × 86 – 4 387426915 = 93(8–5) + 6427 – 1
387426951 = 913–4 + 85 × 76 + 2 387429156 = 913–4 + 8672 – 5 387429165 = 92+3+4 + 8675 + 1
387429516 = 91+8 + 26 × 347 + 5 387429561 = 98+4–3 + 12 × 756 387429615 = 97+8–6 + 54 × 132
387429651 = 92+7 + 4581 × 6 / 3 394618572 = 198652 + 347

416832759 = (748 – 1)3 + 6 × (9 – 5 + 2) 416832795 = (748 – 1)3 + 6 × (9 + 5 – 2) 421583679 = 251 × 68 + 9 × 7 × (4 – 3)
421583769 = 251 × 68 + 9 × (7 × 3 – 4) 421583976 = 251 × 68 + 9 × 4 × (7 + 3)

513962478 = 51 × 69 – 8 – 7 – 4 – 2 + 3 513962487 = 51 × 69 – (4 + 3 + 2) × (8 – 7) 513962748 = 51 × 69 + (7 + 2) × (3 × 8 + 4)
513962784 = 51 × 69 + (3 + 7 + 8 ) × 24 513962874 = 51 × 69 + (7 + 2) × (38 + 4) 536874912 = 4 × (89 + (2 × 5)3) + 7 – 6 – 1 (BC)
536874912 = (1 + 7 – 6)29 + 4 × 8 × 53 (BC) 537219684 = 231784–5–6+9 (BC) 542968713 = 278 × 59 – 36 – 14
542968731 = 278 × 59 – 3 × 4 – 6 – 1 547981236 = 1534 – 9 × (8 – 7 + 6 – 2) (BC) 547981263 = 1534 – 2 × (78 – 69) (BC)
547981326 = 1534 + 9 × (8 – 7 + 6 – 2) 547981362 = 1534 + 92 × (8 – 7)6 547981623 = 1534 + 9 × (6 × 7 – 8 / 2)
594823167 = 8419/3 – 2 × 7 × (5 + 6) 594823176 = 8413 – 5 × (2 × 7 + 6 + 9) 594823617 = 296 + 73 – 48 + 15
594823671 = 296 + 5 × 7 × (8 + 4 – 3 + 1) (BC) 594823716 = (842 – 1)6–3 + 5 × 79 594823761 = 296 + (7 + 3) × (8 × 5 × + 4 × 1) (BC)

639128457 = 1598–4 – 36 × 7 × 2 639128475 = 1594 – 2 × 36+7–8 639128547 = 1598–4 – 6 × (72 – 3)
639128574 = 1596–4/2 – 387 639128745 = 1594 – 63 × (2 + 7 – 8) 639128754 = 1594 – 23 × (7 + 8 – 6)
672935481 = 25941–3+6+7–8 (BC)

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714653289 = (26738 – 5)(9–1)/4 (BC) 742391685 = 354 × 87 – 129 + 6 742391856 = 354 × 87 + 6 × (9 + 1 – 2)
742391865 = 354 × 87 + 19 × 6 / 2 759186234 = 452 × 68 – 9 × (7 × 3 + 1) 759186243 = 452 × 68 – 9 × 7 × 3 × 1
759186342 = 452 × 68 – 9 × 1 × (7 + 3) 759186423 = 452 × 68 – 9 × 137 759186432 = 452 × 68 × 1379
791453268 = 9253 + (6 + 7) × (8 + 4 – 1) 791453286 = 9253 + 7 × (6 × (8 – 4) – 1)

815746329 = 56 + 138 – 7 – 2 × (9 – 4) 815746392 = 56 + 138 + 4 × 7 + 2 × 9 834769125 = 497 × 68 – 25 – 3 + 1
834769152 = 497 × 68 × 1235

914358267 = 436 × 87 – 9 – 2 + 5 + 1 914358276 = 436 × 87 + 9 – 5 × (2 – 1) 932574816 = (972 – 1 + 6)3 – 8 – 5 – 4
932574861 = (971 + 6)3 + 28 × (5 – 4) 952763814 = 9843 – 5 × (2 × 6 + 7 – 1) 952763841 = 9843 – 67 + 5 – 2 + 1
974251368 = 169 × 78 – (5 – 4) × (3 – 2) 974251386 = 169 × 78 + 5 × 2 + 4 + 3 983564271 = 469 × 87 – 5 × 3 – 2 × 1
987654321 = (8 × (97 + 6/2)5 + 1) / 34

10–Digit Pandigital Friedman Numbers
1026753849 = (30249 – 6)7–5 × 18 (BC) 1237069584 = 351726–4 + 89 × 0 (BC) 1436789025 = 379052 × 1468 (BC)
1532487609 = 391472 + 0 × 568 (BC) 1927385604 = 439027–5 × 168 (BC) 2170348569 = 465872 + 139 × 0 (BC)
2913408576 = 539762 + 0 × 148 (BC) 3015986724 = 549182 + 0 × 367 (BC) 3285697041 = 573216–4 + 0 × 89 (BC)
3412078569 = 584132 + 0 × 679 (BC) 3528716409 = 594032 × 1678 (BC) 3719048256 = 609842 × 1357 (BC)
3975428601 = 630512 + 9 – 7 – 8/4 (BC) 3985270641 = 631297–5 + 0 × 48 (BC) 4832057169 = 695132 + 0 × 478 (BC)
5368709124 = (8 – 6)29 × (3 + 7) + 4 + 15 × 0 (BC) 5803697124 = 761825–3 + 0 × 49 (BC) 6154873209 = 784532 + 0 × 169 (BC)
6457890321 = 803612 × (5 – 4)79 (BC) 6714983025 = 819452 + 0 × 367 (BC) 7351862049 = 857432 + 0 × 169 (BC)
7408561329 = 860732 × 1459 (BC) 7680594321 = 876392 + 0 × 145 (BC) 7946831025 = 891452 + 0 × 367 (BC)
8014367529 = 895236–4 + 0 × 17 (BC) 8127563409 = 901532 × (7 – 6)48 (BC) 8326197504 = 912485–3 + 0 × 67 (BC)
8391476025 = 916052 + 3 + 8 – 4 – 7 (BC) 9351276804 = 967023–1 × (5 – 4)8 (BC)

(BC) = Bruno Curfs
(CW) = Chris Wardle