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# Pandigital math expressionsPrev TopicNext Topic

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• United States
Member #197,030
March 28, 2019
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Pandigital expressions or number are those that use all the digits 0 through 9. These are all the pandigital sums that use each digit exactly once with two summands. Since they involve 3-digit and 4-digit numbers, they might be of interest to Pick 3/4 players.

246 + 789 = 1035
249 + 786 = 1035
264 + 789 = 1053
269 + 784 = 1053
284 + 769 = 1053
286 + 749 = 1035
289 + 746 = 1035
289 + 764 = 1053
324 + 765 = 1089
325 + 764 = 1089
342 + 756 = 1098
346 + 752 = 1098
347 + 859 = 1206
349 + 857 = 1206
352 + 746 = 1098
356 + 742 = 1098
357 + 849 = 1206
359 + 847 = 1206
364 + 725 = 1089
365 + 724 = 1089
423 + 675 = 1098
425 + 673 = 1098
426 + 879 = 1305
429 + 876 = 1305
432 + 657 = 1089
437 + 589 = 1026
437 + 652 = 1089
439 + 587 = 1026
452 + 637 = 1089
457 + 632 = 1089
473 + 589 = 1062
473 + 625 = 1098
475 + 623 = 1098
476 + 829 = 1305
479 + 583 = 1062
479 + 826 = 1305
483 + 579 = 1062
487 + 539 = 1026
489 + 537 = 1026
489 + 573 = 1062
624 + 879 = 1503
629 + 874 = 1503
674 + 829 = 1503
679 + 824 = 1503
743 + 859 = 1602
749 + 853 = 1602
753 + 849 = 1602
759 + 843 = 1602
These could all be inverted to make equivalent pandigital subtraction expressions.

With multiplication up to three factors, there are fewer pandigital expressions:
27 x 594 = 16038
36 x 495 = 17820
39 x 402 = 15678
45 x 396 = 17820
46 x 715 = 32890
52 x 367 = 19084
54 x 297 = 16038
63 x 927 = 58401
78 x 345 = 26910
1 x 2 x 3485 = 6970
1 x 2 x 3548 = 7096
1 x 2 x 3845 = 7690
1 x 2 x 4538 = 9076
1 x 2 x 4685 = 9370
1 x 2 x 4835 = 9670
1 x 2 x 4853 = 9706
1 x 2 x 4865 = 9730
1 x 26 x 345 = 8970
2 x 3 x 1465 = 8790
2 x 3 x 1645 = 9870
2 x 14 x 307 = 8596
3 x 4 x 896 = 10752
4 x 5 x 639 = 12780
4 x 5 x 936 = 18720
4 x 7 x 935 = 26180
4 x 8 x 961 = 30752
5 x 9 x 328 = 14760
5 x 39 x 76 = 14820
5 x 76 x 84 = 31920
6 x 9 x 381 = 20574
7 x 8 x 541 = 30296
8 x 31 x 97 = 24056
8 x 35 x 64 = 17920
8 x 37 x 65 = 19240
8 x 42 x 91 = 30576
8 x 45 x 91 = 32760
8 x 65 x 91 = 47320
9 x 32 x 58 = 16704
9 x 47 x 61 = 25803
Which could also be inverted to make pandigital division expressions.

When you increase the number of operations, things get hairy. You can come up with things like

(2 x 487) + 65 = 1039
(12 x 47) + 305 = 869
(17 x 239) + 5 = 4068
(41 x 76) + 89 = 3205
5 + 129 + 604 = 738
10 + 35 + 684 = 729
14 + 89 + 257 = 360
21 + 53 + 790 = 864

(not exhaustive)

• Mexico
Member #193,547
November 3, 2018
257 Posts
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Hello, the topic sounds interesting, where can I find this type of information, greetings.....

• United States
Member #197,030
March 28, 2019
1,453 Posts
Offline

Quote: Originally posted by Mayte on Oct 20, 2022

Hello, the topic sounds interesting, where can I find this type of information, greetings.....

If you google "pandigital expressions" you can find more examples of these kinds of math equations. Some people do not include the 0.

• Mexico
Member #193,547
November 3, 2018
257 Posts
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Thank You cottoneyedjoe

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