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Pandigital pattern (Posted on 2016-06-28) Difficulty: 3 of 5
Find all pandigital sums of the form
abc+def=ghi
(with no zero) in ascending order of ghi and find a pattern in these sums.

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Some Thoughts Computer exploration | Comment 1 of 2
DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 s$ = "123456789": h$ = s$
 
 Do
  DoEvents
   If Val(Mid(s, 1, 3)) + Val(Mid(s, 4, 3)) = Val(Mid(s, 7, 3)) Then
     Text1.Text = Text1.Text & Mid(s, 1, 3) & " + " & Mid(s, 4, 3) & " = " & Mid(s, 7, 3) & crlf
   End If
   permute s
 Loop Until s$ = h$
  
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub

The results (336 valid additions) are then sorted by sum (major) and first addend (minor):

173 + 286 = 459
176 + 283 = 459
183 + 276 = 459
186 + 273 = 459
273 + 186 = 459
276 + 183 = 459
283 + 176 = 459
286 + 173 = 459
173 + 295 = 468
175 + 293 = 468
193 + 275 = 468
195 + 273 = 468
273 + 195 = 468
275 + 193 = 468
293 + 175 = 468
295 + 173 = 468
127 + 359 = 486
129 + 357 = 486
157 + 329 = 486
159 + 327 = 486
327 + 159 = 486
329 + 157 = 486
357 + 129 = 486
359 + 127 = 486
127 + 368 = 495
128 + 367 = 495
167 + 328 = 495
168 + 327 = 495
327 + 168 = 495
328 + 167 = 495
367 + 128 = 495
368 + 127 = 495
162 + 387 = 549
167 + 382 = 549
182 + 367 = 549
187 + 362 = 549
362 + 187 = 549
367 + 182 = 549
382 + 167 = 549
387 + 162 = 549
128 + 439 = 567
129 + 438 = 567
138 + 429 = 567
139 + 428 = 567
218 + 349 = 567
219 + 348 = 567
248 + 319 = 567
249 + 318 = 567
318 + 249 = 567
319 + 248 = 567
348 + 219 = 567
349 + 218 = 567
428 + 139 = 567
429 + 138 = 567
438 + 129 = 567
439 + 128 = 567
182 + 394 = 576
184 + 392 = 576
192 + 384 = 576
194 + 382 = 576
382 + 194 = 576
384 + 192 = 576
392 + 184 = 576
394 + 182 = 576
216 + 378 = 594
218 + 376 = 594
276 + 318 = 594
278 + 316 = 594
316 + 278 = 594
318 + 276 = 594
376 + 218 = 594
378 + 216 = 594
152 + 487 = 639
157 + 482 = 639
182 + 457 = 639
187 + 452 = 639
452 + 187 = 639
457 + 182 = 639
482 + 157 = 639
487 + 152 = 639
251 + 397 = 648
257 + 391 = 648
291 + 357 = 648
297 + 351 = 648
351 + 297 = 648
357 + 291 = 648
391 + 257 = 648
397 + 251 = 648
218 + 439 = 657
219 + 438 = 657
238 + 419 = 657
239 + 418 = 657
418 + 239 = 657
419 + 238 = 657
438 + 219 = 657
439 + 218 = 657
182 + 493 = 675
183 + 492 = 675
192 + 483 = 675
193 + 482 = 675
281 + 394 = 675
284 + 391 = 675
291 + 384 = 675
294 + 381 = 675
381 + 294 = 675
384 + 291 = 675
391 + 284 = 675
394 + 281 = 675
482 + 193 = 675
483 + 192 = 675
492 + 183 = 675
493 + 182 = 675
215 + 478 = 693
218 + 475 = 693
275 + 418 = 693
278 + 415 = 693
415 + 278 = 693
418 + 275 = 693
475 + 218 = 693
478 + 215 = 693
143 + 586 = 729
146 + 583 = 729
183 + 546 = 729
186 + 543 = 729
543 + 186 = 729
546 + 183 = 729
583 + 146 = 729
586 + 143 = 729
142 + 596 = 738
146 + 592 = 738
192 + 546 = 738
196 + 542 = 738
542 + 196 = 738
546 + 192 = 738
592 + 146 = 738
596 + 142 = 738
124 + 659 = 783
129 + 654 = 783
154 + 629 = 783
159 + 624 = 783
214 + 569 = 783
219 + 564 = 783
264 + 519 = 783
269 + 514 = 783
514 + 269 = 783
519 + 264 = 783
564 + 219 = 783
569 + 214 = 783
624 + 159 = 783
629 + 154 = 783
654 + 129 = 783
659 + 124 = 783
134 + 658 = 792
138 + 654 = 792
154 + 638 = 792
158 + 634 = 792
634 + 158 = 792
638 + 154 = 792
654 + 138 = 792
658 + 134 = 792
243 + 576 = 819
246 + 573 = 819
273 + 546 = 819
276 + 543 = 819
352 + 467 = 819
357 + 462 = 819
362 + 457 = 819
367 + 452 = 819
452 + 367 = 819
457 + 362 = 819
462 + 357 = 819
467 + 352 = 819
543 + 276 = 819
546 + 273 = 819
573 + 246 = 819
576 + 243 = 819
142 + 695 = 837
145 + 692 = 837
192 + 645 = 837
195 + 642 = 837
241 + 596 = 837
246 + 591 = 837
291 + 546 = 837
296 + 541 = 837
541 + 296 = 837
546 + 291 = 837
591 + 246 = 837
596 + 241 = 837
642 + 195 = 837
645 + 192 = 837
692 + 145 = 837
695 + 142 = 837
317 + 529 = 846
319 + 527 = 846
327 + 519 = 846
329 + 517 = 846
517 + 329 = 846
519 + 327 = 846
527 + 319 = 846
529 + 317 = 846
125 + 739 = 864
129 + 735 = 864
135 + 729 = 864
139 + 725 = 864
271 + 593 = 864
273 + 591 = 864
291 + 573 = 864
293 + 571 = 864
571 + 293 = 864
573 + 291 = 864
591 + 273 = 864
593 + 271 = 864
725 + 139 = 864
729 + 135 = 864
735 + 129 = 864
739 + 125 = 864
214 + 659 = 873
219 + 654 = 873
254 + 619 = 873
259 + 614 = 873
614 + 259 = 873
619 + 254 = 873
654 + 219 = 873
659 + 214 = 873
234 + 657 = 891
237 + 654 = 891
254 + 637 = 891
257 + 634 = 891
324 + 567 = 891
327 + 564 = 891
364 + 527 = 891
367 + 524 = 891
524 + 367 = 891
527 + 364 = 891
564 + 327 = 891
567 + 324 = 891
634 + 257 = 891
637 + 254 = 891
654 + 237 = 891
657 + 234 = 891
243 + 675 = 918
245 + 673 = 918
273 + 645 = 918
275 + 643 = 918
342 + 576 = 918
346 + 572 = 918
372 + 546 = 918
376 + 542 = 918
542 + 376 = 918
546 + 372 = 918
572 + 346 = 918
576 + 342 = 918
643 + 275 = 918
645 + 273 = 918
673 + 245 = 918
675 + 243 = 918
341 + 586 = 927
346 + 581 = 927
381 + 546 = 927
386 + 541 = 927
541 + 386 = 927
546 + 381 = 927
581 + 346 = 927
586 + 341 = 927
152 + 784 = 936
154 + 782 = 936
182 + 754 = 936
184 + 752 = 936
752 + 184 = 936
754 + 182 = 936
782 + 154 = 936
784 + 152 = 936
162 + 783 = 945
163 + 782 = 945
182 + 763 = 945
183 + 762 = 945
317 + 628 = 945
318 + 627 = 945
327 + 618 = 945
328 + 617 = 945
617 + 328 = 945
618 + 327 = 945
627 + 318 = 945
628 + 317 = 945
762 + 183 = 945
763 + 182 = 945
782 + 163 = 945
783 + 162 = 945
216 + 738 = 954
218 + 736 = 954
236 + 718 = 954
238 + 716 = 954
271 + 683 = 954
273 + 681 = 954
281 + 673 = 954
283 + 671 = 954
671 + 283 = 954
673 + 281 = 954
681 + 273 = 954
683 + 271 = 954
716 + 238 = 954
718 + 236 = 954
736 + 218 = 954
738 + 216 = 954
215 + 748 = 963
218 + 745 = 963
245 + 718 = 963
248 + 715 = 963
715 + 248 = 963
718 + 245 = 963
745 + 218 = 963
748 + 215 = 963
314 + 658 = 972
318 + 654 = 972
354 + 618 = 972
358 + 614 = 972
614 + 358 = 972
618 + 354 = 972
654 + 318 = 972
658 + 314 = 972
235 + 746 = 981
236 + 745 = 981
245 + 736 = 981
246 + 735 = 981
324 + 657 = 981
327 + 654 = 981
354 + 627 = 981
357 + 624 = 981
624 + 357 = 981
627 + 354 = 981
654 + 327 = 981
657 + 324 = 981
735 + 246 = 981
736 + 245 = 981
745 + 236 = 981
746 + 235 = 981

All the sums are multiples of 9, though several multiples of 9 are missing, such as 513, to take an example where the reason is not obvious, as it would be for 504 or 522.

  Posted by Charlie on 2016-06-28 10:16:49
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