Despite the advice given by Polonius we sometimes need to "borrow" during the subtraction process, so while 345-122 is achieved without "borrowing", 322-145 needs two acts of "borrowing".

Having stated the above, please find the largest set of 3-digit numbers, such that for any pair(a,b; a>b) of members of the set the operation a-b cannot be done without borrowing.

Based upon a NSH contest problem.

54 terms:

990
981
972
963
954
945
936
927
918
909

891
882
873
864
855
846
837
828
819

792
783
774
765
756
747
738
729

693
684
675
666
657
648
639

594
585
576
567
558
549

495
486
477
468
459

396
387
378
369

297
288
279

198
189

Posted by tomarken on 2014-07-01 14:23:12