As you know from Tough Puzzle Part 1 and Tough Puzzle Part 2 TOUGH+TOUGH=PUZZLE,
TOUGH+TOUGH+TOUGH=PUZZLE
and TOUGH+TOUGH+TOUGH+TOUGH=PUZZLE have valid solutions.

Besides these three, there are several other valid ones. How many of them can you find? What is the greatest number of times that TOUGH can be added to make PUZZLE?

This problem was suggested by Brian Smith and endorsed by Jer, whom I wish to thank.

 2 * 93852 = 187704
 
 3 * 34089 = 102267
 3 * 65908 = 197724
 
 4 * 37524 = 150096
 4 * 79152 = 316608
 4 * 80294 = 321176
 4 * 87524 = 350096
 4 * 92785 = 371140
 4 * 94715 = 378860
 
 5 * 35764 = 178820
 5 * 87321 = 436605
 5 * 95762 = 478810
 
 6 * 82951 = 497706
 6 * 91467 = 548802
 
 7 * 24758 = 173306
 7 * 41908 = 293356
 7 * 56972 = 398804
 7 * 58091 = 406637
 7 * 72069 = 504483
 
 8 * 80419 = 643352
 8 * 89165 = 713320
 
 9 * 40621 = 365589
 9 * 72589 = 653301
 9 * 81356 = 732204
 9 * 94567 = 851103
 
12 * 17038 = 204456
12 * 17039 = 204468
12 * 25097 = 301164
12 * 25098 = 301176
12 * 65932 = 791184
12 * 70461 = 845532

16 * 25073 = 401168

18 * 31604 = 568872

19 * 19708 = 374452
19 * 46903 = 891157
19 * 50643 = 962217

20 * 16279 = 325580
20 * 31279 = 625580

22 * 21765 = 478830
22 * 32069 = 705518
22 * 35912 = 790064

23 * 24683 = 567709

24 * 23796 = 571104

27 * 34278 = 925506

28 * 18094 = 506632
28 * 20713 = 579964

29 * 19734 = 572286
29 * 30956 = 897724

30 * 15629 = 468870

32 * 17604 = 563328
32 * 26597 = 851104

33 * 20841 = 687753
33 * 26971 = 890043

34 * 10586 = 359924
34 * 12057 = 409938

36 * 14073 = 506628

38 * 25701 = 976638

43 * 13902 = 597786

47 * 17069 = 802243

48 * 15302 = 734496

49 * 15602 = 764498

52 * 16537 = 859924
52 * 16795 = 873340

55 * 13496 = 742280

63 * 10723 = 675549

70 * 13254 = 927780

So 70 is the highest. Also, 52 is the highest that has multiple solutions.

OPEN "tuffpuzz.txt" FOR OUTPUT AS #2
FOR t = 1 TO 9
 taken(t) = 1

FOR p = 1 TO 9
IF taken(p) = 0 THEN
 taken(p) = 1

FOR o = 0 TO 9
IF taken(o) = 0 THEN
 taken(o) = 1

FOR u = 0 TO 9
IF taken(u) = 0 THEN
 taken(u) = 1

FOR g = 0 TO 9
IF taken(g) = 0 THEN
 taken(g) = 1

FOR h = 0 TO 9
IF taken(h) = 0 THEN
 taken(h) = 1

FOR z = 0 TO 9
IF taken(z) = 0 THEN
 taken(z) = 1

FOR l = 0 TO 9
IF taken(l) = 0 THEN
 taken(l) = 1

FOR e = 0 TO 9
IF taken(e) = 0 THEN
 taken(e) = 1

 tough = 10000 * t + 1000 * o + 100 * u + 10 * g + h
 puzzle = 100000 * p + 10000 * u + 1100 * z + 10 * l + e

 q = INT(puzzle / tough + .5)
 IF q * tough = puzzle THEN PRINT USING "## * ##### = ######"; q; tough; puzzle
 IF q * tough = puzzle THEN PRINT #2, USING "## * ##### = ######"; q; tough; puzzle

 

 taken(e) = 0
END IF
NEXT

 taken(l) = 0
END IF
NEXT

 taken(z) = 0
END IF
NEXT

 taken(h) = 0
END IF
NEXT

 taken(g) = 0
END IF
NEXT

 taken(u) = 0
END IF
NEXT

 taken(o) = 0
END IF
NEXT

 taken(p) = 0
END IF
NEXT

 taken(t) = 0
NEXT

CLOSE

resulting file then sorted and blank lines placed at changes of q.

Posted by Charlie on 2007-08-23 11:16:52