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Quaint Quadruplets (Posted on 2014-08-18) Difficulty: 3 of 5
Determine the total number of quadruplets (A, B, C, D) of positive integers such that:
  • A divides B, and:
  • B divides C, and:
  • C divides D, and:
  • A+B+C+D=4200

No Solution Yet Submitted by K Sengupta    
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Some Thoughts re: software solution--similar puzzle solution Comment 3 of 3 |
(In reply to software solution by Charlie)

Just for the heck of it, if a, b, c and d were required to be unique (no repeated integer):


95 such cases among the original set:

 1 13 26 4160
 1 13 91 4095
 1 13 182 4004
 1 13 299 3887
 1 13 598 3588
 1 17 34 4148
 1 17 51 4131
 1 17 102 4080
 1 17 697 3485
 1 17 1394 2788
 1 19 38 4142
 1 19 76 4104
 1 19 95 4085
 1 19 190 3990
 1 19 209 3971
 1 19 380 3800
 1 19 418 3762
 1 19 836 3344
 1 19 1045 3135
 1 221 442 3536
 1 221 663 3315
 1 221 1326 2652
 1 247 494 3458
 1 247 988 2964
 1 323 646 3230
 1 323 969 2907
 1 323 1292 2584
 6 18 36 4140
 6 18 72 4104
 6 18 144 4032
 6 18 522 3654
 6 18 1044 3132
 8 16 48 4128
 8 16 144 4032
 8 16 464 3712
 8 16 1392 2784
 8 32 64 4096
 8 32 160 4000
 8 32 320 3840
 8 32 416 3744
 8 32 832 3328
 14 182 364 3640
 14 322 644 3220
 14 322 966 2898
 14 322 1288 2576
 15 45 90 4050
 15 45 180 3960
 15 45 1035 3105
 15 135 270 3780
 15 135 405 3645
 15 135 675 3375
 15 135 810 3240
 15 135 1350 2700
 15 465 930 2790
 20 220 440 3520
 20 220 660 3300
 20 220 1320 2640
 20 380 760 3040
 24 48 96 4032
 24 72 216 3888
 24 72 1368 2736
 24 144 288 3744
 24 144 576 3456
 24 144 1008 3024
 35 245 490 3430
 35 245 980 2940
 35 595 1190 2380
 40 80 240 3840
 40 80 1360 2720
 40 160 800 3200
 40 320 640 3200
 40 320 960 2880
 40 320 1280 2560
 42 126 252 3780
 42 126 504 3528
 42 126 1008 3024
 42 378 756 3024
 42 462 924 2772
 56 112 224 3808
 56 112 336 3696
 56 112 448 3584
 56 112 672 3360
 56 112 1008 3024
 56 112 1344 2688
 60 180 360 3600
 75 375 750 3000
 84 588 1176 2352
 105 315 630 3150
 105 315 945 2835
 105 315 1260 2520
 120 240 480 3360
 120 240 960 2880
 150 450 900 2700
 200 400 1200 2400
 280 560 1120 2240

95 done

 tot = 4200
 For a = 1 To tot / 4
  For b = a + 1 To (tot - a) / 3
   If b Mod a = 0 Then
   For c = b + 1 To (tot - a - b) / 2
     If c Mod b = 0 Then
     d = tot - a - b - c
     If d Mod c = 0 And d > c Then
       Text1.Text = Text1.Text & Str(a) & Str(b) & Str(c) & Str(d) & crlf
       ct = ct + 1
       DoEvents
     End If
     End If
   Next c
   End If
  Next b
 Next a


  Posted by Charlie on 2014-08-19 10:03:12
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