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Sum Number and Reversal (Posted on 2016-06-24) Difficulty: 3 of 5
It is observed that the sum of 2016 and its reversal 6102 is 8118 and, 8118 is divisible by 41.

Determine the five positive integers following 2016 with the property that the sum of the number and its reversal is divisible by 41.

*** As an extra challenge, try to solve this problem without using a computer program assisted method.

No Solution Yet Submitted by K Sengupta    
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Solution computer assisted | Comment 1 of 5
The next five are 2065, 2106, 2155, 2245 and 2294 based on this table:

 n   rev  sum sum/41
2016 6102 8118 198
2065 5602 7667 187
2106 6012 8118 198
2155 5512 7667 187
2245 5422 7667 187
2294 4922 7216 176
2335 5332 7667 187
2384 4832 7216 176
2425 5242 7667 187
2474 4742 7216 176
2515 5152 7667 187
2564 4652 7216 176
2605 5062 7667 187
2654 4562 7216 176
2744 4472 7216 176
2793 3972 6765 165
2834 4382 7216 176
2883 3882 6765 165
2924 4292 7216 176
2973 3792 6765 165
3015 5103 8118 198
3064 4603 7667 187
3105 5013 8118 198
3154 4513 7667 187
3244 4423 7667 187
3293 3923 7216 176
3334 4333 7667 187
3383 3833 7216 176
3424 4243 7667 187
3473 3743 7216 176
3514 4153 7667 187
3563 3653 7216 176
3604 4063 7667 187
3653 3563 7216 176
3743 3473 7216 176
3792 2973 6765 165
3833 3383 7216 176
3882 2883 6765 165
3923 3293 7216 176
3972 2793 6765 165
4014 4104 8118 198
4063 3604 7667 187
4104 4014 8118 198
4153 3514 7667 187
4243 3424 7667 187
4292 2924 7216 176
4333 3334 7667 187
4382 2834 7216 176
4423 3244 7667 187
4472 2744 7216 176
4513 3154 7667 187
4562 2654 7216 176
4603 3064 7667 187
4652 2564 7216 176
4742 2474 7216 176
4791 1974 6765 165
4832 2384 7216 176
4881 1884 6765 165
4899 9984 14883 363
4922 2294 7216 176
4971 1794 6765 165
4989 9894 14883 363
5013 3105 8118 198
5062 2605 7667 187
5103 3015 8118 198
5152 2515 7667 187
5242 2425 7667 187
5291 1925 7216 176
5332 2335 7667 187
5381 1835 7216 176
5399 9935 15334 374
5422 2245 7667 187
5471 1745 7216 176
5489 9845 15334 374
5512 2155 7667 187
5561 1655 7216 176
5579 9755 15334 374
5602 2065 7667 187
5651 1565 7216 176
5669 9665 15334 374
5741 1475 7216 176
5759 9575 15334 374
5790 975 6765 165
5831 1385 7216 176
5849 9485 15334 374
5880 885 6765 165
5898 8985 14883 363
5921 1295 7216 176
5939 9395 15334 374
5970 795 6765 165
5988 8895 14883 363
6012 2106 8118 198
6061 1606 7667 187
6079 9706 15785 385
6102 2016 8118 198
6151 1516 7667 187
6169 9616 15785 385
6241 1426 7667 187
6259 9526 15785 385
6290 926 7216 176
6331 1336 7667 187
6349 9436 15785 385
6380 836 7216 176
6398 8936 15334 374
6421 1246 7667 187
6439 9346 15785 385
6470 746 7216 176
6488 8846 15334 374
6511 1156 7667 187
6529 9256 15785 385
6560 656 7216 176
6578 8756 15334 374
6601 1066 7667 187
6619 9166 15785 385
6650 566 7216 176
6668 8666 15334 374
6709 9076 15785 385
6740 476 7216 176
6758 8576 15334 374
6830 386 7216 176
6848 8486 15334 374
6897 7986 14883 363
6920 296 7216 176
6938 8396 15334 374
6987 7896 14883 363
7011 1107 8118 198
7029 9207 16236 396
7060 607 7667 187
7078 8707 15785 385
7101 1017 8118 198
7119 9117 16236 396
7150 517 7667 187
7168 8617 15785 385
7209 9027 16236 396
7240 427 7667 187
7258 8527 15785 385
7330 337 7667 187
7348 8437 15785 385
7397 7937 15334 374
7420 247 7667 187
7438 8347 15785 385
7487 7847 15334 374
7510 157 7667 187
7528 8257 15785 385
7577 7757 15334 374
7600 67 7667 187
7618 8167 15785 385
7667 7667 15334 374
7708 8077 15785 385
7757 7577 15334 374
7847 7487 15334 374
7896 6987 14883 363
7937 7397 15334 374
7986 6897 14883 363
8010 108 8118 198
8028 8208 16236 396
8077 7708 15785 385
8100 18 8118 198
8118 8118 16236 396
8167 7618 15785 385
8208 8028 16236 396
8257 7528 15785 385
8347 7438 15785 385
8396 6938 15334 374
8437 7348 15785 385
8486 6848 15334 374
8527 7258 15785 385
8576 6758 15334 374
8617 7168 15785 385
8666 6668 15334 374
8707 7078 15785 385
8756 6578 15334 374
8846 6488 15334 374
8895 5988 14883 363
8936 6398 15334 374
8985 5898 14883 363
9027 7209 16236 396
9076 6709 15785 385
9117 7119 16236 396
9166 6619 15785 385
9207 7029 16236 396
9256 6529 15785 385
9346 6439 15785 385
9395 5939 15334 374
9436 6349 15785 385
9485 5849 15334 374
9526 6259 15785 385
9575 5759 15334 374
9616 6169 15785 385
9665 5669 15334 374
9706 6079 15785 385
9755 5579 15334 374
9845 5489 15334 374
9894 4989 14883 363
9935 5399 15334 374
9984 4899 14883 363

DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 For n = 2016 To 9999
  DoEvents
  ns$ = LTrim(Str(n))
  rev = 0
  For i = Len(ns) To 1 Step -1
    rev = rev * 10 + Val(Mid(ns, i, 1))
  Next
  If (n + rev) Mod 41 = 0 Then
    Text1.Text = Text1.Text & n & Str(rev) & Str(n + rev) & Str((n + rev) / 41) & crlf
  End If
 Next
 
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub


  Posted by Charlie on 2016-06-24 14:03:57
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