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 Sum Number and Reversal (Posted on 2016-06-24)
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 No Rating

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 computer assisted | Comment 1 of 5
The next five are 2065, 2106, 2155, 2245 and 2294 based on this table:

` n   rev  sum sum/412016 6102 8118 1982065 5602 7667 1872106 6012 8118 1982155 5512 7667 1872245 5422 7667 1872294 4922 7216 1762335 5332 7667 1872384 4832 7216 1762425 5242 7667 1872474 4742 7216 1762515 5152 7667 1872564 4652 7216 1762605 5062 7667 1872654 4562 7216 1762744 4472 7216 1762793 3972 6765 1652834 4382 7216 1762883 3882 6765 1652924 4292 7216 1762973 3792 6765 1653015 5103 8118 1983064 4603 7667 1873105 5013 8118 1983154 4513 7667 1873244 4423 7667 1873293 3923 7216 1763334 4333 7667 1873383 3833 7216 1763424 4243 7667 1873473 3743 7216 1763514 4153 7667 1873563 3653 7216 1763604 4063 7667 1873653 3563 7216 1763743 3473 7216 1763792 2973 6765 1653833 3383 7216 1763882 2883 6765 1653923 3293 7216 1763972 2793 6765 1654014 4104 8118 1984063 3604 7667 1874104 4014 8118 1984153 3514 7667 1874243 3424 7667 1874292 2924 7216 1764333 3334 7667 1874382 2834 7216 1764423 3244 7667 1874472 2744 7216 1764513 3154 7667 1874562 2654 7216 1764603 3064 7667 1874652 2564 7216 1764742 2474 7216 1764791 1974 6765 1654832 2384 7216 1764881 1884 6765 1654899 9984 14883 3634922 2294 7216 1764971 1794 6765 1654989 9894 14883 3635013 3105 8118 1985062 2605 7667 1875103 3015 8118 1985152 2515 7667 1875242 2425 7667 1875291 1925 7216 1765332 2335 7667 1875381 1835 7216 1765399 9935 15334 3745422 2245 7667 1875471 1745 7216 1765489 9845 15334 3745512 2155 7667 1875561 1655 7216 1765579 9755 15334 3745602 2065 7667 1875651 1565 7216 1765669 9665 15334 3745741 1475 7216 1765759 9575 15334 3745790 975 6765 1655831 1385 7216 1765849 9485 15334 3745880 885 6765 1655898 8985 14883 3635921 1295 7216 1765939 9395 15334 3745970 795 6765 1655988 8895 14883 3636012 2106 8118 1986061 1606 7667 1876079 9706 15785 3856102 2016 8118 1986151 1516 7667 1876169 9616 15785 3856241 1426 7667 1876259 9526 15785 3856290 926 7216 1766331 1336 7667 1876349 9436 15785 3856380 836 7216 1766398 8936 15334 3746421 1246 7667 1876439 9346 15785 3856470 746 7216 1766488 8846 15334 3746511 1156 7667 1876529 9256 15785 3856560 656 7216 1766578 8756 15334 3746601 1066 7667 1876619 9166 15785 3856650 566 7216 1766668 8666 15334 3746709 9076 15785 3856740 476 7216 1766758 8576 15334 3746830 386 7216 1766848 8486 15334 3746897 7986 14883 3636920 296 7216 1766938 8396 15334 3746987 7896 14883 3637011 1107 8118 1987029 9207 16236 3967060 607 7667 1877078 8707 15785 3857101 1017 8118 1987119 9117 16236 3967150 517 7667 1877168 8617 15785 3857209 9027 16236 3967240 427 7667 1877258 8527 15785 3857330 337 7667 1877348 8437 15785 3857397 7937 15334 3747420 247 7667 1877438 8347 15785 3857487 7847 15334 3747510 157 7667 1877528 8257 15785 3857577 7757 15334 3747600 67 7667 1877618 8167 15785 3857667 7667 15334 3747708 8077 15785 3857757 7577 15334 3747847 7487 15334 3747896 6987 14883 3637937 7397 15334 3747986 6897 14883 3638010 108 8118 1988028 8208 16236 3968077 7708 15785 3858100 18 8118 1988118 8118 16236 3968167 7618 15785 3858208 8028 16236 3968257 7528 15785 3858347 7438 15785 3858396 6938 15334 3748437 7348 15785 3858486 6848 15334 3748527 7258 15785 3858576 6758 15334 3748617 7168 15785 3858666 6668 15334 3748707 7078 15785 3858756 6578 15334 3748846 6488 15334 3748895 5988 14883 3638936 6398 15334 3748985 5898 14883 3639027 7209 16236 3969076 6709 15785 3859117 7119 16236 3969166 6619 15785 3859207 7029 16236 3969256 6529 15785 3859346 6439 15785 3859395 5939 15334 3749436 6349 15785 3859485 5849 15334 3749526 6259 15785 3859575 5759 15334 3749616 6169 15785 3859665 5669 15334 3749706 6079 15785 3859755 5579 15334 3749845 5489 15334 3749894 4989 14883 3639935 5399 15334 3749984 4899 14883 363`

DefDbl A-Z
Dim crlf\$

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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