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Six Term Settlement (Posted on 2014-06-26) Difficulty: 3 of 5
Find six strictly increasing terms - consisting entirely of positive integers - in arithmetic sequence that use precisely three different digits.

*** The highest term is less than 1000.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (2 votes)

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Solution computer solutions Comment 3 of 3 |
 Initial number limited to 2000; increment limited to 4000, so this is an expansion of what's asked for.

 1 6 11 16 21 26
 2 7 12 17 22 27
 11 61 111 161 211 261
 12 62 112 162 212 262
 16 66 116 166 216 266
 21 71 121 171 221 271
 22 72 122 172 222 272
 27 77 127 177 227 277
 111 611 1111 1611 2111 2611
 112 612 1112 1612 2112 2612
 116 616 1116 1616 2116 2616
 121 621 1121 1621 2121 2621
 122 622 1122 1622 2122 2622
 126 626 1126 1626 2126 2626
 161 661 1161 1661 2161 2661
 162 662 1162 1662 2162 2662
 166 666 1166 1666 2166 2666
 211 711 1211 1711 2211 2711
 212 712 1212 1712 2212 2712
 217 717 1217 1717 2217 2717
 221 721 1221 1721 2221 2721
 222 722 1222 1722 2222 2722
 227 727 1227 1727 2227 2727
 271 771 1271 1771 2271 2771
 272 772 1272 1772 2272 2772
 277 777 1277 1777 2277 2777

from

DefDbl A-Z
Dim crlf$

Private Sub Form_Load()
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 DoEvents
 
 For t1 = 1 To 2000
  For incr = 1 To 4000
   ReDim used(9): diffct = 0
   good = 1
   For i = 0 To 5
    t = t1 + i * incr
    ts$ = LTrim(Str(t))
    For j = 1 To Len(ts$)
     v = Val(Mid(ts$, j, 1))
     If used(v) = 0 Then diffct = diffct + 1: If diffct > 3 Then good = 0: Exit For
     used(v) = used(v) + 1
    Next
    If good = 0 Then Exit For
   Next
   If good Then Text1.Text = Text1.Text & Str(t1) & Str(t1 + incr) & Str(t1 + 2 * incr) & Str(t1 + 3 * incr) & Str(t1 + 4 * incr) & Str(t1 + 5 * incr) & crlf
   DoEvents
  Next
 Next
 Text1.Text = Text1.Text & "done"
End Sub

Edited on June 26, 2014, 3:30 pm
  Posted by Charlie on 2014-06-26 15:25:55

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