All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Squares needing 2 digits only (Posted on 2018-10-21) Difficulty: 4 of 5
List all perfect square numbers over 1000, employing only 2 different decimal digits. Example: 88^2=7744 will be on your list.

Ignore trivial solutions like 1 or 4 or 9 followed by an even number of zeroes.

How far can you go?

Known largest solution is a 10-digit number 6,661,661,161.

See The Solution Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer solution | Comment 1 of 3
square square root

16        4
25        5
36        6
49        7
64        8
81        9
121      11
144      12
225      15
441      21
484      22
676      26
1444      38
7744      88
11881      109
29929      173
44944      212
55225      235
69696      264
9696996      3114
6661661161      81619

Those above 1000 in bold face.
Numbers tested through squares of 10,000,000.

DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 For i = 2 To 10000000
   c$ = LTrim(Str(i * i))
   ReDim had(9)
   ct = 0
   good = 1
   For j = 1 To Len(c)
     If had(Val(Mid(c, j, 1))) = 0 Then ct = ct + 1
     If ct > 2 Then good = 0: Exit For
     had(Val(Mid(c, j, 1))) = had(Val(Mid(c, j, 1))) + 1
   Next
   If good Then
     good = 0
     For j = 2 To Len(c)
       If Mid(c, j, 1) <> "0" Then good = 1: Exit For
     Next
     If Len(c) Mod 2 = 0 Then good = 1
     If good Then Text1.Text = Text1.Text & c & "      " & i & crlf
   End If
   DoEvents
 Next
 
 Text1.Text = Text1.Text & crlf & tot & " done"
  
End Sub


  Posted by Charlie on 2018-10-21 19:41:09
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information