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

Home > Just Math
AABBCC and Perfect Square (Posted on 2016-11-09) Difficulty: 4 of 5
N is a perfect square such that the last six digits of N is of the form AABBCC where A, B and C are distinct base ten digits and A is nonzero.

Find the smallest value of N.

What if C shouldn't be zero?

** AABBCC represents the concatenation of the digits and not their product.

*** For an extra challenge solve this puzzle without using a computer program.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer solution | Comment 4 of 6 |
DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 For mils = 0 To 10000
 For a = 1 To 9
   pt1 = 110000 * a
 For b = 0 To 9
   pt2 = pt1 + 1100 * b
 For c = 0 To 9
   pt3 = pt2 + 11 * c
   
   n = pt3 + 1000000 * mils
   
   sr = Int(Sqr(n) + 0.5)
   If sr * sr = n Then
     Text1.Text = Text1.Text & n & crlf
   End If
   DoEvents
 
 Next
 Next
 Next
 Next mils
 
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub

lists the following perfect squares. Note that some are not in the "spirit" of the pattern, in that two of A, B and C are equal in some of them


774400
1440000
5116644
5664400
14440000
25887744
38440000
47334400
70224400
77440000
125440000
190440000
246113344
262440000
276224400
309337744
328334400
353440000
427993344
434222244
449440000
511664400
544662244
566440000
581774400
669774400
686440000
718883344
749664400
829440000
885776644
914336644
973440000
1016334400
1071776644
1101443344
1114224400
1142440000
1310440000
1505440000
1533662244
1697440000
1732224400
1798777744
1859334400
1918440000
1963553344
2134440000
2267664400
2381440000
2412774400
2588774400
2621440000
2743664400
2894440000
3117882244
3158440000
3235334400
3408224400
3457440000
3589447744
3745440000
3876556644
4070440000
4194116644
4236447744
4255996644
4382440000
4438224400
4640334400
4733440000
5069440000
5135442244
5273664400
5446440000
5493774400
5757774400
5806440000
5987664400
6209440000
6510553344
6593440000
6704334400
6820777744
6945222244
6952224400
7022440000
7430440000
7885440000
8317440000
8394224400
8429443344
8600336644
8671334400
8798440000
9254440000
9529664400
9640883344
9761440000
9824774400

  Posted by Charlie on 2016-11-09 13:37:06
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 (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information