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

Home > Numbers
The smallest non-conformist (Posted on 2017-05-02) Difficulty: 3 of 5
a. What is the smallest number not dividing any 10 digit-pandigital?
b. Same question, but for the non-zero pandigital numbers.

Source: Rodolfo Kurchan

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution with computer assistance | Comment 1 of 3
The digits of either kind of pandigital number add up to 45.

45 is divisible by 9, and therefore all pandigital numbers are divisible by both 3 and 9. Some pandigital numbers are divisible by 2, and some of those by 4 and some of those are divisible by 8 (such as those ending in ...128). Those that are divisible by 2 are also divisible by 6 as all are divisible by 3. Any ending in 5 or 0 is divisible by 5.

7 is the first number attempted by the program.

It turns out 100, 200 and 300 are the first three, as each requires the number end with two zeros.

Likewise, when using only digits 1 through 9, all the multiples of 10 fail, including 10 as the first.

Private Sub Form_Load()
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 
 s$ = "123456789"
 h$ = s
 Do
   v = Val(s)
   For i = 7 To 300
     q = Int(v / i): r = v - q * i
     If r = 0 Then
       If dvsr(i) = 0 Then ct = ct + 1
       dvsr(i) = 1
     End If
   Next i
   permute s
   DoEvents
 Loop Until s = h Or ct = 294
 
 If ct = 294 Then
   Text1.Text = Text1.Text & "not found" & v
 Else
   For i = 7 To 300
     If dvsr(i) = 0 Then Text1.Text = Text1.Text & Str(i)
   Next
   Text1.Text = Text1.Text & crlf
 End If


  Posted by Charlie on 2017-05-02 12:47:47
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 (2)
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