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

Home > Just Math
Eight Digit Product Poser (Posted on 2016-04-20) Difficulty: 3 of 5
Determine the total number of values of a 8-digit positive integer N such that the product of the digits of N is 2016.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution with a little help from a Mintoris Basic program (Android) Comment 1 of 1
Factoring 2016 into primes produces one set of digits

22222337

These can be permuted of course, and also multiplied together by digit, with the resulting set padded out with 1's:

11114789      
11116678      
11122789      
11123678      
11124479      
11124667      
11133478      
11134467      
11222479      
11222667      
11223378      
11223467      
11233447      
12222279      
12222367      
12223347      
22222337      


from this Mintoris Basic program (Android):

global n, cell(), numcells, highdig,tot
dim cell(20)


''input "n:",n0
'Input "number of cells:",numcells
'input "size of grid:",highdig

n0=2016
numcells=8
highdig=9

open 2,"8 dig prod.txt","w"

'writeln 2, str$(n0 ), str$(numcells ), str$(highdig )
n = n0

addon(1)

 close 2

End 

Sub addon(wh)
  If wh = 1 Then 
    st = 1 
  Else 
    st = cell(wh - 1)
  endif
  For factr = st To highdig
    If n % factr = 0 Then
      n = n / factr
      tot=tot+factr
      
      cell(wh) = factr
      If wh = numcells Then
        If n = 1 Then
          For i = 1 To wh
            write 2, str$(cell(i))
          Next
          writeln 2,  "      "
        EndIf
      Else
        addon(wh + 1)
      EndIf
      
      n = n * factr
      tot=tot-factr
    Endif
  Next

End Sub

Now annotating for permutations

11114789    8!/4!                  1680
11116678    8!/(4!*2!)              840
11122789    8!/(3!*2!)             3360
11123678    8!/3!                  6720
11124479    8!/(3!*2!)             3360
11124667    8!/(3!*2!)             3360
11133478    8!/(3!*2!)             3360
11134467    8!/(3!*2!)             3360
11222479    8!/(3!*2!)             3360
11222667    8!/(3!*2!*2!)          1680
11223378    8!/(2!*2!*2!)          5040 
11223467    8!/(2!*2!)            10080
11233447    8!/(2!*2!*2!)          5040
12222279    8!/5!                   336
12222367    8!/4!                  1680
12223347    8!/(3!*2!)             3360
22222337    8!/(5!*2!)              168
                                --------
                                  56784

So the answer is 56,784.



  Posted by Charlie on 2016-04-20 13:46:12
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 (9)
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