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

Home > Numbers
USA = n*UK (Posted on 2013-01-21) Difficulty: 2 of 5
Each of the letters in bold represents a base ten digit from 0 to 9 to satisfy these alphametic relationships. None of the numbers can contain any leading zero.
               USA is a multiple of UK, and:
               SA is a multiple of K
Determine the respective minimum and maximum values that USA can assume.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer solution | Comment 1 of 7

DEFDBL A-Z
CLS
FOR u = 1 TO 9
 used(u) = 1
FOR k = 0 TO 9
 IF used(k) = 0 THEN
  used(k) = 1
  FOR s = 1 TO 9
    IF used(s) = 0 THEN
      used(s) = 1
      FOR a = 0 TO 9
        IF used(a) = 0 THEN
          used(a) = 1
          uk = 10 * u + k
          usa = 100 * u + 10 * s + a
          sa = 10 * s + a
          IF INT(usa / uk) = usa / uk THEN
            IF INT(sa / k) = sa / k THEN PRINT usa, uk, sa
          END IF
          used(a) = 0
        END IF
      NEXT
      used(s) = 0
    END IF
  NEXT
  used(k) = 0
 END IF
NEXT
 used(u) = 0
NEXT

produces results that I had to sort separately, as I neglected to cycle through the variables in U, S, A order.  The sorted output, with heading added is:

USA           UK            SA
120           15            20
156           12            56
168           12            68
168           14            68
169           13            69
180           12            80
180           15            80
196           14            96
216           24            16
273           21            73
294           21            94
324           36            24
372           31            72
384           32            84
432           48            32
492           41            92

so USA can be as small as 120 and as large as 492.


  Posted by Charlie on 2013-01-21 12:12:29
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 (7)
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