 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Elegant Exponent Exposition (Posted on 2009-02-09) Substitute each of the capital letters in bold by a different decimal digit from 1 to 9 and determine the minimum positive integer value that the following cryptarithmetic expression can assume.

(A/B)C + (D/E)F + (G/H)I

How about the maximum positive integer value that this expression can assume?

 See The Solution Submitted by K Sengupta No Rating Comments: ( Back to comment list | You must be logged in to post comments.) re: computer solution -- extension to non-integral results | Comment 2 of 3 | (In reply to computer solution by Charlie)

If the result could be a rational, rather than an integer, we get:

5   MinVal=9999999999999:MaxVal=0
10   D\$="123456789":H\$=D\$
20   loop
40    Tval=0
50    for I=1 to 7 step 3
60     Term=(val(mid(D\$,I,1))//val(mid(D\$,I+1,1)))^val(mid(D\$,I+2,1))
70     Tval=Tval+Term
80    next
90    if Tval<MinVal then MinVal=Tval:MinStr=D\$
100    if Tval>MaxVal then MaxVal=Tval:MaxStr=D\$
110
390    gosub *Permute(&D\$)
398    if D\$=H\$ then goto 400
399   endloop
400   print MinStr,MinVal,MinVal/1.0
410   print MaxStr,MaxVal,MaxVal/1.0
700   end
giving (after manual reformatting):

(3/9)^7 + (2/5)^8 + (1/4)^6 = 4747532587/3499200000000 ~= 0.0013567479958276177

(8/1)^9 + (6/2)^7 + (5/3)^4 = 10871813740/81 ~= 134,219,922.7160493827160493827

The maximum is not much larger, due to most of it coming from the (8/1)^9.

Edited on February 9, 2009, 1:02 pm
 Posted by Charlie on 2009-02-09 13:01:14 Please log in:

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