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 Elegant Exponent Exposition II (Posted on 2010-12-04)
Each of the capital letters in bold denotes a different base ten digit from 1 to 9 in this cryptarithmetic expression:

AB/C + DE/F + GH/I

(I) Determine the respective smallest and the largest positive integer that this expression can assume.

(II) Determine the respective smallest and the largest prime number that this expression can assume. What are the respective smallest and the largest palindrome assumed by the above expression?

 No Solution Yet Submitted by K Sengupta No Rating

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 re: computer solution for integers and primes -- now palindromes | Comment 2 of 3 |
(In reply to computer solution for integers and primes by Charlie)

100           :spal=cutspc(str(sum))
110           :pal=1
120           :for i=1 to int(len(spal))
130              :if mid(spal,i,1)<>mid(spal,len(spal))+1-i,1) then pal=0:endif
140           :next
150           :if pal=1 and sum<lowpal then lowpal=sum:lowpalstr=s\$:endif
155           :if pal=1 and sum>highpal then highpal=sum:highpalstr=s\$:endif

finds

157263948        8
693742851        33033

where 693742851 represents 6^(9/3)+7^(4/2)+8^(5/1), which equals the largest palindrome: 33033.

 Posted by Charlie on 2010-12-04 19:55:33

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