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Product Sum Settlement (Posted on 2011-09-17) Difficulty: 3 of 5
Each of the capital letters in bold denotes a different base ten digit from 1 to 9 in this cryptarithmetic expression. It is known that A < B, D < E, G < H and, C < F < I

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

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

(II) Which positive integer value assumed by the above expression gives a unique solution?

No Solution Yet Submitted by K Sengupta    
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Solution answers Comment 1 of 1
(I) The smallest value that the expression may assume, given a different base ten digit from 1 to 9, such that A < B, D < E, G<H and C<F<I is 70
=(8+9)*1+(6+7)*2+(4+5)*3;
and the largest is 198
=(1+2)*3+(4+5)*6+(7+8)*9
=(1+2)*3+(4+5)*7+(6+8)*9
=(1+2)*3+(4+5)*8+(6+7)*9.

(II) Given the givens, the smallest value, 70, is the only unique solution to the expression.
  Posted by Dej Mar on 2011-09-17 15:07:01
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