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Sum with letters - Paenza Olympiad 2010

Source:

August 27, 2010
modular arithmeticnumber theory unsolvednumber theory

Problem Statement

a) Replace each letter in the following sum by a digit from 00 to 99, in such a way that the sum is correct.
\tab \tab ABCABC \tab \tab DEFDEF +GHI+GHI \tab \tab \tab JJJJ J J
Different letters must be replaced by different digits, and equal letters must be replaced by equal digits. Numbers ABCABC, DEFDEF, GHIGHI and JJJJJJ cannot begin by 00.
b) Determine how many triples of numbers (ABC,DEF,GHI)(ABC,DEF,GHI) can be formed under the conditions given in a).
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