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The 16th Japanese Mathematical Olympiad - The First Round

Japan algebra

Problem

is a positive 3-digit number, and its hundred's place and its one's place are not . Make a new number by exchanging the hundred's place and the one's place of , and call it . Answer the maximum value of .
Solution
Let . Then, Since and can be any natural number between and , the maximum value of is .
Final answer
792

Techniques

Integers