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    OlympiadEasyNumber Theory5–6

    A Difference That Cannot Be

    Uma Diferença Impossível

    Marta writes down a whole number and then writes a second number using exactly the same digits in a different order. She subtracts the smaller from the larger and announces 20262026. Show that she is mistaken.

    Compare each number with the sum of its digits; ask what the two numbers share when divided by 99.

    Solution

    Step 1 of 5

    1. 1.Every number leaves the same remainder on division by 99 as the sum of its digits.