Math Trivia [2]

Question:
Find the largest three-digit number such that the number minus the sum of its digits is a perfect square.

Answer:
Please find the solution and answer in the comments below.
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1 comment:

  1. Anonymous8/23/13, 2:53 PM

    Let ABC be the three-digit number.

    (100A+10B+C)-(A+B+C)=99A+9B=9(11A+B)

    9(11A+B) is a perfect square.

    To maximize the number 100A+10B+C, we set
    A=9,B=1 and C=9.

    Therefore the answer is 919.

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