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81 : 8 + 1 = 9, and 9 x 9 = 81.

Here's how to figure: If the 2-digit number is ab,. then the number is equal to 10*a + b. And nine time the sum equals 9*(a + b). Set these two equal and you have:

  • 9*a + 9*b = 10*a + b --> 8*b = a.

Knowing that the digits must be in the range 1 through 9: 1 x 8 = 8, and 2 x 8 = 16, so the only possibility is a=8 and b=1.

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