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24 September, 10:55

How many three-digit palindromes (numbers that read the same forward and backward) satisfy the following property: the sum of three things - - the hundreds digit, the units digit, and the product of the units and tens digits - - is eight more than the tens digit?

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  1. 24 September, 11:47
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    Let the 3-digit palindrome be 101a+10b. a+a+ab=8+b, so 2a+ab-b=8.

    2a+b (a-1) = 8; b=2 (4-a) / (a-1). From this we know that a > 1. And we know 4-a > 0 so a < 4.

    This limits a to 2 and 3 which make b=4 and 1.

    The palindromes are 242 and 313.
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