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?

Question

Brodie Moody

Mathematics

29 December, 02:29

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?

+1

Answers (1)

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Jordan Freeman · Answer 1

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.