Just Digits
Number Theory
Level
3
How many 2 digit numbers are equal to the sum of the product of their digits and the sum of their digits?
1
10
19
9
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1 solution
Our equation can be written in the following form:
10A + B = AB + A + B
10A = A(B + 1)
A ≠ 0, because our 2-digit number cannot start with a zero. Therefore, we can divide by A:
10 = B + 1
B = 9
As we can see, A can be any possible decimal digit (except 0), and our 2 digit numbers are: 19, 29, ... , 89, 99 (9 distinct values).
Hence, our answer is: 9