2021 Fall AMC 10A Problems/Problem 8
A two-digit positive integer is said to be cuddly if it is equal to the sum of its nonzero tens digit and the square of its units digit. How many two-digit positive integers are cuddly?
Solution 1
Note that the number By the problem statement,
From this we see that
must be divisible by
This only happens when
Then,
Thus, there is only
cuddly number which is
Thus, the answer is
~NH14