MathDB
cuddly numbers

Source: 2021 AMC 10A #8

November 11, 2021

Problem Statement

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?
<spanclass=latexbold>(A)</span>0<spanclass=latexbold>(B)</span>1<spanclass=latexbold>(C)</span>2<spanclass=latexbold>(D)</span>3<spanclass=latexbold>(E)</span>4<span class='latex-bold'>(A) </span>0\qquad<span class='latex-bold'>(B) </span>1\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>3\qquad<span class='latex-bold'>(E) </span>4