MathDB
Digital Sum

Source:

January 4, 2009
modular arithmetic

Problem Statement

Let (x) \clubsuit(x) denote the sum of the digits of the positive integer x x. For example, \clubsuit(8)\equal{}8 and \clubsuit(123)\equal{}1\plus{}2\plus{}3\equal{}6. For how many two-digit values of x x is \clubsuit(\clubsuit(x))\equal{}3? <spanclass=latexbold>(A)</span> 3<spanclass=latexbold>(B)</span> 4<spanclass=latexbold>(C)</span> 6<spanclass=latexbold>(D)</span> 9<spanclass=latexbold>(E)</span> 10 <span class='latex-bold'>(A)</span>\ 3 \qquad <span class='latex-bold'>(B)</span>\ 4 \qquad <span class='latex-bold'>(C)</span>\ 6 \qquad <span class='latex-bold'>(D)</span>\ 9 \qquad <span class='latex-bold'>(E)</span>\ 10