MathDB
2020 Individual #22

Source:

May 1, 2022
2020 Individual

Problem Statement

Jane's uncle gives her a "44-balance." The 44-balance acts like a normal balance scale, but it compares four masses instead of two, tilting towards the weight that is heaviest (if all four are equal, it stays balanced). He then gives her 2525 coins, one of which is a counterfeit heavier than the rest. What is the minimum number of uses of the 44-balance needed to ensure she identifies the counterfeit?
<spanclass=latexbold>(A)</span>1<spanclass=latexbold>(B)</span>2<spanclass=latexbold>(C)</span>3<spanclass=latexbold>(D)</span>4<spanclass=latexbold>(E)</span>5<span class='latex-bold'>(A) </span>1\qquad<span class='latex-bold'>(B) </span>2\qquad<span class='latex-bold'>(C) </span>3\qquad<span class='latex-bold'>(D) </span>4\qquad<span class='latex-bold'>(E) </span>5