MathDB
n crates in a supermarket

Source: 1976 AHSME Problem 12

May 17, 2014
pigeonhole principleprobabilityexpected valueAMC

Problem Statement

A supermarket has 128128 crates of apples. Each crate contains at least 120120 apples and at most 144144 apples. What is the largest integer nn such that there must be at least nn crates containing the same number of apples?
<spanclass=latexbold>(A)</span>4<spanclass=latexbold>(B)</span>5<spanclass=latexbold>(C)</span>6<spanclass=latexbold>(D)</span>24<spanclass=latexbold>(E)</span>25<span class='latex-bold'>(A) </span>4\qquad<span class='latex-bold'>(B) </span>5\qquad<span class='latex-bold'>(C) </span>6\qquad<span class='latex-bold'>(D) </span>24\qquad <span class='latex-bold'>(E) </span>25