MathDB
An Array of Digits

Source: 2010 AMC 10B Problem 23; AMC 12B Problem 17

February 26, 2010
reflectionrotationAMCMATHCOUNTSBAD MATHCOUNTSHook length formulaUSAMO

Problem Statement

The entries in a 3×3 3\times3 array include all the digits from 1 through 9, arranged so that the entries in every row and column are in increasing order. How many such arrays are there? <spanclass=latexbold>(A)</span> 18<spanclass=latexbold>(B)</span> 24<spanclass=latexbold>(C)</span> 36<spanclass=latexbold>(D)</span> 42<spanclass=latexbold>(E)</span> 60 <span class='latex-bold'>(A)</span>\ 18\qquad<span class='latex-bold'>(B)</span>\ 24\qquad<span class='latex-bold'>(C)</span>\ 36\qquad<span class='latex-bold'>(D)</span>\ 42\qquad<span class='latex-bold'>(E)</span>\ 60