MathDB
Turkey NMO 2010 1st Round - P12 (Combinatorics)

Source:

July 26, 2012

Problem Statement

How many integer quadruples a,b,c,da,b,c,d are there such that 77 divides abcdab-cd where 0a,b,c,d<70\leq a,b,c,d < 7?
<spanclass=latexbold>(A)</span> 412<spanclass=latexbold>(B)</span> 385<spanclass=latexbold>(C)</span> 294<spanclass=latexbold>(D)</span> 252<spanclass=latexbold>(E)</span> None <span class='latex-bold'>(A)</span>\ 412 \qquad<span class='latex-bold'>(B)</span>\ 385 \qquad<span class='latex-bold'>(C)</span>\ 294 \qquad<span class='latex-bold'>(D)</span>\ 252 \qquad<span class='latex-bold'>(E)</span>\ \text{None}