MathDB
P04 [Combinatorics] - Turkish NMO 1st Round - 2005

Source:

November 8, 2013

Problem Statement

How many 66-digit positive integers whose digits are different from 00 are there such that each number generated by rearranging the digits of the original number is always divisible by 77?
<spanclass=latexbold>(A)</span> 11<spanclass=latexbold>(B)</span> 77<spanclass=latexbold>(C)</span> 133<spanclass=latexbold>(D)</span> 166<spanclass=latexbold>(E)</span> 255 <span class='latex-bold'>(A)</span>\ 11 \qquad<span class='latex-bold'>(B)</span>\ 77 \qquad<span class='latex-bold'>(C)</span>\ 133 \qquad<span class='latex-bold'>(D)</span>\ 166 \qquad<span class='latex-bold'>(E)</span>\ 255