MathDB

4

Part of 2005 National Olympiad First Round

Problems(1)

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

Source:

11/8/2013
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=′latex−bold′>(A)</span> 11<spanclass=′latex−bold′>(B)</span> 77<spanclass=′latex−bold′>(C)</span> 133<spanclass=′latex−bold′>(D)</span> 166<spanclass=′latex−bold′>(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