MathDB
P02 [Combinatorics] - Turkish NMO 1st Round - 2001

Source:

April 18, 2014

Problem Statement

Each of the football teams Istanbulspor, Yesildirek, Vefa, Karagumruk, and Adalet, played exactly one match against the other four teams. Istanbulspor defeated all teams except Yesildirek; Yesildirek defeated Istanbulspor but lost to all the other teams. Vefa defeated all except Istanbulspor. The winner of the game Karagumruk-Adalet is Karagumruk. In how many ways one can order these five teams such that each team except the last, defeated the next team?
<spanclass=latexbold>(A)</span> 5<spanclass=latexbold>(B)</span> 7<spanclass=latexbold>(C)</span> 8<spanclass=latexbold>(D)</span> 9<spanclass=latexbold>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 5 \qquad<span class='latex-bold'>(B)</span>\ 7 \qquad<span class='latex-bold'>(C)</span>\ 8 \qquad<span class='latex-bold'>(D)</span>\ 9 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}