MathDB
Tourism In Five Villages

Source: 2008 Greek TST,Pr.2

May 25, 2016
combinatorics

Problem Statement

In a village X0X_0 there are 8080 tourists who are about to visit 55 nearby villages X1,X2,X3,X4,X5X_1,X_2,X_3,X_4,X_5.Each of them has chosen to visit only one of them.However,there are cases when the visit in a village forces the visitor to visit other villages among X1,X2,X3,X4,X5X_1,X_2,X_3,X_4,X_5.Each tourist visits only the village he has chosen and the villages he is forced to.If X1,X2,X3,X4,X5X_1,X_2,X_3,X_4,X_5 are totally visited by 40,60,65,70,7540,60,65,70,75 tourists respectively,then find how many tourists had chosen each one of them and determine all the ordered pairs (Xi,Xj):i,j∈{1,2,3,4,5}(X_i,X_j):i,j\in \{1,2,3,4,5\} which are such that,the visit in XiX_i forces the visitor to visit XjX_j as well.
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