## 16. Pre-Election Discussion

Before the election to the legislative assembly, three brothers had a long discussion, which they concluded with the following rather complicated statements.

P i e r r e. If Jean votes for Dubois, I will vote for Dupont. But if he votes for Durand, I will vote for Dubois. On the other hand, if Jacques votes for Dupont, I will vote for Durand.

J e a n. If Pierre votes for Durand, I will not vote for Dupont. But if Jacques votes for Dubois, I will vote for Dupont.

J a c q u e s. If Pierre votes for Dupont, I will not vote for Durand.

Election day arrived. All three brothers voted for different candidates. For whom exactly?
16. Since all three brothers voted for different candidates, there are six possibilities:
1) Pierre - for Dupont; Jacques - for Dubois, Jean - for Durand
2) Pierre - for Dupont, Jacques - for Durand, Jean - for Dubois
3) Pierre - for Durand, Jacques - for Dupont, Jean - for Dubois;
4) Pierre - for Durand, Jacques - for Dubois, Jean - for Dupont
5) Pierre - for Dubois, Jacques - for Durand, Jean - for Dupont
6) Pierre - for Dubois, Jacques - for Dupont, Jean - for Durand.

However, during the discussion, six conditions were put forward. It is clear that the first condition rules out possibility 3, the second condition rules out possibility 1, the third condition rules out possibility 6, the fourth condition rules out possibility 4, the fifth condition again rules out possibility 1, and finally, the sixth condition rules out possibility 2. Therefore, only the fifth possibility remains.

130

Thus, Pierre voted for Dubois, Jacques - for Durand, and Jean - for Dupont.