booklet - CUMC - Canadian Mathematical Society

3. The Dane drinks tea.4. The green house is on the left of the white house (next to it).5. The green house owner drinks coffee.6. The person who smokes Pall Mall rears birds.7. The owner of the yellow house smokes Dunhill.8. The man living in the house right in the center drinks milk.9. The Norwegian lives in the first house.10. The man who smokes blend lives next to the one who keeps cats.11. The man who keeps horses lives next to the man who smokes Dunhill.12. The owner who smokes Blue Master drinks beer.13. The German smokes Prince.14. The Norwegian lives next to the blue house.15. The man who smokes blend has a neighbour who drinks water.Who keeps fish?3.8.2 A fixed point problemLet f : R → R be a continuous function such that f ◦ f has a fixed point. Prove that f hasalso a fixed point.3.8.3 An infinite problemImagine an infinite chessboard that contains a positive integer in each square. If thevalue of each square is equal to the average of its four neighbours to the north, south,west and east, prove that the values in all the squares are equal.3.8.4 A monk puzzle300 monks live together in a monastery. They have very strict rules which are followedby all of the monks at all times. One of the rules is that absolutely no communicationbetween monks is allowed. Another is, that they refuse to look at themselves. Themonks have breakfast all together in a large hall where they see each other.One morning, a letter arrives to the monastery and is read by all monks at breakfast.It tells them that the monastery has been hit by a malediction. Some of the monks willhave a disease which is not contagious. The unique symptom of the disease is a largered spot on the forehead of the afflicted. In order to save the monastery from doom, theafflicted monks must quit the monastery.Only on the morning of the eleventh day after the letter arrives, all afflicted monksand only them don’t show up for breakfast; they have left the monastery during thepreceeding night.How many monks quit?52