Logical Puzzles

August 2020. The spaceship landed. “Earth!” they shouted. They knew that earthlings are divided into three groups: those who always tell the truth, those who always lie, and those who do both, alternating between true and false statements, starting with either. “Let’s go!” said the captain. The aliens approached three earthlings, who each were from a different group, and asked, “Who won the last World Cup? Who came in second? Who came in third?” One of them responded, “Zaire first. Uruguay second. Spain third.” Another one said, “Zaire first. Spain second. Uruguay third.” The third one said, “Uruguay first. Spain second. Zaire third.” The aliens returned to their spaceship and flew back to where they came from. Do you know which response was the true ranking in the World Cup? (see [2] and [1]).

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Suppose you are visiting a forest in which every inhabitant is either a knight or a knave. Knights always tell the truth and knaves always lie. In addition some of the inhabitants are werewolves and have the annoying habit of sometimes turning into wolves at night and devouring people. A werewolf can be either a knight or a knave.

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A prisoner is faced with a decision where he must open one of nine doors. The rooms behind each door may be empty or contain either a lady or a tiger. If the prisoner opens a door and finds a lady he will marry her and if he opens a door and finds a tiger he will be eaten alive.

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In this puzzle a prisoner is faced with a decision where he must open one of two doors. Behind each door there either is a lady or a tiger. There might be two tigers, two ladies or one of each. If the prisoner opens a door and finds a lady he will marry her and if he opens a door and finds a tiger he will be eaten alive. Of course, the prisoner would prefer to be married than eaten alive. Each of the doors has a sign bearing a statement that may be either true or false.

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“Last week my friends Anne, Carl, Eva, Gustaf and I went out for dinner every night, Monday to Friday. I missed the meal on Friday because I was visiting my sister and her friends. But otherwise, every one of us had selected a restaurant for a particular night and served as a host for that dinner. Overall, the following restaurants were selected: a French bistro, a sushi bar, a pizzeria, A Greek restaurant, and the Brauhaus. Eva took us out on Wednesday. The Friday dinner was at the Brauhaus. Carl, who doesn’t eat sushi, was the first host. Gustaf had selected the bistro for the night before one of the friends took everyone to the pizzeria. Tell me, who selected which restaurant for which night?”. This puzzle has been published in [1] p. 56.

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The six following persons arrived first at the marathon of New York, but we do not know their rankings. However, we have the following additional information:

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Downs, Heath, Field, Forest, and Marsh – five elderly pigeon fanciers – were worried by the depredations of marauding cats owned by five not less elderly ladies. Hoping to get control of the cats, they married the cat owners.

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Mr. Greenfan wants to give a dress party where all male guests are obliged wear green clothing. The following rules are imposed for every male guest:

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