The Magic of Logic (10)
Teaching children the joys of thinking — quick puzzles for kids
Recently during a walk we met a young lady with a cute 1½-year-old child. “Is it a boy or a girl,” I asked? “A boy,” she replied. Afterwards I asked our grandsons Enders and Hennes: what could the lady have replied? She had three possible truthful answers!
This they could not say: “Boy,” “girl,” and “I don’t know”? But the last is hardly plausible. They thought about it for a good period of time, but could not come up with a reasonable third reply. So I told them the solution: the third possible answer was “Yes.” Enders, 8½, got it at once, and was delighted. He explained it to his brother, 7: yes, it is really either a boy or a girl! That’s logical.
So they got another puzzle: Two logicians sit down in a cafeteria. The waitress comes up and asks: “Do both of you want coffee?” The first logician replies “I don’t know.” The second says “Yes”. What does this mean, and what do they want?
This was a tough one, and took Enders half an hour to work out. He had to deduce that the first logician wanted coffee, but he did not know what his friend wanted. The second logician wanted coffee, and knew that if his friend didn’t want one he would have answered the waitress’s question with “no” because at least one of the two, he himself, didn’t want coffee.
Not a trivially easy puzzle for young children. Hennes protested that the question “do both of you want coffee” is the same as asking each person if he wanted coffee. So the second logician was merely saying yes he wanted a coffee. But then, said Enders, why did the first logician say “I don’t know” instead of yes or no. It’s wonderful to watch these kids discuss logic at this early age.
The next puzzle they got, a few days later, was a classic from my childhood. A man looks at a picture and says: “Brothers and sisters I have none, but this man’s father is my father’s son.” Who was the person in the picture?
This was unusually difficult, and even the virtuoso problem-solver Enders struggled for quite a while, and then solved it. His younger brother didn’t — he said the picture had to be one of the man himself. That is the answer many people will give. So I helped Hennes: what does “my father’s son” mean? That is the man himself. So “this man’s father is my father’s son” is the same as “This man’s father is me!” And that in turn means it is a picture of his son. The seven-year-old understood clearly.
Some more? A group of boys are walking along a path. One says: “There are two boys ahead of me,” another boy says: “There are two boys behind me,” and a third boy says: “I am exactly in the middle.” What is the smallest number of boys on the path. “Five” both Enders and Hennes said. Then after a few minutes — it is remarkable how he keeps thinking even after he has “solved” a puzzle — Enders said: “No, wait, just three boys!” And that is of course the correct answer.
That was a very easy puzzle, but try it even on grown-ups: you will often hear the answer five. There are thought patterns that lead us to such false conclusions. Like with this puzzle I tried on the kids: you are running in a race, and you manage to overtake the runner who is in second place. In what place are you now? In first place, both the boys said, until after a minute they switched to the correct answer: second place, of course. Big smiles.
Another sneaky question: I give of you 100 Euros, which you divide between yourselves, so each of you have fifty Euros. But then you decide that Enders, who is older, should have ten Euros more than you, Hennes. So how much should you give him? Ten Euros, Hennes said. That was so easy. But Enders immediately corrected him: No, Hennes, just think about it. Then I would have sixty Euros and you would have forty left. So I would have twenty more. Hennes got it and gave me the correct answer: I give him five Euros and now he has ten more than me.
Socks: you have ten pairs of socks, five blue and five red, all tossed together in a drawer. You go into the dark room at night and, without switching on the light, take some socks out of the drawer. How many must you take to make sure you will have a matching pair? This they got after a short think: Three, of course, because there are only two colours and so at least two must be the same. Now, these days it is fashionable for kids to wear non-matching socks. How many must you take to make sure you will have a non-matching pair? And finally: say you want a matching pair of blue socks. They got the answers at once.
Another little trick question: Two trains depart from Hamburg and Munich. The cities are eight hundred kilometres apart, and the journey takes the trains, which travel at the same speed, exactly six hours. But the train from Munich starts one hour earlier than the one that leaves Hamburg. Which train will be closer to Hamburg when they pass each other?
Gotcha! All the details about distance, time and speed were only given to distract. Like the bus driver problem I have pulled on so many kids. Try it on your own brood:
You are a bus driver and come to the first stop with the bus still empty. Seven people get in. At the second stop five people get out and nine get in. At the third stop nobody gets out and ten people get in. So: what is the name of the bus driver?
You will be amazed.