The Magic of Logic (6)
Marco is a soccer star. He played in one of the top clubs in the country and in the German national team. Now, at 50, he is often on TV and active in the organisation and promotion of football.
Marco is also a chess player, hobby level. He is very keen to promote the game, especially amongst children, and has helped organise a major initiative for chess in schools. Here is an inspiring video of a thousand students from 73 school classes playing chess on the town square. The video is in German, but even if you don’t speak the language, it is inspiring to watch.
My company, too, has joined the initiative and we have reached thousands of young school children, encouraging them to take up chess. For our part we supply a software program, Fritz & Chesster. Any child, six years or older, can use it to learn chess, without a chess teacher (who is not always available). It is estimated that in the last twelve years we have generated 1½ million new chess players with that program, just counting the number of children that have learnt the game from legal copies of our software. It is my goal to find a way to make it available to any child world-wide, free, and with a single click. Here’s my plan in case you are interested.
A few days ago we had a Christmas dinner at ChessBase, with our staff, press, dignitaries, personalities. Marco was a guest, and I watched him playing against someone from our company. Not bad at all — he actually had a better position against a fairly strong player.
Well, I got into chatting with Marco during dinner and asked him about his other interests in life. Apart from football and chess, turns out he is passionately interested in (would you believe it?) logic! Extraordinary. I told him about my own activities, how I am doing logic courses at a local school. I also mentioned that some of the students wanted to attend my classes again next year, which is quite inconvenient for me. It means I have to find new puzzles and problems. “Don’t worry, Frederic,” Marco said, “I have a hundred in my head for you.” Really? I asked for a sample, which he gladly gave:
“You have two ropes which each burn from one end to the other in 60 minutes — but not at a constant rate. If you cut a rope in half, then one half may burn faster than the other. All we know is that the total burning time for each rope is 60 minutes. How can you use the ropes to measure 45 minutes?”
Perfect, I said, exactly the kind of puzzles I am looking for. They must not be full of complicated mathematics — I am often working with children who are six and seven years old, and it is logical thinking that I am trying to teach them. I tried Marco’s problem on the usual suspects: my grandchildren Enders and Hennes. Enders, 7, is very good at these kinds of puzzles, having practised with me for two years now. But he was stumped. He said he was going to try to solve it, over Christmas, all by himself. I am pretty sure he will — and he’ll be pleased as Punch if he succeeds.
December 26: Yesterday was Boxing Day, where our families exchange gifts and spend the afternoon together. Enders was disappointed that he was not able to bring his special gift for me: the solution to the rope problem. “I only figured out how to measure half an hour, but 45 minutes…?!” he began, and then suddenly exclaimed: “Hey, I have it!!” He gave me the correct solution with absolute certainty — and that wonderful look of pleasure on his face.
A few days later, at his eighth birthday party, Enders gave the puzzle to his friends Mina and Enna, twins, both his age. Like him they could not solve it immediately, and so he has given them four days to work on it. That’s how long it took him.
I am not going to tell you the solution. Just think for a while — and give it to your family and your children to solve. Starting from six years it should be possible. Wait, let me change my mind: if you cannot for the life of you figure it out, and haven’t googled it already, here is the solution, explained step by step. It is really neat and simple.