Puzzle Diary

Gréta Tóth

Friday, 5 March 2021 – 5 p.m.

Today was the most interesting day at university. One of my students finally interrupted my lesson with an amazing question! Don’t get me wrong, I love teaching mathematics to university students, but in the past few years I felt as if I were giving lectures in kindergarten. At first, I always believed that at some point someone was going to raise their hand and ask something crucial about the proofs or the new theorems or about a practice exercise. After months, no, years of waiting I simply lost my faith in this generation. Apart from the cliché topics like: when are they going to write the exams or is it possible to reschedule, I never heard anything worth responding to.

The last time one of my students asked me something was around 1992. I remember that whole class just as if it were yesterday: the topic was statistics with a class of future economists, about a hundred of them in the second-largest auditorium on campus. There was this one student, Adam; he got a scholarship after high school and proceeded to keep up the good work during college as well. He passed all his exams with the best grades, but when statistics came around in his fifth semester, he miserably failed the exam twice. Before retaking it for the third time, he asked me why he always got a different result in every problem during practice, and it turned out that the battery of his calculator had been running out for the past couple of weeks and certain buttons simply refused to function.

But today, during my third lecture (by the time I was tempted to just give my students a whole page of exercises to work on by themselves), someone raised their hand, and I was beyond shocked when the girl started explaining a strange puzzle that she had found online the other day. It went somehow like this:

Suppose there are four people trying to cross a rather dodgy rope bridge in the middle of the night.

Only two of them can cross it any one time, and they only have a single flashlight between them. For this reason, one person of each pair must return to help the others get across.

But time is limited; they are being chased and need to get across within 17 minutes total. Sounds simple enough, except each person can only cross the bridge at a certain rate.

One person takes 1 minute to cross the bridge. The second takes 2 minutes, the third 5 and the last person 10 minutes.

Each pair can only cross as fast as the slowest member of the pair. How can they all cross the bridge in time?”

I decided that it might interest other students as well, so we went through the text together multiple times and started debating and trying to crack this brain-teasing riddle. Eventually, the lecture ended and no one could come up with a solution, so it made me even more curious. On my way home, I couldn’t stop thinking about it, and I was eager to get home and set myself to work. I will update as soon as I finally solve this mystery; this sounds like an amazing way to spend my otherwise lonely weekend!

Saturday, 6 March 2021 – 6 a.m.

This puzzle is probably the trickiest one that I have ever seen. I almost stayed up all night trying to find a possible solution. Even the odds seem promising: as far as I was not mistaken last night, there are about 14 arrangements. I have already excluded 7, so I will probably be done by noon.

Saturday, 6 March 2021 – 1 p.m.

All the calculations are done, but I still wasn’t able to find a solution. At this point, I am considering if this puzzle is really possible or not. If so, I need to prove the opposite. Either way, I need to hurry; I’m having dinner with my mother at six.

Saturday, 6 March 2021 – 5 p.m.

Still nothing, though I feel like I’m on the verge of cracking it. Fingers crossed!

Saturday, 6 March 2021 – 6:15 p.m.

I canceled dinner with my mother. I couldn’t possibly have a normal conversation while the only thing I’m seeing is bridges and people. As far as I can remember, I am on my fourth cup of coffee today, but I need every cell in my brain to focus.

Sunday, 7 March 2021 – 4 a.m.

I am questioning everything. The puzzle? Well, that too, but mainly my job as a university professor. I am highly considering my retirement after this weekend, since this puzzle was totally made for elementary school students. Truth is, I always thought that there was a problem with this generation, but now I am convinced that it might just be me. Afterall, everyone in that class has probably solved it by now. And me? Well I am sitting in the middle of my living room, on the same spot where I have been sitting for at least six hours by now. All I did this weekend was procrastinate over a puzzle given by one of my students, while I had tons of assignments to correct. I think I should quit.

Monday, 8 March 2021 – 9 a.m.

UNBELIEVABLE!!! Today started off as a usual Monday, except that I was determined to quit everything or at least skip university for a week. I decided that the first option would be it, so I got ready to visit campus and hand in my retirement application. I was already on the bus, when a family of four wanted to get on the vehicle. They had huge suitcases and bags, and while the mother helped the children, the father loaded the packages into the already crowded bus. He moved fast, climbing the small stairs up and down, just like one would the bridge from the puzzle. And it all hit me; I did  recalculations again and again, searching for the mistake, but there wasn’t any. I got 17 minutes. During my first lecture with the same class, I presented my solution and it was in fact 17 again. Maybe a key to a puzzle like this is to take a step back and observe it before jumping to conclusions.