A Crazy Mixed-Up Day: Thirty Brainteasers


Arts & Culture

Walter Benjamin credit Doyle Saylor

Image: Doyle Saylor

From 1927 to early 1933, Walter Benjamin wrote and delivered some eighty to ninety broadcasts over the new medium of German radio, working between Radio Berlin and Radio Frankfurt. These broadcasts, many of them produced under the auspices of programming for children, cover a fascinating array of topics: typologies and archaeologies of a rapidly changing Berlin; scenes from the shifting terrain of childhood and its construction; exemplary cases of trickery, swindle, and fraud that play on the uncertain lines between truth and falsehood; catastrophic events such as the eruption of Vesuvius and the flooding of the Mississippi River, and much more. Now the transcripts of many of these broadcasts are available for the first time in English—Lecia Rosenthal has gathered them in a new book, Radio Benjamin. Below is one of his broadcasts for children, including thirty brainteasers. (Want the answers? They’re here.)

Perhaps you know a long poem that begins like this:

Dark it is, the moon shines bright,
a car creeps by at the speed of light
and slowly rounds the round corner.
People standing sit inside,
immersed they are in silent chatter,
while a shot-dead hare

skates by on a sandbank there.

Everyone can see that this poem doesn’t add up. In the story you’ll hear today, quite a few things don’t add up either, but I doubt that everyone will notice. Or rather, each of you will find a few mistakes—and when you find one, you can make a dash on a piece of paper with your pencil. And here’s a hint: if you mark all the mistakes in the story, you’ll have a total of fifteen dashes. But if you find only five or six, that’s perfectly alright as well.

But that’s only one facet of the story you’ll hear today. Besides these fifteen mistakes, it also contains fifteen questions. And while the mistakes creep up on you, quiet as a mouse, so no one notices them, the questions, on the other hand, will be announced with a loud gong. Each correct answer to a question gives you two points, because many of the questions are more difficult to answer than the mistakes are to find. So, with a total of fifteen questions, if you know the answers to all of them, you’ll have thirty dashes. Added to the fifteen dashes for mistakes, that makes a total of forty-five possible dashes. None of you will get all forty-five, but that’s not necessary. Even ten points would be a respectable score.

You can mark your points yourselves. During the next Youth Hour, the radio will announce the mistakes along with the answers to the questions, so you can see whether your thoughts were on target, for above all, this story requires thinking. There are no questions and no mistakes that can’t be managed with a little reflection.

One last bit of advice: don’t focus on just the questions. To the contrary, keep a lookout for the mistakes above all; the questions will all be repeated at the end of the story. It goes without saying that the questions don’t contain any mistakes; there, everything is as it should be. Now pay attention. Here’s Heinz with his story.


Radio Benjamin_RGBWhat a day! It all started early this morning—I had hardly slept a wink, because I couldn’t stop thinking about a riddle—anyway, the doorbell rang early. I opened the door and there was my friend Anton’s deaf housekeeper. She handed me a letter from Anton.

“Dear Heinz,” writes Anton, “yesterday, while I was at your house, I left my hat hanging by the door. Please give it to my housekeeper. Best regards, Anton.” But the letter continues. Below he writes: “I just now found the hat. Forgive the disturbance. Many thanks for your trouble.”

That’s Anton for you, the absent-minded professor type. By the same token, he’s also a great fan and solver of riddles. And when I looked at the letter, it occurred to me: I could use Anton today. Perhaps he knows the solution to my riddle; I made a bet that I would figure out the riddle by this morning. The riddle goes like this (Gong):

The peasant sees it often, the king only seldom, and God never at all. What is it?

Yes, that’s it, I thought to myself, I have to ask Anton. I was hoping to ask his housekeeper whether he was already at school—Anton is a teacher—but she had already left.

I thought to myself, Anton must be at school. I put on my hat and just as I was heading down the stairs, it occurred to me that summer daylight saving time began today, so everything starts an hour earlier. I pulled out my watch and set it back one hour. When I reached the street, I realized that I had forgotten to shave. Just around the corner to the left I saw a barbershop. In three minutes I was there. In the window hung a large enamel sign: “A shave today ten pfennigs, a shave tomorrow free.” (Gong): A shave today ten pfennigs, a shave tomorrow free. The sign struck me as odd. I wish I knew why. I went in, took a seat and got a shave, all the while looking in the large mirror hanging before me. Suddenly the barber nicked me, on my right cheek. And sure enough, blood appeared on the right side of my mirror image. The shave cost me ten pfennigs. I paid with a twenty-mark note and got back nineteen marks in five-mark coins, along with five groschen and twenty five-pfennig coins. Then the barber, a jolly young man, held open the door and said to me as I went out: “Say hello to Richard if you see him.” Richard is his twin brother who has a pharmacy on the main square.

Now I’m thinking: the best thing is to go straight to Anton’s school and see if I can’t track him down. On my way there, walking down a street, I saw a large crowd of people standing around a carnival magician performing his tricks. With chalk he drew a tiny circle on the sidewalk. He then said: “Using the same center point, I will draw another circle whose circumference is five centimeters greater than the first.” After doing so he stood up, looked around with a mysterious smile and said (Gong): “If I now draw a gigantic circle, let’s say as big as the circumference of the Earth, and then I draw a second one whose circumference is five centimeters greater than that of the giant circle, which ring is wider: the one that lies between the tiny circle and the one five centimeters larger, or the ring between the giant circle and the one five centimeters larger?” Yes, I would like to know this, too.

I’d finally managed to push my way through the crowd, when I noticed that my cheek still hadn’t stopped bleeding, and as I was on the main square, I went into the pharmacy to buy a bandage. “Greetings from your twin brother, the barber,” I said to the pharmacist. He’s old as the hills and a bit of an odd bird to boot. And more than anything, he’s terribly anxious. Whenever he leaves his ground-floor shop, not only does he double-lock the door, he also walks around the whole building, and if he sees he’s left a window open somewhere, he reaches inside to close it. But the most interesting thing about him is his collection of curiosities, which he’ll show to anyone who comes into his shop. Today was no exception and, before long, I was left to admire everything at my leisure. There was a skull of an African Negro when he was six years old, and next to it a skull of the same man when he was sixty. The second was much larger, of course. Then there was a photograph of Frederick the Great, playing with his two greyhounds at Sanssouci. Next to it lay a bladeless antique knife that was missing its handle. He also had a stuffed flying fish. And hanging on the wall was a large pendulum clock. As I paid for my bandage, the pharmacist asked (Gong): “If the pendulum on my clock swings ten times to the right and ten times to the left, how often does it pass through the middle?” This, too, I wanted to know. So, that was the pharmacist.

Now I needed to hurry if I wanted to make it to the school before lessons were over. I jumped onto the next streetcar and just managed to get a corner seat. A fat man was seated to my right and on my left was a small woman talking to the man across from her about her uncle (Gong): “My uncle,” she said, “has just turned one hundred years old, but has only had twenty-five birthdays. How can that be?” This, too, I wanted to know, but we had already reached the school. I went through all the classrooms looking for Anton. The teachers were very annoyed at being disturbed.

And they asked the oddest questions. For example, I walked into a math class where the teacher was getting cross with a young boy. He had not been paying attention and the teacher was going to punish him. He said to the boy (Gong): “Add up all the numbers from one to a thousand.” The teacher was more than a little surprised when, after a minute, the boy stood up and gave the right answer: 501,000. How was he able to calculate so fast? This I also wanted to know. First I tried it with just the numbers one through ten. Once I came upon the quickest way to do this, I had figured out the boy’s trick.

Another class was geography. (Gong): The teacher drew a square on the blackboard. In the middle of this square he drew a smaller square. He then drew four lines, each connecting one corner of the small square with the nearest corner of the large square.This resulted in five shapes: one in the middle, this was the small square, and four other shapes surrounding the small square. Every boy had to draw this diagram in his notebook. The diagram represented five countries. Now the teacher wanted to know how many different colors were needed so that each country was a different color than the three, or four, countries that it bordered. I thought to myself, five countries need five colors. But I was wrong, the answer was smaller than five. Why? This, too, I wanted to know.

I then entered another class, where students were learning to spell. The teacher was asking very strange things, for example (Gong): “How do you spell dry grass with three letters?” And (Gong): “How can you write one hundred using only four nines?” And (Gong): “In your ABC’s, which is the middlemost letter?” To conclude the lesson he told the children a fairy tale (Gong):

“An evil sorcerer transformed three princesses into three flowers, perfectly identical and planted in a field. Once a month, one of them was allowed to return to her house for the night as a human. On one of these occasions, one of the princesses said to her husband just as dawn broke and she had to return to her two friends in the field and become a flower again: ‘If you come to me this morning and pluck me, I will be redeemed and can stay with you for evermore.’ This came to pass. Now the question is, how did her husband recognize her, since the flowers looked identical?” This, too, I wanted to know, but it was high time for me to get hold of Anton, and because he wasn’t at school, I headed to his home.


Benjamin in 1928.

Anton lived not far away, on the sixth floor of a building on Kramgasse. I climbed the stairs and rang the bell. His housekeeper, who had been at my house in the morning, answered right away and let me in. But she was alone in the apartment: “Herr Anton is not here,” she said. This irritated me. I thought the smartest thing to do was to wait for him, so I went into his room. He had a gorgeous view onto the street. The only hindrance was a two-story building across the way, which obstructed the view. But you could clearly see the faces of passersby, and on looking up, you could see birds fluttering about in the trees. Looming nearby was the large train station clock tower. The clock read exactly 14:00. I pulled out my pocket watch for comparison and sure enough, it was 4 pm on the nose. I had waited for three hours when, out of boredom, I started browsing the books in Anton’s room. (Gong) Unfortunately a bookworm had gotten into his library. Every day it ate through one volume. It was now on the first page of the first volume of Grimm’s Fairy Tales. I thought to myself, how long will it need to reach the last page of the second volume of Grimm’s Fairy Tales? I wasn’t concerned about the covers, just the pages. Yes, this is something I wanted to know. I heard voices outside in the hallway.

The housekeeper was standing there with an errand boy, who had been sent by the tailor to collect money for a suit. (Gong) Because the errand boy knew the housekeeper was deaf, he had handed her a piece of paper with one word written on it in large capital letters: MONEY [GELD]. But the housekeeper had no money with her, so to convey her request that he be patient, she drew just two more letters on the piece of paper. What were these two letters?

I had had enough of waiting. I headed out to find a little something to eat after such a tedious day. As I reached the street the moon was already in the sky. There had been a new moon a few days prior, and by now it had waxed to a narrow crescent that looked like the beginning of a capital German “Z” hovering over the rooftops. In front of me was a small pastry shop. I went in and ordered an apple cake with whipped cream. (Gong): When the apple cake with whipped cream arrived, it didn’t appeal to me. I told the waiter I would prefer a Moor’s Head [i.e., a mallomar]. He brought me the Moor’s Head, which was delicious. I stood up to go. As I was just on my way out, the waiter ran after me, shouting: You didn’t pay for your Moor’s Head!—But I gave you the apple cake in exchange, I told him.—But you didn’t pay for that either, the waiter said.—Sure, but I didn’t eat it either! I retorted, and left. Was I right? This, too, I’d like to know.

As I arrived home, imagine my astonishment at seeing Anton, who had been waiting there for five hours. He wanted to apologize for the silly letter he had sent to me early this morning via his housekeeper. I said that it didn’t matter all that much, and then told Anton my whole day as I’ve just told it to you now. He couldn’t stop shaking his head. When my story was over he was so astounded that he was speechless. He then left, still shaking his head. As he disappeared around the corner, I suddenly realized: this time he really has forgotten his hat. And I—of course I had forgotten something as well: to ask him the answer to my riddle (Gong): The peasant sees it often, the king only seldom, and God never at all.

But perhaps you’ve found the answer by now. And with this, I say goodbye.


Repetition of the fifteen questions:

  1. The first question is an old German folk riddle: The peasant sees it often, the king only seldom, and God never at all. What is it?

  2. What’s fishy about a barber who hangs an enamel sign in his window reading, “A shave today ten pfennigs, a shave tomorrow free”?
  3. If I have a small circle and then around its center point I draw a circle whose circumference is five centimeters greater than that of the original, this creates a ring between the two circles. If I then take a giant circle, one as big as the circumference of the Earth, and around the same center point I draw another one, whose circumference is five centimeters greater than that of the first giant one, there is then a ring between those two circles. Which of the two rings is wider, the first or the second?
  4. If the clock pendulum swings ten times to the right and ten times to the left, how often does it pass through the middle?

  5. How can a man who is a hundred years old have had only twenty-five birthdays?
  6. What is the quickest way to add up all the numbers from one to 1,000? Try it first with the numbers from one to ten.

  7. A country is surrounded by four other countries, each of which borders the middle country and two of the others. What is the fewest number of colors needed so that each country has a different color than its neighbors?
  8. How do you spell dry grass with three letters?
  9. How can you write 100 using only four nines?

  10. In your ABC’s, which is the middlemost letter?

  11. There are three identical flowers in a field. In the morning, how can you tell which of them has not been there overnight?

  12. If each day a bookworm eats through one volume in a series of books, how long will it take for it to eat its way from the first page of one volume to the last page of the next, provided he eats in the same direction in which the series of books is arranged?

  13. You have a piece of paper with the word money [Geld] written on it. Which two letters can you add to convey a request for patience [Geduld]?

  14. What’s wrong with the logic of a man who orders a piece of cake, exchanges it for another once it arrives, and then won’t pay for the new piece because he claims he traded the old piece for it?

  15. The old riddle once more, whose solution is worth four points because it has now appeared twice: The peasant sees it often, the king only seldom, and God never at all.

You can find the answers to these fifteen questions, as well as a list of the fifteen mistakes, here.

Translated from German by Jonathan Lutes. Broadcast on Southwest German Radio, Frankfurt, probably on July 6, 1932. The Südwestdeutsche Rundfunk-Zeitung announced for the Youth Hour on July 6, 1932, at 3:15 pm, “‘Denksport’ [Mental Exercise], by Dr. Walter Benjamin (for children ten years and older).” “A Crazy Mixed-Up Day” was most likely the text Benjamin prepared for this broadcast.

This transcript appears in Radio Benjamin, available now. Reprinted with the permission of Verso Books.

Walter Benjamin (1892–1940) was a German Jewish Marxist literary critic, essayist, translator, and philosopher. He was at times associated with the Frankfurt School of critical theory and is the author of Illuminations, The Arcades Project, and The Origin of German Tragic Drama.