Last week, we published a transcript of one of Walter Benjamin’s radio broadcasts for children from 1932. It had thirty brainteasers in it. Here are the answers:

1. His equal.
2. If the barber were serious about his offer, he wouldn’t have made a permanent sign out of enamel, because “tomorrow,” when shaves are free, will never come.
3. The two rings are of equal width.

4. The pendulum passes through the middle twenty times.

5. The man was born on February 29.

6. Calculate: 999+1=1,000; 998+2=1,000; 997+3=1,000; there are 500 such pairs. Then all that’s left is 1,000 at the high end, and 0 at the low end; so adding 1,000 to 500,000 gives a total of 501,000. Using the same method, the numbers from 1 to 10 add up to 60. [Benjamin has made a mistake here. There are only 499 number pairs adding up to 1,000, giving a subtotal of 499,000. Adding the two remaining numbers, 1,000 and 500, gives a correct total of 500,500. Correspondingly, the sum of the numbers between 1 and 10 is 55. Benjamin’s mistake was corrected in a later broadcast.]
7. Three colors are needed: one for the country in the middle, one for the two countries above and below the one in the middle, and a third color for the two countries to the left and the right of the one in the middle.
8. Hay.
9. 99 9/9.
10. B.
11. The flower that was not there overnight is the one with no dew on it.
12. The bookworm needs only a moment to get from the first page of the first book to the last page of the second, because in a properly arranged library, the first page of the first book is right up against the last page of the second.
13. Inserting the letters “du” into the middle of the German word for “money” [Geld] spells the German word for “patience” [Geduld]. 14. The first piece of cake, which he did not pay for, does not belong to him, so he should neither eat it nor exchange it for the second piece.
14. His equal.

And here’s the list of fifteen mistakes:

1. Heinz realizes that summer daylight saving has just begun and sets his watch back one hour. He should set it one hour forward.
2. If the barbershop is just around the corner and it would take him as long as three minutes to get there, it would be impossible for him to see it.
3. If Heinz is cut on his right side, the wound will be on the left side of his reflection.
4. Nineteen marks cannot be disbursed in five-mark notes.
5. Five groschen and twenty five-pfennig coins equals 1.50 marks. Heinz should have received only ninety pfennig in addition to the nineteen marks, because he gave the barber twenty marks for a shave that cost ten pfennig. [There were ten pfennig in one groschen, and 100 pfennig in one mark.]
6. If the barber, the pharmacist’s twin brother, is a young man, then the pharmacist cannot be an old man.
7. A window cannot be closed from the outside.
8. Even if he is dead, a man has only one skull, not two.
9. One could not yet take photographs in the time of Frederick the Great.
10. A bladeless knife missing its handle is simply not there.
11. Someone with a corner seat cannot have neighbors to the right and the left.
12. If Anton’s housekeeper is deaf and alone in the apartment, she wouldn’t know to open the door after Heinz rings the bell.
13. If someone lives on the sixth floor, a two-story building cannot block his view and he cannot see the faces of passersby.
14. If the train station clock reads 14:00, it’s 2 pm, not 4 pm.
15. The crescent of a waxing moon looks like the start of a German uppercase “A,” not “Z.”

Did you get all of them? Good on you! Pat yourself on the back—you’ve successfully passed a test designed for the German children of the 1930s!

These riddles appears in Radio Benjamin, available now. Reprinted with the permission of Verso Books.