## Linguistics Puzzles

I have an old book which I value a great deal. The book is called *200 Problems in Linguistics and Mathematics* and only 1,550 copies were printed in 1972. Luckily, a new extended edition just appeared on the web. Both editions are in Russian, so I decided to translate some of the problems into English. Here is a sample:

**Problem 1.** Here are phrases in Swahili with their English translations:

- atakupenda — He will love you.
- nitawapiga — I will beat them.
- atatupenda — He will love us.
- anakupiga — He beats you.
- nitampenda — I will love him.
- unawasumbua — You annoy them.

Translate the following into Swahili:

- You will love them.
- I annoy him.

**Problem 2.** You are given words in Swahili: mtu, mbuzi, jito, mgeni, jitu and kibuzi. Their translations in a different order are: giant, little goat, guest, goat, person and large river. Make the correspondence.

**Problem 3. **In Russian the middle name is the patronymic. Thus, the middle initial is the first letter of the father’s first name. And, as in many languages, the first initial is the first letter of the first name. Here are names of males in a family:

- A.N. Petrov
- B.M. Petrov
- G.K. Petrov
- K.M. Petrov
- K.T. Petrov
- M.M. Petrov
- M.N. Petrov
- N.M. Petrov
- N.K. Petrov
- N.T. Petrov
- T.M. Petrov

Draw the family tree of the Petrovs, given that every father has two sons, the patriarch of the family has four grandsons, and his sons have two grandsons each. Prove that the solution is unique.

**Problem 4.** In Latvian a noun can be one of two genders; furthermore, adjectives agree with nouns in gender, number and case. You are given phrases in either the nominative or the genitive case with their translations:

- silts ezers — warm lake
- melns lauva — black lion
- liela krāsns — big oven
- lielas jūras — big sea’s
- sarkana ezera — red lake’s
- melna kafija — black coffee
- sarkans putns — red bird
- liela kalna — big mountain’s
- sarkanas lapas — red leaf’s
- sarkana pils — red castle
- liels ezers — big lake
- melna putna — black bird’s
- liela lauvas — big lion’s
- silta jūra — warm sea
- melnas kafijas — black coffee’s
- liels kalns — big mountain

Indicate which words are nouns and which are adjectives. Divide Latvian nouns into two groups, so that each group contains words of the same gender.

**Problem 5.** The Portuguese language takes its roots from Latin. In this problem modern Portuguese words are written on the left and their roots (in Latin and other languages on the right). All the words on the left belong to one of three classes: ancient borrowing, early borrowing and late borrowing.

- chegar — plicare
- praino — plaine
- plátano — platanum
- chão — planum
- plebe — plebem
- cheio — plenum
- prancha — planche

For every Portuguese word, indicate which class it belongs to. (Note that in Portuguese “ch” is pronounced as “sh”.)

Share:
## Alex S:

Are the answers to Problem 1: “Utawapenda” and “Ninamsumbua” respectively?

20 February 2009, 1:39 am## Math Teachers at Play #1 « Let’s Play Math!:

[…] Khovanova offers a treat at her Math Blog: Five Linguistics Puzzles translated from the Russian book 200 Problems in Linguistics and […]

20 February 2009, 4:20 am## Language Puzzles « 360:

[…] Khovanova posted this past Thursday on Lingustic Puzzles. In it, she included five puzzles she’d tranlsated from the Russian book 200 Problems in […]

22 February 2009, 5:51 pm## patientia:

Makes me want to learn Russian.

23 February 2009, 3:46 pm## James S:

Alex S: Those are the answers I got, too; but I can’t be certain there’s not another way to do it.

23 February 2009, 7:44 pm## Xi_Heather:

Thanks for sharing these — they’re really neat!

Just to double check (because I gave these to one of my math classes) — in Problem 4, is there any chance that the word “melns” with black lion is really supposed to be “melnas”?

25 February 2009, 10:13 am## Tanya Khovanova:

The answer to problem 4 is: krasns, jura, lapas, kafija, pils are gender 1 and ezers, kalns, lauva, putns are gender 2.

25 February 2009, 10:42 am## Tanya Khovanova’s Math Blog » Blog Archive » Phonetics Puzzles:

[…] to the popularity of my previous posting of linguistics puzzles, I’ve translated some more puzzles from the online book Problems from Linguistics Olympiads […]

18 April 2009, 5:58 pm## Tanya Khovanova’s Math Blog » Blog Archive » The Solution to the Swahili Puzzle:

[…] would like to discuss the solution to one of the linguistics puzzles I posted a while ago. Here is problem number 211 from the online book Problems from Linguistics […]

13 May 2009, 4:29 pm## Tanya Khovanova’s Math Blog » Blog Archive » More Linguistics Puzzles:

[…] to the popularity of my previous posting of linguistics puzzles, I’ve translated some more puzzles from the online book Problems from Linguistics Olympiads […]

10 June 2009, 7:50 am## Val:

i found the solution for problem 3 by trying differnt combinations. But still don’t know how to prove that the solution is unique.

and the solution is:

NM

14 March 2013, 4:05 pmMM

## Val:

The solution is:

MM is the patriarch of the family. His suns are NM & TM. NM is the father of AN & MN, TM is the father os NT & KT. AN is not a father, MN is the father of BM & KM, NT is not a father and KT is the father of GK & NK

14 March 2013, 4:11 pm## Nikolai Toporkov:

Perhaps, there’s an elegant proof to problem 3 but it eludes me.

I believe, it’s relatively easy to draw up a table and prove that there are dead ends given there’s only one, what I like to call, transit point, namely MM-NM-MN which yields a success. The last leg of the journey is to prove that the second branch off MM (patriarch) can only be TM, and that’s not too hard as we arrive at contradictions following other pathways, i.e. KM and BM.

I wish there was a pearl here from number theory which would prove this on an abstract level dealing with pure numbers.

Besides, I got problem 2 wrong and later read the answer. I’m loath to admit but I fell for the same line of reasoning as your students did.

3 May 2020, 3:13 pm