Problematics | Who owns the badger? - Hindustan Times

Problematics | Who owns the badger?

May 20, 2024 10:59 AM IST

Crack this one loosely modelled on the original Einstein puzzle: 4 persons of different nationalities in houses of different colours, each with a different pet

Longtime readers of Problematics are familiar with what puzzle solvers worldwide call “Einstein puzzles”. There have been several Einstein puzzles in these columns already, with hopefully many more to come.

Welcome to Problematics!
Welcome to Problematics!

The name derives from an anecdote or legend that is impossible to verify today: It is said that Albert Einstein created such a puzzle himself. The original Einstein puzzle involves five people in five houses of different colours, each of a different nationality and owning a different pet. One of the pets is a zebra, which is why Einstein puzzles are sometimes also called “zebra puzzles”. Other variables in the original puzzle include favourite drinks and favourite cigarette brands, but we need not go into those.

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For this week, I have designed an Einstein puzzle directly modelled on the original zebra puzzle. I have kept it simpler with four persons instead of five, and done away with smokes and drinks. But I have placed each character in a house of a different colour, just like the original does, and retained several other variables: nationality, profession, and, of course, pets.

#Puzzle 91.1

Four persons, each in a different profession, live on the same street. Their houses stand in a row, each painted a different colour. Three of the persons keep mammals as pets (a different kind each) and the remaining one rears bees.

(1) The person who rears bees lives immediately left of the brown house

(2) The neighbour to the left of the black house owns the bobcat, not the badger

(3) The botanist lives in the brown house while the Brazilian lives in the beige house, not the blue one

(4) The beautician lives exactly between the Barbadian and the brown house, which lies to her right

(5) The Brazilian lives on the far left, two houses away from the Belgian

(6) The Bulgarian lives at one end of the row

(7) The beaver’s owner lives on the far left, next door to the banker

(8) One person is a boxer

Left to right, determine the colour of each house, and the nationality, profession and pet(s) of the person living there. Please send in your answers in tabular form.

#Puzzle 91.2

The source of the following puzzle is the late Martin Gardner. I have changed the numbers but otherwise retained Gardner’s original version.

A recruiter at a campus interview tests a student candidate like this: “Suppose we hire you and offer you two options. One, we pay you 6 lakh over the course of the first year, followed by regular annual increments of 1.2 lakh. Two, we pay you 3 lakh over the course of the first six months, followed by regular half-yearly increments of 30,000. Which option would you choose?”

It is a hypothetical question, meant to test how smart the candidate is. If the candidate chooses the better option, there’s no guarantee that he will get the job, but if he chooses the wrong option, he is certainly not getting recruited.

Which is the better option?


#Puzzle 90.1

Hi Kabir,

Let N be the number of hard discs sold and M be the total sales proceeds. Then M = 5072 x N. M is a 6-digit number of the form abc264, where a, b and c are the left-most digits and a is non-zero. The value of M lies between 1,00,264 and 9,99,264. Accordingly, N lies between 100264/5072 and 999264/5072. This limits the range of N to 20–197. Thus N can be considered a 3-digit number pqr, where p can be 0 or 1.

M is of the form abc264 and is a multiple of 5072. The units digit of M is 4, which is feasible only with r = 2 or 7. We can get the two rightmost digits of M as 64 only if 72 multiplied by q2 or q7 gives the two rightmost digits as 64. The only feasible values for qr are 12, 37, 62 and 87. We can now consider possible values of N as 37, 62, 87, 112, 137, 162 and 187. Out of these, only 87 gives the value of M of the form abc264. Therefore, N = 87 and M = 5072 x 87 = 4,41,264.

— Professor Anshul Kumar, Delhi

#Puzzle 90.2

Hi Kabir,

The 10-letter word is METROPOLIS. From the clues, “request” is IMPLORE, “upgrade” is PROMOTE, “rejoinder” is RIPOSTE, “one who works hard” is TOILER, and “easy” is SIMPLE.

— Shishir Gupta, Indore

Notes about #Puzzle 90.1

Solved both puzzles: Professor Anshul Kumar (Delhi), Shishir Gupta (Indore), Akshay Bakhai (Mumbai), Dr Sunita Gupta (Delhi), Yadvendra Somra (Sonipat), Kanwarjit Singh (Chief Commissioner of Income Tax, retired), Sanjay S (Coimbatore), YK Munjal (Delhi), Ajay Ashok (Mumbai), Sundarraj C (Bengaluru), Sampath Kumar V (Coimbatore)

Problematics will be back next week. Please send in your replies by Friday noon to

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