Seating Trouble - Futility Closet

The Fall 1978 issue of Pi Mu Epsilon Journal included this problem, submitted by Pier Square. Four men are playing bridge. Their names are Banker, Waiter, Baker, and Farmer, and, as it happens, each man’s name is another man’s job. Mr. Baker’s partner is the baker, Mr. Banker’s partner is the farmer, and the waiter sits at Mr. Farmer’s right. Who is sitting at the banker’s left?

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In his 1994 book Mathematics: A Human Endeavor, Harold R. Jacobs gives a similar problem, by French puzzlist Pierre Berloquin. Around a table sit the four members of the street storekeepers’ committee: a grocer, a baker, a tobacconist, and a butcher, whose name is Andre. If Andre sits on Charmeil’s left, Berton sits at the grocer’s right, and Duclos, who faces Charmeil, is not the baker, then what are the professions of the other members? That’s simple enough that it doesn’t require a solution, I think. But here’s a much harder one, composed by J.B. Parker for the January 1941 issue of Eureka: Seven men, Messrs. Black, Blue, Brown, Gray, Green, Purple and White sat down at a circular table laid for eight. Each man was wearing a tie and a pair of socks — and also had a car, their colours being three of the names of the other six men. There was a tie, a pair of socks and a car of each of the seven colours. Mr. Blue sat next to the man with the green tie; between Mr. Gray and the man with white socks there sat a man wearing a white tie, and opposite him sat Mr. Green. Mr. Brown’s socks were of the same colour as the tie of the man who occupied the chair on his right, and Mr. Green wore a brown tie. The empty chair lay between Mr. Black and the man who wore a green tie. The man with black socks had a gray car, and the man with gray socks had a black car. Mr. Purple’s car was the same colour as Mr. Gray’s tie, and this was of the same colour as Mr. White’s socks. The man with the name of the colour of Mr. White’s car wore socks of the colour of Mr. Black’s car, i.e. blue. Mr. Purple’s tie was of the colour of the car of the man who occupied the chair on his right, and Mr. Brown sat opposite the man with the white car. The colour of the socks of the man whose tie was the colour of Mr. Gray’s car was the same as that of the tie of the man whose socks were the colour of Mr. Black’s car, and this colour was not black. Find the colours of the socks, tie, and car of each man. The answer (but not the solution) appears on page 11 of the May 1941 issue. (The Eureka Digital Archive is published under a Creative Commons license.) (Pier Square, “The Bridge Game,” Pi Mu Epsilon Journal 6:9 [Fall 1978], 530.) 05/24/2021 Reader Dharmesh Jain kindly offers this walkthrough of the Eureka puzzle.

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seating trouble solution

In his 1994 book Mathematics: A Human Endeavor, Harold R. Jacobs gives a similar problem, by French puzzlist Pierre Berloquin. Around a table sit the four members of the street storekeepers’ committee: a grocer, a baker, a tobacconist, and a butcher, whose name is Andre. If Andre sits on Charmeil’s left, Berton sits at the grocer’s right, and Duclos, who faces Charmeil, is not the baker, then what are the professions of the other members?

That’s simple enough that it doesn’t require a solution, I think. But here’s a much harder one, composed by J.B. Parker for the January 1941 issue of Eureka:

Seven men, Messrs. Black, Blue, Brown, Gray, Green, Purple and White sat down at a circular table laid for eight. Each man was wearing a tie and a pair of socks — and also had a car, their colours being three of the names of the other six men. There was a tie, a pair of socks and a car of each of the seven colours.

Mr. Blue sat next to the man with the green tie; between Mr. Gray and the man with white socks there sat a man wearing a white tie, and opposite him sat Mr. Green.

Mr. Brown’s socks were of the same colour as the tie of the man who occupied the chair on his right, and Mr. Green wore a brown tie. The empty chair lay between Mr. Black and the man who wore a green tie. The man with black socks had a gray car, and the man with gray socks had a black car.

Mr. Purple’s car was the same colour as Mr. Gray’s tie, and this was of the same colour as Mr. White’s socks. The man with the name of the colour of Mr. White’s car wore socks of the colour of Mr. Black’s car, i.e. blue. Mr. Purple’s tie was of the colour of the car of the man who occupied the chair on his right, and Mr. Brown sat opposite the man with the white car. The colour of the socks of the man whose tie was the colour of Mr. Gray’s car was the same as that of the tie of the man whose socks were the colour of Mr. Black’s car, and this colour was not black.

Find the colours of the socks, tie, and car of each man.

The answer (but not the solution) appears on page 11 of the May 1941 issue. (The Eureka Digital Archive is published under a Creative Commons license.)

(Pier Square, “The Bridge Game,” Pi Mu Epsilon Journal 6:9 [Fall 1978], 530.)

05/24/2021 Reader Dharmesh Jain kindly offers this walkthrough of the Eureka puzzle.