Henry Ernest Dudeney/Puzzles and Curious Problems/273 - City Luncheons

Puzzles and Curious Problems by Henry Ernest Dudeney: $273$

City Luncheons

The clerks attached to the firm of Pilkins and Popinjay arranged that three of them would lunch together every day at a particular table

so long as they could avoid the same three men sitting down twice together.

The same number of clerks of Messrs. Radson, Robson, and Ross decided to do precisely the same, only with four men at a time instead of three.

On working it out they found that Radson's staff could keep it up exactly three times as many days as their neighbours.

What is the least number of men there could have been in each staff?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Combination and Group Problems: $273$. -- City Luncheons
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Combinatorial & Topological Problems: Miscellaneous Combinatorial Puzzles: $457$. City Luncheons