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

by : $273$

 * 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?