Henry Ernest Dudeney/Puzzles and Curious Problems/284 - Lamp Signalling

by : $284$

 * Lamp Signalling
 * Two spies on the opposite sides of a river devised a method for signalling by night.
 * They each put up a stand, like the diagram, and each had three lamps which could show either white, red or green.


 * Dudeney-Puzzles-and-Curious-Problems-284.png


 * They constructed a code in which every different signal meant a sentence.


 * Note that a single lamp on any one of the hooks could only mean the same thing,
 * that two lamps hung on the upper hooks $1$ and $2$ could not be distinguished from two on, for example, $4$ and $5$.
 * However, two red lamps on $1$ and $5$ could be distinguished from two on $1$ and $6$,
 * and two on $1$ and $2$ from two on $1$ and $3$.


 * Remembering the variations of colour as well as of position, what is the greatest number of signals that could be sent?