Question 171
Some Christmas lights are arranged using magic wires. Each lamp can be either green or yellow. Each wire is connected to two lamps and has a magic property: when someone touches a wire joining two lamps, each of them changes color, going from green to yellow or from yellow to green.
a) In the following arrangement, each dot represents a lamp and the segments represent the magic wires. At the beginning all of them are yellow. What is the smallest number of wires we must touch so that all the lamps become green? Show an example of how to make this change with this minimum number of wires.
b) Consider the arrangement in the following figure, where all the lamps are yellow. Show that it is not possible to touch some magic wires and change the color of all the lamps to green.
a) In the following arrangement, each dot represents a lamp and the segments represent the magic wires. At the beginning all of them are yellow. What is the smallest number of wires we must touch so that all the lamps become green? Show an example of how to make this change with this minimum number of wires.
b) Consider the arrangement in the following figure, where all the lamps are yellow. Show that it is not possible to touch some magic wires and change the color of all the lamps to green.