WATER, GAS, AND ELECTRICITY.
(
Unicursal and Route Problems)
There are some half-dozen puzzles, as old as the hills, that are
perpetually cropping up, and there is hardly a month in the year that
does not bring inquiries as to their solution. Occasionally one of
these, that one had thought was an extinct volcano, bursts into eruption
in a surprising manner. I have received an extraordinary number of
letters respecting the ancient puzzle that I have called "Water, Gas,
and Electricity." It is much older than electric lighting, or even gas,
but the new dress brings it up to date. The puzzle is to lay on water,
gas, and electricity, from W, G, and E, to each of the three houses, A,
B, and C, without any pipe crossing another. Take your pencil and draw
lines showing how this should be done. You will soon find yourself
landed in difficulties.
Answer:
According to the conditions, in the strict sense in which one at first
understands them, there is no possible solution to this puzzle. In such
a dilemma one always has to look for some verbal quibble or trick. If
the owner of house A will allow the water company to run their pipe for
house C through his property (and we are not bound to assume that he
would object), then the difficulty is got over, as shown in our
illustration. It will be seen that the dotted line from W to C passes
through house A, but no pipe ever crosses another pipe.
